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A super fast factoring record on large semi-primes.
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djoyce099
Oct 27, 2014, 2:15:10 PM10/27/14
to
The list of 9 discrete semi-primes below where each
of the two factors for each semi-prime has 1002 digits.
Each of the semi-primes have 2002 digits.
These (9) semi-primes all can be factored in less then 29 minutes
each using ECM.
Call me a crank or whatever but please do not be dishonest and just
try it using ECM @ the web site listed below.
If you refuse to do that and continue to refute my claim then you are
being dishonest.
http://www.alpertron.com.ar/ECM.HTM
Each semi-prime below takes about 29 minutes to factor
and longer on some to obtain the sum of three squares but
still obtains the 2 factors in about 29 minutes for each semi-prime.
Stops on curve 19 for each semi-prime before the prime check routine
kicks in.
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730789819842774150688286766366508472324928922777064060353237824316976051776180075758787464376924783909927143093975863575152054720127750969101645873959326673918113473633129633778198494507502731789667069624297464526153057245918328476412473468041932921241449550573329882125190488537936899121506957767736032220126494761367447621334927611179302845497787576402642608192672340712559522028624887896336605456038041488708250414393594552371912315005136328110505947991683115737690722470649415431446144357751165127053372131509
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4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730781052505931993936385344137834890244667531766684378465397045280724011066610243042460915186608196799326662001704382207878503388731022647418053125546288278424056421022296218587619107458243982365325286933743681686503083619903012914430201752924853624279739030491342218733332463707003232969576498922487244247793252183621912031350037118923100212905909113690778302258832831349354755590492605167158549650334720384364683236329640433823527508930553397512762154041869536986691628570329696658483545736308612279132990601281
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730758535719373819497549858638584049451063492546597744030981943982978105072502985439180709411976030856309577749575104200518400417387738635668075662612074128530901137069232921654304814989200042232951882832466904733656674686181019767286106502118937525953734880139313997137720489104224023059873413981785113864224466910284468348469670957835759141882109079335252727041437485539952519315832188967893103069674921440934789072994351278958553517034893334244387479559319636179860169687649876991043230463691861189530239083159
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730754406572797255915959554024286085779608293735652061800867605099275629668271213872401600974784252523225733063151026491225099377351835168268952217412444093046778064918888185825621543867774105990991253783292007900277109813810376370372276046606674736162714685403153963913407081345157685515163109613498859847940546039593073499384552883257892552591124777842645811233581741232202991288933058969277865190820721461757350680604687569064845036013776294455216056317590283680401854834280415141213246369246165974058622986167
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730729751349460893826577290900580713527675301332822931780754269348830327073727476487159352036453802426423367300282615074385270157805109005936843535798205164235597372614129649652070285658780495553116694098425969918753485083810461598912547499968757818763965822121456258388213211295892904686120152794201862447804448476904931445852914027651344081509494529734669930508431879340026519560547166844306440909344150728508107157259798014024585411154628645633663267956022615029624788270456254492357369619085200511350759993699
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730718572485725004690903211269865612271659397388693798905780397755075770672370235863279831053984568031752637956259625937970036808303611487740406988188255549335228521027754327520596189016505067118137736810945725336013607663629574927027566925682609269754825417120351324507967619720473307588234597795233678133853267402080780863393000273053393816612542611819532907648771212144353020857525125315148845120880210265359411592084025299060788408005007820554245014476991982285416234934888475634444202173464800696854375569323
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730653544953345269685839513761340346686462464749485051440807920609439309849323760476031544095341405829841478910714034400558070418139733432446332544986566827954210787330467609289773295069513326139827323191469356481732779435090326409841847646288733839743432608110570129390970309173034914221387173867913334812506711135311347194043604115671231823151461784589520784627839752383807002002893751205317150837234187787494099096476111954116430701717700967605813059284707948031153961432698692462100191537644466093923516490537
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730642624652783472448867149520483378286791188870777862441065193040720323358575652780981190514415453555025599088803451304702687002164449872645848144653329312342271476071779928039963849616588113226189528191489357230937081862124533526480416567976857962650829938692714979624846395581893430221393785518395622269268896679922817298719886154165135718753374605530281913324790727096728362844408715429233883740673686243526119620454514231673157489746189319133127322250206566416570386825218916423042437007259927880160815039459
Quite significant I would say!
It should go down in the annals of factoring large semi-primes
in a record amount of time but probably will not.
This is just a very small part of a much larger listed semi-prime
super cycle.
All having about the same factoring time of about 29 minutes each
for each semi-prime.
Dan
samsoia
Oct 27, 2014, 2:44:50 PM10/27/14
to
On 10/27/2014 1:15 PM, djoyce099 wrote:
>
> The list of 9 discrete semi-primes below where each
> of the two factors for each semi-prime has 1002 digits.
>
> Each of the semi-primes have 2002 digits.
>
> These (9) semi-primes all can be factored in less then 29 minutes
> each using ECM.
> Call me a crank or whatever but please do not be dishonest and just
> try it using ECM @ the web site listed below.
> If you refuse to do that and continue to refute my claim then you are
> being dishonest.
>
> http://www.alpertron.com.ar/ECM.HTM
>
That is excellent website, glad to find it again !
>
> The list of 9 discrete semi-primes below where each
> of the two factors for each semi-prime has 1002 digits.
>
> Each of the semi-primes have 2002 digits.
>
> These (9) semi-primes all can be factored in less then 29 minutes
> each using ECM.
> Call me a crank or whatever but please do not be dishonest and just
> try it using ECM @ the web site listed below.
> If you refuse to do that and continue to refute my claim then you are
> being dishonest.
>
> http://www.alpertron.com.ar/ECM.HTM
>
djoyce099
Oct 27, 2014, 5:11:33 PM10/27/14
to
All prime factors are 1001 digits long not 1002 as I show above.
djoyce099
Nov 4, 2014, 4:02:18 PM11/4/14
to
On Monday, October 27, 2014 2:15:10 PM UTC-4, djoyce099 wrote:
so just enter 19 in curve box on lower left side of ECM window
and click on new curve tab after one of the new semi-primes
was pasted into ECM. Then start factoring.
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730833669251711846141192863608902033788761656335508739287199108147055198779340661448861903433283215235223598600459934390282182278898615695548177965441663844995792143149721721944724717688555925572369222239171681747392257703463723870593762771806018926074620018211253667391290276008760431138273809989401233022246021499990256972696223164611631251755571585843984260221715808442027773328775608193502904884853200451796686547352064643108826744225764454147987971142710100318159340149171550252388255895474003412848108045101
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730833233470774542031848616496562194074493632331277162319745963412073399201411508168559370688407384698655476990639268216315063777563221402376670908900418899115123959171522644868952601485066635308868999518058954399995788574547715657366671589394632552527674646770438026386192814930389493665545846365092427552944657271500123849240045251214978960341337520219179254340211405314003128332338172897979279201667332703227138752779091921001419501284435449029512500666604670095571417927019640126069369559614975002184214768663
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730813674637097717780663708630259102954934564616822809043258169803838329680715838326966730524945990287297129086891697289285063673389345674842715872172756460640189179600840137724034479687303938850514119526346447758993637952112556879407653870684300695975770212022542539415380794667765168255702192441575042608442873693205832657016391444829834735451186533974876328544080829781138874966323986311320935329893373966814994125574968260358194340244058578909759628259630978879681539012671524477270157259109840601329220575631
4056232641945509788616948104409912084570707999593358375478976947209897639352212717065108936565167643200261088606779734511205279686047664540305669028870241274045107140148954328580329899488928676525105447130585009702509298378904281653621794440343033945082107660752965478056843989995741993591993853530458807837346633129869761259243654029944782593999660684248874035839404768404960977206242409933234634827184261257174741433365295082430539465271779302813141943268941042178728174739874893073534787484720083441787084555746624193868740094776151079610723817226717204726236445266082782028582711218457875073615750350184486647059590034893928833226805693577529349690636935390167039641828903644783766604342889243956987219439659388237282055964008330283006045889492189447734830893140427745713160927567379795923055991233577863930750025796081778220947714884276158344329109989551177253911326652557975694909007902798168385701417175726314089604495848912168181070819157991255548210191553177182519702597414544538631393485098752192048223424927111856819929796713680714330820496699661850388684793689000313590498531746112271394381353913928591320370508521204056765638157004600722396468773431677445662891459971675041646201882144158072795971066605887822892493444930720078896384690787759204478240573229153268053976734607932035749559096519016880514472790323173702258014905006824449895523403128721349033630507756901711694821912065716083957966836780131012654529401918895779782463751713026995809828997636093136079887318945196730810029357819169664803090013245553077378067814460593437823931471791815710214538351575608818702248617411925601421451562114535980283900686984860992792467263617463451901506595941512114582911038730442327285124275319114006218684934068895481147632077165489961620891323489874902652922154123148910273650251758259181960161874370068576894814289105723944538822674107541956117185443850949128589049146635056878700905706708449079875766148042232356178913089386857102620294522147142077582231559929174032796935715710253336925919
djoyce099
Nov 11, 2014, 2:26:46 PM11/11/14
to
A proof that a discrete curve number and not a random
curve for any list below will stay the same throughout the
entire list.
Rsa2048 as a reference and surrogate --
2.5195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357e+616
ratio = 2 is derived from sqrt(rsa2048)/sqrt(2) to find the smallest almost
numerator of rsa2048. The 10 discrete entries of semi-primes reflect the
most trailing zeros in the denominator quotient.
Each set of entries (10 count) have the potential of e+140 plus number of
semi-primes possible. It would take 50,000 years or more to process
them all from just one list.
That is the reason why I call these super cycles and in the process
rattle a lot of cages.
Contrary to other ECM methods the curve matters in finding the factors
as observed below the spesific curve used will find the discrete factors for
each list of 10 discrete semi-primes.
---------------------------------------------------------------------
sqrt(rsa2048)/sqrt(2) starts the numerator build process.
Once the build process is complete a next prime has to be found from
the built numerator.
In turn a next prime is chosen for the next largest prime match look-up.
If no match then another next prime for the numerator and so-on.
Using ECM @ curve 1 will produce the factors of the 10 discrete
semi-primes below.
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952626180436144515672053007713352825786117035602490573213407176015408751718459212909265271917426802676397306273041826966207971581804369915708148781704191684914773269
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952618643012489581184258831603809234486170595527671845842241924007805431119672647030236931331699830787493762902639404557258562359301163558657038935068900436978178009
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952615607211441344309111730241446390196309104617691611939081053670368749583741809656389663106732542992523043489183947484219730281695644338253649129625646728146567719
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952603685243296220513168937775697304560683392465161744239508616653622801864149843149912357312603611007726211558540625027441084093238697847283100387771246614537115559
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952599086542311737858923368051267992029946116947656050171248660730135421228785263789196801545845118730989630738262931330967218833222711495221227347990918152503817339
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952598656105457092059164863430176813641201435653787988439577636875849106726795245045970067464916948265030220179246830377658346096727353807186186158261258015614813819
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952597913991258272224301619237645846953698784064483390231972125765231295580888933947964435885421956997033588405416850403470803586807520424813271804422251036407500839
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952588605351804461157114665580581709714047410581611773148760092827623742918506515859708487851138790232271162975247310276495677295851480160274220055558512382788985469
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952578585925176202091642286529478850266666333120050133074433408656951289335074790504676814459533447237536289845649866601622346683445868976677304236812240991426255619
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952563870011230322294470976815150265435019428983555946914269366967605111052812414507830584240432435081836803686129829651038657313115683808354304746161607795113866107
--------------------------------------------------------
1.9 ratio
Set on curve 189 in ECM to produce the 2 factors for each below.
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952592910868050151557956947769504002053720359318456113357308656567310684711605858993095665860427214375008183163218060578088115354093167781341447820868136988807768629
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952523387492542113249363540082695580502850713475558500581898953208995099862920703028128684340652595627269091048249066798093320290986636601090934648317191775594001143
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952421632423355384454523529493230607116822675739785474543607370575630363131966239405506763306132916766018513206495921319365139897032740934396387516475081536667202791
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952173321204150058252938977243703831327295091243813950771956546388841481370310142409467333246797885606864628513375696845713000776095066670099689042629012772384708223
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952166188392092840248407945263166439045342617766852066654669452950578710494833940358389676945450768486839065802413512673559021250926111808254804058321298637209365243
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951934395935844185362909577143958026768739419273902785474104980278979136138754944846188255394291432277686215826045084743561914802147055156892836984375296587114900403
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951517823754628700390457195315069759578146841880454117937028014103139664279679697631371521900538479007074728085918490646431358452805440319420357290101531522058441191
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951493332837524856557449974098674256950986536975664185625591255693641452334084899179483408049738578882208433569621487811035546875111230203179799182908055022950941039
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951470557305871014817255025674018731214899813499897525221555755773210908999482699654867884920179875827594371696341117634491083840941992453042876726303123109784637857
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951439042084812836833029548802516830192850294222493227387904727718246764751014021688697032134585790118309167324640192041640726878506453633929570587583343625860811357
-------------------------------------------------------------------------
1.8 ratio is null and void because the polynomial nature of this
ratio allways produces and even larger integer that is a 0(mod 3) and the
next odd is also a 0(mod 3) so making it impossible for a prime (denominator) match
because the denominator will allways be a 0(mod 3).
-------------------------------------------------------------------------
1.7 ratio
Curve 169 will factor the 10 semi-primes below
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952629643035278983143809106675881475138796103058905683460664962180600802136209371151415348392952549293422043240405888051754224117745997467655299371715519452705026067
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952530866906456981117581054747108536317833050626432167277500493127432182319647107655840677023374835572867937232478386010073250585870334655703679540264479930195045971
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952430416718109793767623387522383055058385026847132833865347505138675964645797179860669248428683030107183861448291126598580829686392545457670618134767445209262364599
----------
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952394229241654305485104549366001811595640725282743923093259718345282396734705337748042112997264185229255779604952735074870135404115750179095898891854352486814566171
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952360740331508519763301369068115872050533264881518895561840512471113368979596970300179974225828332775789513336388800918701346068164648752129405954402585801785393797
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952293587165061148275905147581661216776050155380685899168693026605016138199743385191256826855029657784880916771312776202015928047481986019812395566802511328982202851
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952254725384028206495333399614552097546951403542217537289690115688565966333498324418206676752397589928072613118073257127717117911163585677833528881819996314350823933
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952208516709347844012069492818960871779521374290999771998617696768898023106745740875779980777756247231965324847282681664957265374999753198783144564232861074920437371
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952200550038722060890447133861147191558430838711638965897028065154481154252301678359121895010810134737354717690694745407040337981351689290316521421342487194279660683
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952195817898127482350181139635236546233306324845216316536297014592816870717636745875874408019397376055962952005628461563917201845396007918330048566117875274799124141
-------------------------------------------------------------------------------------------
1.6 ratio
Curve 39 will factor the 10 semi-primes below.
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952625769170024645446235858417061540800980376909448581742494763907785626828673147875782690239534745405747530305623792027813134301806785326416552820129854646603825239
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952617999634806498224049059996303108915246696954548671534810817595713858294989812497914215561235893658400038085579745558091989608479844614758699933687118730995833001
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952612008616677350234690227687397903805413537676489839361318228728094889823946321480533852167213351994809078716430998925842847836527229318221563563103689307823335347
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952595630163255457363350978260905058881903898887658267330705785315157663498208200916676159403345662765874634380812013998097168925795790234041045438405713697694303803
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952562719378977107155499505284475088897963973966539943955815202649203881587010252413603054878261330137279200563296773936782468595361232859113637444568777157550214313
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952492632033215068076354976495138631616886141691465701978391828328872481030561204171251055649282706994366999434874491957322911787989931927963068475181991724680027071
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952483739164386214519093280421833005508770424776241057333560886970623067587970229684877980408384860159063660143296193008994530067842113914594170294146151710758082057
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952474377295273375345144158613167741045951814024150258427004850556514925002028563290186258868016443982043134448239289658018575875598293899627951234565513063649003553
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952456658436206013007381027779876654782415173514245024971643343932573596653300247725514549792066704610315764621107435349896451168483719185504636882969101765909034269
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952453581170898581097043410825030544272615340176160693172203581266972424588257852902292688664603917612305536732663830994397968102326325991942517595888760175940852563
--------------------------------------------------------------------------------
1.5 ratio =
The best in time -- just a little over an hour for producing 10 semi-primes
Curve 5 will factor the 10 semi-primes below
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952632435737113233344621661093370659313750374444665512161730074084610857672133767343305662569483170697193108177356722201699184767030871370436649935161219278845409403
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952628670982569876581614175070492181971740343491904715027120405225433570765063858182210478219959872567669190341173422112716798989320894631129563730649596913302517889
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952628490842991043853574219969865159142224077685863321560649013792382628572670873535097599325687833308693018084773305251152667680168510316999211593799565179244481789
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952626619709194206837601638941568893792293835910469479493000915193773349795478280185910438531121718974203499714964867918224111880925403270789696113629314504419797539
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952619767980355796677494109698803184372918721737475638338712763120135052383777800034843651188672493001524702229884305629322758081928010006154013414993501440772845063
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952614500219240698313174474594801452442967332607987530750894161947542658182073692560749317924909214038981082601136418759949080780766469154231560239319151837412258833
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952613356271919767770235418863234995052459073092060559870809921813323898417649438815246042743495893850828107902028498319876362498808257974747346624451184591799523289
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952613258191408674194607343986776218739864663808951792141435430586118735309737050786163364663815496854744467386805680741977336603170436086331452865064666141417076913
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952610896207757189354668555730563747391042583535877214061648242599618277479637974891761855983751010986372020053790514145856765220907367176494966584913210539286795613
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952609052440537452660585566075342422529659620967586274432585978410589875473434202912215094172445637604769852457922771767292241108133685557691710018535300088413282489
-----------------------------------------------------------------------
1.4 ratio
curve 34 will factor the 10 semi-primes below
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952629926965724387864861488144135237330842326541024189116593220886122993198653418553472645945981997492192098444668957915368605907197340013518394406295802371926603379
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952615941033059677445865256196189308325228632318448677763652092088411323734996519498144112693320079191926055376836458849291873990743264247642991833278313163982272439
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952604102348467389809482904563603380715383355338534071576734498269938936118344273131353935617314532356038504003665503043678185751693166732780951197020528498276112631
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952591230924300093159755626814836548126729635106174066160318561087243107228090306266098820089448840036570001439081927706834925181220643934077381895379250775574333171
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952584592321880876125520775401959961273335920618407580885143506496563700843526826844573876401216749645451730541121371191141325327072448622574642373248800607474323063
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952570580920207547831728534706850661164035684034887282197226802014178988975013812672186964358623921026380520310585760981424034701165529807793079349184393067362525431
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952556318275381537945963636295362843099571961905806374610904418597275242255589347119494841997314142495486909196843520542711157407573422420343226762912837384089736311
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952554510933251195823221301289889937260522437074250713953013566627770172954596757083427330573495107992605949184873874124067600266100244258115088890876976068337057079
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952552220254446030272019371714188845965045597062058638005811789634845862827612929788297051737754136311798358205515862844155094382830255152735454940326756382251654711
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952538130913776405173400247108587124508373760922865193112368323470792517434465037024611191067327619724654192822948927555778349661078921895060603919449610090399197411
*----------*
----------------------------------------------------------------------------------
1.3 RATIO
Curve 129 will factor the 10 semi-primes below
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952628352004426127114280327340588150231015263364437817743586606627881627788726987779697090531981235504535339668339546165075969120199749222155989847410336793946915659
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952622111562629000600112457592259806216832005169449507023801843401878120116449694249720320419786746895511429045838132270190331759461348673015990514609653404385677531
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952620528780274915605488136404956727137848649264862326489287860540060245895302160899814768145644775102532385411566088827731826552389415563708683690191313730921743327
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952611826311315548555814664093567416337869884459112846406281928806976562341875503721260650606125598946238028670400686140302184896854700084021284529792708991599010709
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952574724447601865067232825411606654417940878794154528120295473782439132020106086114052031116424329079213150426925261363567832981574520524891590494736494229733503427
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952546516347044327029644318808524832371994893124846557752730695957722549996485722285430877023904872962083498119446685885482369098690928396887510858482054799390111103
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952543708809499510196446179406158523196979355226647154262085779774301050631967387987657495132678409119210494430364911423538664249142862028125161779298906085626167967
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952541513177218709212408233408194225047574959547007193440036167917195593061986991456163624721950579850436073560799529763655536390272709518839869098514439013811862933
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952536708386560120848392743322297307133233512832768729104809820360692362529422597841745770198313096095115476315310910868278292517118654145987413511705790114655049643
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952532774811076736833104367658955008544820087594510883837297898763193330445353168495874854251116933429663529020110201292392159612166383500117150535353619323599077771
-------------------------------------------------------------------------------------------
1.2 RATIO
Curve 29 will factor the 10 semi-primes below.
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952631795095596374273344044766149370144607108858615500755965761086499379482813761184593346909257603137136795087640132732129289512506481184435387527947395518809195227
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952623928068117872282396998061039751888342966086896465346304149427584536958348425666451762650457772760487214922441718360795885943167083933923579442542621029925081359
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952621383477019704522521942522998905013001464381758232868785568837099951775232953261662031892894485307123469316447622068181307969256766763946714293624634285187709999
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952607571458287491786601849396321205616783479805769660299041016969561507884916212770449739065035470098192009993997188708931708765999547304775281520555481993131725563
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952600679676157938564592671199060433303269523691839003020542331390233385650361443990924503895013990845940600420383833607581143093925920473896344615088571996163166259
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952591485165951621063873199687086129652529680831851806372876101245919373312952427729985029113865706127968886730178029044277976250376685751055793738854031768463758133
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952586216738698584125710237476594008725228960527958410369386954580335583662811140882774724028993398223280088936684981670345414489436585336949134692280169249776314097
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952581565247919775325340344286863358080240382090467474718709292838541646431710101048805461928362217846458113795813294964508295992256507689694416455315767270254067037
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952580030428139516516615137176899048125551670752151013056610567786510399307549604035987667418360458601528563962169348778325493031283607336849040207907505367874698523
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952574319144166509997166227800651741347830939093805674670014821998928811659193028241405303422796847784283191212248482722697509526807192107582945976762337000386088473
-------------------------------------------------------------------------------------
1.1 RATIO
Curve 109 will factor the 10 semi-primes below.
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952602344312550890398608919686922855002663894757027885722887850066217612834496200646065257790020171452025863335751295389311197457664676360599758405561552653921077697
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952422861504500620609586372883640384338743862029498335636298397402363604669682098877012303366021021279549797696813564508729168927499875285665744722430021076426849211
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952394178630870287079710631741369666152785324658492446741196230321427169625159095353911363845240413400327961761315384165651793583505622363361811826752027848108279931
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952389664088880474564679139850704060270367518609496815659853575302342756494821242843285886770858007608650822603337879540088231500498129978310252922990496058848851889
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952263333546797560912770317365500643283013113268763054245719431397584744206167350036101424328091662332971289863764882567209844942474587384063598858228542748491868361
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952121078262327424394107487262329461623425907384785231330044070015686593815742741961821273278296503417477610903705610563205913686070266103898487393323143997104234267
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951971470254574092166664964546685924581531677584089152639875199868241140682273186467234760203446277415387609210753603684041928148975051648564529008165840000076671079
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951854918711296634784054426708556293479523632360397761552286861591363460685039206979519730671724694730591627978578984417825322326074740513420160462130544159880331419
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951754725711500904835419776733723616823839459070532916068326925284214508956995493909512173994555182016607565962670836898800841735145197481005811660128382232122100891
*----------*
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414951724367845631853355135261394976784178929907875953019157594746156185221026284696669222515486492347799400638081321045260879634930223035895681839935046206562717442219
*----------*
All list with a potential number of semi-primes of e+140 and still
reside on the same triangle index as rsa2048.
These ratios like 1.25 as in the OP as a large semi-prime with 2002
digits has the same starting curve as a 1.25 ratio of 617 digit
semi-prime.
So matching ratios are for any digit length semi-prime will have the same
starting curve.
Dan
djoyce099
Nov 11, 2014, 3:32:04 PM11/11/14
to
On Tuesday, November 11, 2014 2:26:46 PM UTC-5, djoyce099 wrote:
> A proof that a discrete curve number and not a random
> curve for any list below will stay the same throughout the
> entire list.
>
> Rsa2048 as a reference and surrogate --
>
> 2.5195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357e+616
>
> ratio = 2 is derived from sqrt(rsa2048)/sqrt(2) to find the smallest almost
> numerator of rsa2048. The 10 discrete entries of semi-primes reflect the
> most trailing zeros in the denominator quotient.
Correction above -- should be " most trailing zeros in the quotient remainder".
> A proof that a discrete curve number and not a random
> curve for any list below will stay the same throughout the
> entire list.
>
> Rsa2048 as a reference and surrogate --
>
> 2.5195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357e+616
>
> ratio = 2 is derived from sqrt(rsa2048)/sqrt(2) to find the smallest almost
> numerator of rsa2048. The 10 discrete entries of semi-primes reflect the
> most trailing zeros in the denominator quotient.
djoyce099
Nov 11, 2014, 3:42:30 PM11/11/14
to
On Tuesday, November 11, 2014 2:26:46 PM UTC-5, djoyce099 wrote:
most trailing zeros in the quotient remainder.
and not --
Phil Carmody
Nov 11, 2014, 8:03:39 PM11/11/14
to
djoyce099 <hlauk.h...@gmail.com> writes:
> The list of 9 discrete semi-primes below where each
> of the two factors for each semi-prime has 1002 digits.
Factoring results aren't intresting unless they are
> The list of 9 discrete semi-primes below where each
> of the two factors for each semi-prime has 1002 digits.
of arbitrary numbers. It looks like all you've done
is stuck some factors up your sleeve, and then pulled
them out again.
Are you willing to post factoring times for numbers
that I provide, of varying lengths but all smaller
than the ones you posted?
And if not, why not?
Phil
--
The best part of re-inventing the wheel is that you get to pick how
many sides the new one has. -- egcagrac0 on SoylentNews
djoyce099
Nov 11, 2014, 10:07:43 PM11/11/14
to
The point here is---
These are unique semi-primes because of the fast factoring of each list
that has a discrete starting curve in ECM that is the same for each
semi-prime in each discrete list that I show.
Can you duplicate a list with < 2002 digit length say (5984 bit) semi-primes
where the new semi-prime has 1802 digits where each of the prime difference
within these semi-primes list has a ratio of ~ 1.25 and can be factored using
only curve 19 in ECM for a very fast factorization.
A list of (10) of these semi-primes would be easy to construct but no one
seems to be able to do it.
These are not factors up my sleeve but are constructed cycles that work.
I do not understand the ECM algorithm on why it produces these fast
factorization's so if someone could shed some light on why a particular
curve works for any of my 9 discrete semi-prime cycles it would be appreciated.
By using very large semi-primes like in my OP it makes rsa2048 look like
child's play.
Dan
Phil Carmody
Nov 12, 2014, 6:03:31 AM11/12/14
to
djoyce099 <hlauk.h...@gmail.com> writes:
> On Tuesday, November 11, 2014 8:03:39 PM UTC-5, Phil Carmody wrote:
> > djoyce099 <hlauk.h...@gmail.com> writes:
> > > The list of 9 discrete semi-primes below where each
> > > of the two factors for each semi-prime has 1002 digits.
> >
> > Factoring results aren't intresting unless they are
> > of arbitrary numbers. It looks like all you've done
> > is stuck some factors up your sleeve, and then pulled
> > them out again.
> >
> > Are you willing to post factoring times for numbers
> > that I provide, of varying lengths but all smaller
> > than the ones you posted?
> >
> > And if not, why not?
> >
> > Phil
>
> On Tuesday, November 11, 2014 8:03:39 PM UTC-5, Phil Carmody wrote:
> > djoyce099 <hlauk.h...@gmail.com> writes:
> > > The list of 9 discrete semi-primes below where each
> > > of the two factors for each semi-prime has 1002 digits.
> >
> > Factoring results aren't intresting unless they are
> > of arbitrary numbers. It looks like all you've done
> > is stuck some factors up your sleeve, and then pulled
> > them out again.
> >
> > Are you willing to post factoring times for numbers
> > that I provide, of varying lengths but all smaller
> > than the ones you posted?
> >
> > And if not, why not?
> >
> > Phil
>
> Hi Phil
> The point here is---
> These are unique semi-primes because of the fast factoring of each list
> that has a discrete starting curve in ECM that is the same for each
> semi-prime in each discrete list that I show.
> Can you duplicate a list with < 2002 digit length say (5984 bit) semi-primes
> where the new semi-prime has 1802 digits where each of the prime difference
> within these semi-primes list has a ratio of ~ 1.25 and can be factored using
> only curve 19 in ECM for a very fast factorization.
What the fuck do you mean by "curve 19 in ECM"? There are an
> The point here is---
> These are unique semi-primes because of the fast factoring of each list
> that has a discrete starting curve in ECM that is the same for each
> semi-prime in each discrete list that I show.
> Can you duplicate a list with < 2002 digit length say (5984 bit) semi-primes
> where the new semi-prime has 1802 digits where each of the prime difference
> within these semi-primes list has a ratio of ~ 1.25 and can be factored using
> only curve 19 in ECM for a very fast factorization.
infinitude of ECs, and they're not sensibly indexed using the
natural numbers.
Lack of answers to my two simple questions, and subsequent
misdirection noted. Another loon found...
djoyce099
Nov 12, 2014, 9:29:36 AM11/12/14
to
where each discrete 2002 digit semi-prime can be factored @ curve 19 in ECM?
I don't think so!
Pubkeybreaker
Nov 12, 2014, 10:06:31 AM11/12/14
to
(1) How ECM works
(2) What an Elliptic Curve is.
(3) That it has coefficients that are randomly selected for the algorithm; that
the curve changes; His babbling about "curve 19" is a lot of horsesh*t
(4) That it only finds SMALL factors; the largest factor ever found by ECM has 83 digits.
(5) That there isn't enough computer CPU time on the entire planet for ECM
to find even one of his claimed factors
(6) That an integer which is the product of nearly equal factors (regardless of
whether they are prime) is readily done by Fermat's method or one of its variations
(7) Constructing such number [as in 6] is easy
(8) That he is using [apparently] Dario Alpertron's app to do his factoring
and that it is NOT using ECM to achieve his results [even assuming that he is
not lying about some algorithm producing the factors]
He continues to babble the same word salad/gibberish over and over, as if repeating it will improve his credibility [currently 0].
He babbles about "curve 19" without being able to say what this elliptic
curve is, produce its coefficients, or tell us what the Step 1/Step 2 limits
were to produce the factorizations. He may know just enough to realize
that if he WERE to produce the ECM parameters it would show him to be a liar
because we could verify for ourselves whether that curve was capable of
factoring the number(s) he claims.
He is a fraud, a crank, and tells the same nonsense over and over despite
my having tried to correct his gibberish in the past.
(6)
Professor Gavin
Nov 12, 2014, 12:14:07 PM11/12/14
to
"The guys tjjjjjjjjkookkjkjjhhat kill the killers"
With semi primes numbers
Sensibly indexed
1, 2, 3, 5, 7, ,9 ,11, 13, 17, 19, 23, 31
higher the number
contains more numbers - FG
djoyce099
Nov 12, 2014, 3:02:33 PM11/12/14
to
viewers know this works but keep silent.
What a bunch of cowards.
Dan
Peter Percival
Nov 12, 2014, 5:15:02 PM11/12/14
to
djoyce099 wrote:
> This is really hilarious in as much the silence is deafening when other
> viewers know this works but keep silent.
It's a curious thing, someone makes dubious claims and his opponents
> This is really hilarious in as much the silence is deafening when other
> viewers know this works but keep silent.
make their opposition clear. Meanwhile his supporters keep quiet.
Another curious thing is, he (the maker of the dubious claims) knows his
supporters are out there even though they keep quiet.
--
[Dancing is] a perpendicular expression of a horizontal desire,
legitimised by music.
G.B. Shaw quoted in /New Statesman/, 23 March 1962
djoyce099
Nov 12, 2014, 6:19:56 PM11/12/14
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Phil Carmody
Nov 13, 2014, 12:53:43 PM11/13/14
to
Pubkeybreaker <pubkey...@aol.com> writes:
> On Wednesday, November 12, 2014 6:03:31 AM UTC-5, Phil Carmody wrote:
> > djoyce099 <hlauk.h...@gmail.com> writes:
[SNIP - bibble babble]
> On Wednesday, November 12, 2014 6:03:31 AM UTC-5, Phil Carmody wrote:
> > djoyce099 <hlauk.h...@gmail.com> writes:
> > What the fuck do you mean by "curve 19 in ECM"? There are an
> > infinitude of ECs, and they're not sensibly indexed using the
> > natural numbers.
> >
> > Lack of answers to my two simple questions, and subsequent
> > misdirection noted. Another loon found...
>
> > infinitude of ECs, and they're not sensibly indexed using the
> > natural numbers.
> >
> > Lack of answers to my two simple questions, and subsequent
> > misdirection noted. Another loon found...
>
> The OP is a total cretin who does not understand:
Happy to be on the same page as you.
Cheers,
someg...@gmail.com
Nov 13, 2014, 2:41:43 PM11/13/14
to
Mystery Solved.
Dario Alpern's webpage is factoring these huge numbers using Lehman's method not ECM, but it doesn't clearly tell you it is using Lehman's.
The reason I know is that I downloaded the applet source and ran it in a debugger. It is calling the Lehman method with parms n and k. k=20 in this case and n is the number to be factored.
Lehman's is an old algorithm from 1974 designed to factor integers where the ratio of the two prime factors is a small fraction. In this case 5/4 = 1.25 for the first of his 9 numbers.
http://www.ams.org/journals/mcom/1974-28-126/S0025-5718-1974-0340163-2/S0025-5718-1974-0340163-2.pdf
The output from the Alpern website showing the factorization of the first number in the thread:
http://pastebin.com/KBDtm7tu
It is the output when I clicked on the "Show factorization in a new window" button.
Dario Alpern's webpage
http://www.alpertron.com.ar/ECM.HTM
The source code to the webpage in Java:
http://www.alpertron.com.ar/ecm.zip
Dario Alpern's webpage is factoring these huge numbers using Lehman's method not ECM, but it doesn't clearly tell you it is using Lehman's.
The reason I know is that I downloaded the applet source and ran it in a debugger. It is calling the Lehman method with parms n and k. k=20 in this case and n is the number to be factored.
Lehman's is an old algorithm from 1974 designed to factor integers where the ratio of the two prime factors is a small fraction. In this case 5/4 = 1.25 for the first of his 9 numbers.
http://www.ams.org/journals/mcom/1974-28-126/S0025-5718-1974-0340163-2/S0025-5718-1974-0340163-2.pdf
The output from the Alpern website showing the factorization of the first number in the thread:
http://pastebin.com/KBDtm7tu
It is the output when I clicked on the "Show factorization in a new window" button.
Dario Alpern's webpage
http://www.alpertron.com.ar/ECM.HTM
The source code to the webpage in Java:
http://www.alpertron.com.ar/ecm.zip
Pubkeybreaker
Nov 13, 2014, 2:44:53 PM11/13/14
to
On Thursday, November 13, 2014 2:41:43 PM UTC-5, someg...@gmail.com wrote:
> Mystery Solved.
>
> Dario Alpern's webpage is factoring these huge numbers using Lehman's method not ECM, but it doesn't clearly tell you it is using Lehman's.
I said that the app was using a Fermat variation months ago. I have stated
> Mystery Solved.
>
> Dario Alpern's webpage is factoring these huge numbers using Lehman's method not ECM, but it doesn't clearly tell you it is using Lehman's.
months ago that only Fermat's (or a variation) could produce the claimed results.
But, of course, like all cranks the OP refused to listen.
David Bernier
Nov 13, 2014, 3:19:07 PM11/13/14
to
On 11/13/2014 02:41 PM, someg...@gmail.com wrote:
> Mystery Solved.
>
Hallelujah!
David Bernier
--
pub 4096R/41C769D6 2014-11-04
uid David Bernier (doubledeckerpot5)
<davi...@videotron.ca>
> Mystery Solved.
>
Hallelujah!
David Bernier
pub 4096R/41C769D6 2014-11-04
uid David Bernier (doubledeckerpot5)
<davi...@videotron.ca>
djoyce099
Nov 13, 2014, 3:24:08 PM11/13/14
to
the algorithm is or variation you insisted it could not work.
The algorithm is listed as ECM.
Did you even go to the web site?
Just keep on calling me what ever you like but you just want to crush nuts.
djoyce099
Nov 13, 2014, 3:31:42 PM11/13/14
to
On Thursday, November 13, 2014 2:41:43 PM UTC-5, someg...@gmail.com wrote:
A wrong tag of ECM is a bit of a let down because I was under the impression
it was ECM
Dan
Pubkeybreaker
Nov 13, 2014, 5:19:52 PM11/13/14
to
djoyce099
Nov 13, 2014, 10:00:30 PM11/13/14
to
claims something it is not. I know nothing about ECM and I
admitted it before. I was just using it as a tool.
It still does not explain these semi-prime polynomial cycles
where more then 2/3 of the high order digits match.
Like on the (13) 2002 semi-primes I submitted early in this
post all their high order digits match.
No one can duplicate it unless someone copies what I posted
in the past.
I would love to see someone produce a 6028 bit semi-prime list
of 10 or more semi-primes that have two equal length prime factors
and > 2/3 of the semi-primes high order digits match.
This is a smaller semi-prime then I first listed in this post
so I am making it an easier challenge.
Dan
Pubkeybreaker
Nov 14, 2014, 7:41:05 AM11/14/14
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Pubkeybreaker
Nov 14, 2014, 8:13:43 AM11/14/14
to
On Thursday, November 13, 2014 10:00:30 PM UTC-5, djoyce099 wrote:
> On Thursday, November 13, 2014 5:19:52 PM UTC-5, Pubkeybreaker wrote:
> > On Thursday, November 13, 2014 3:31:42 PM UTC-5, djoyce099 wrote:
> > > On Thursday, November 13, 2014 2:41:43 PM UTC-5, someg...@gmail.com wrote:
> > > > Mystery Solved.
> >
> On Thursday, November 13, 2014 5:19:52 PM UTC-5, Pubkeybreaker wrote:
> > On Thursday, November 13, 2014 3:31:42 PM UTC-5, djoyce099 wrote:
> > > On Thursday, November 13, 2014 2:41:43 PM UTC-5, someg...@gmail.com wrote:
> > > > Mystery Solved.
> >
> > I told you that it wasn't. But you refused to listen.
>
> Okay, I guess you can not trust anything on the internet that
> claims something it is not.
The app you used DOES perform ECM. It just tries some other methods
>
> Okay, I guess you can not trust anything on the internet that
> claims something it is not.
FIRST. If you would have bothered to RTFM, you might have realized this.
I know nothing about ECM and I
> admitted it before. I was just using it as a tool.
>
> It still does not explain these semi-prime polynomial cycles
> where more then 2/3 of the high order digits match.
polynomial cycles". Finding two large primes whose top 2/3 bits are
the same is totally trivial.
djoyce099
Nov 14, 2014, 9:09:10 AM11/14/14
to
> > Okay, I guess you can not trust anything on the internet that
> > claims something it is not. I know nothing about ECM and I
> > admitted it before. I was just using it as a tool.
> >
> > It still does not explain these semi-prime polynomial cycles
> > where more then 2/3 of the high order digits match.
> > Like on the (13) 2002 semi-primes I submitted early in this
> > post all their high order digits match.
> >
> > No one can duplicate it unless someone copies what I posted
> > in the past.
> > I would love to see someone produce a 6028 bit semi-prime list
> > of 10 or more semi-primes that have two equal length prime factors
> > and > 2/3 of the semi-primes high order digits match.
> > This is a smaller semi-prime then I first listed in this post
> > so I am making it an easier challenge.
>
>
> This is totally trivial to do with sieve methods.
Are you sure?
> > claims something it is not. I know nothing about ECM and I
> > admitted it before. I was just using it as a tool.
> >
> > It still does not explain these semi-prime polynomial cycles
> > where more then 2/3 of the high order digits match.
> > Like on the (13) 2002 semi-primes I submitted early in this
> > post all their high order digits match.
> >
> > No one can duplicate it unless someone copies what I posted
> > in the past.
> > I would love to see someone produce a 6028 bit semi-prime list
> > of 10 or more semi-primes that have two equal length prime factors
> > and > 2/3 of the semi-primes high order digits match.
> > This is a smaller semi-prime then I first listed in this post
> > so I am making it an easier challenge.
>
>
> This is totally trivial to do with sieve methods.
Because these huge semi-prime polynomial cycles have prime factors
never to be found in the generating surrogate as in my second list of 617 digit
semi-primes created from rsa2048 as the generating surrogate.
As with a possible method, all these ratio types and their many different
cycles could eliminated both factors from each semi-prime in each discrete
list. Including all primes between the final chosen ones.
Each discrete list, as with the case of rsa2048, hold > e+145 semi-primes
created from simple ratios making all their factors non divisors of rsa2048.
I know (e+145 * 2) is a tiny number compared to rsa2048 but accumulative
discrete list could make a difference in the final factorization if removed
as prime candidates.
I am not sure how many of these discrete list are possible.
As the ratios become more complex the number of these semi-primes is reduced
for any discrete list but the factors passed up can also be excluded because
of remainders in the quotients have certain patterns because of the polynomial
nature of these factors that create these semi-primes.
You probably think this is all horse do do but just a thought.
Dan
Pubkeybreaker
Nov 14, 2014, 9:27:36 AM11/14/14
to
And despite repeated prods, you still refuse
to define your terminology.
And (responding to your question) yes, I am sure.
djoyce099
Nov 14, 2014, 10:02:38 AM11/14/14
to
I always have trouble explaining the complete concept but will
give it a try again.
someg...@gmail.com
Nov 14, 2014, 12:23:46 PM11/14/14
to
So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
1. The maximum ratio of the integer factors of
rsa2048 <= 1.28262912617470817127798623899421 (approximately)
2. So rsa2048 = p*q with p and q both prime. For Lehman's to work you have to approximate p/q with another fraction m/n. I assure you that m and n are very large numbers because the smaller ratios have been tried. The Lehman's pdf I mentioned earlier in the thread rigorously shows you this in detail.
Somewhere on the rsa challenge website either now or in the past they discussed how the challenge numbers were created and said that the 2048 in rsa2048 meant it was 2048 bit product composed of two 1024 bit factors.
The older rsa challenge numbers indicated number of decimal digits like RSA120. You can confirm this by looking at the # of bits in the solved challenge numbers.
Both factors have to be exactly 1024 bits, not 1023 bits or 1025 bits.
So it can't be a 1024 bit factor times a 1023 bit factor.
So the minimum odd 1024 bit factor is 2^1023+1. (100000...1 base 2)
The maximum odd 1024 bit factor is 2^1024-1. (111111...1 base 2)
If you want to prove it too yourself what the max possible ratio is:
Divide rsa2048 by the minimum 1024 bit factor and count bits in the result.
Divide rsa2048 by the maximum 1024 bit factor and count bits in the result.
Use some logic.
Try it with smaller numbers with exactly the same bit length factors to find the max ratio possible.
Or I can give you the pseudocode.
1. The maximum ratio of the integer factors of
rsa2048 <= 1.28262912617470817127798623899421 (approximately)
2. So rsa2048 = p*q with p and q both prime. For Lehman's to work you have to approximate p/q with another fraction m/n. I assure you that m and n are very large numbers because the smaller ratios have been tried. The Lehman's pdf I mentioned earlier in the thread rigorously shows you this in detail.
Somewhere on the rsa challenge website either now or in the past they discussed how the challenge numbers were created and said that the 2048 in rsa2048 meant it was 2048 bit product composed of two 1024 bit factors.
The older rsa challenge numbers indicated number of decimal digits like RSA120. You can confirm this by looking at the # of bits in the solved challenge numbers.
Both factors have to be exactly 1024 bits, not 1023 bits or 1025 bits.
So it can't be a 1024 bit factor times a 1023 bit factor.
So the minimum odd 1024 bit factor is 2^1023+1. (100000...1 base 2)
The maximum odd 1024 bit factor is 2^1024-1. (111111...1 base 2)
If you want to prove it too yourself what the max possible ratio is:
Divide rsa2048 by the minimum 1024 bit factor and count bits in the result.
Divide rsa2048 by the maximum 1024 bit factor and count bits in the result.
Use some logic.
Try it with smaller numbers with exactly the same bit length factors to find the max ratio possible.
Or I can give you the pseudocode.
djoyce099
Nov 14, 2014, 1:15:08 PM11/14/14
to
On Friday, November 14, 2014 12:23:46 PM UTC-5, someg...@gmail.com wrote:
> So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
>
> 1. The maximum ratio of the integer factors of
> rsa2048 <= 1.28262912617470817127798623899421 (approximately)
To maintain the highest ratio between the 2 factors of rsa2048
> So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
>
> 1. The maximum ratio of the integer factors of
> rsa2048 <= 1.28262912617470817127798623899421 (approximately)
and still maintain the equal bit length of the 2 factors of rsa2048
that ratio must be much higher then you show?
Like 2.519590047.. or ((rsa2048)-1)/e+316 unless I am understanding
it wrong.
Dan
djoyce099
Nov 14, 2014, 1:21:37 PM11/14/14
to
On Friday, November 14, 2014 1:15:08 PM UTC-5, djoyce099 wrote:
> On Friday, November 14, 2014 12:23:46 PM UTC-5, someg...@gmail.com wrote:
> > So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
> >
> > 1. The maximum ratio of the integer factors of
> > rsa2048 <= 1.28262912617470817127798623899421 (approximately)
>
> To maintain the highest ratio between the 2 factors of rsa2048
> and still maintain the equal bit length of the 2 factors of rsa2048
> that ratio must be much higher then you show?
> Like 2.519590047.. or ((rsa2048)-1)/e+316 unless I am understanding
> it wrong.
>
> Dan
Correction above -- should be ((rsa2048)-1)/(e+616)
> On Friday, November 14, 2014 12:23:46 PM UTC-5, someg...@gmail.com wrote:
> > So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
> >
> > 1. The maximum ratio of the integer factors of
> > rsa2048 <= 1.28262912617470817127798623899421 (approximately)
>
> To maintain the highest ratio between the 2 factors of rsa2048
> and still maintain the equal bit length of the 2 factors of rsa2048
> that ratio must be much higher then you show?
> Like 2.519590047.. or ((rsa2048)-1)/e+316 unless I am understanding
> it wrong.
>
> Dan
djoyce099
Nov 14, 2014, 1:26:09 PM11/14/14
to
On Friday, November 14, 2014 1:15:08 PM UTC-5, djoyce099 wrote:
> On Friday, November 14, 2014 12:23:46 PM UTC-5, someg...@gmail.com wrote:
> > So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
> >
> > 1. The maximum ratio of the integer factors of
> > rsa2048 <= 1.28262912617470817127798623899421 (approximately)
>
> To maintain the highest ratio between the 2 factors of rsa2048
> and still maintain the equal bit length of the 2 factors of rsa2048
> that ratio must be much higher then you show?
> Like 2.519590047.. or ((rsa2048)-1)/e+316 unless I am understanding
> it wrong.
>
> Dan
Mistake above -- should be ((rsa2048)-1)/e+616
> > So if you want to factor rsa2048 using the ratio of the factors, maybe I can save you some time.
> >
> > 1. The maximum ratio of the integer factors of
> > rsa2048 <= 1.28262912617470817127798623899421 (approximately)
>
> To maintain the highest ratio between the 2 factors of rsa2048
> and still maintain the equal bit length of the 2 factors of rsa2048
> that ratio must be much higher then you show?
> Like 2.519590047.. or ((rsa2048)-1)/e+316 unless I am understanding
> it wrong.
>
> Dan
someg...@gmail.com
Nov 14, 2014, 2:21:12 PM11/14/14
to
Dan,
and others forgive me if I've dumbed this down too much.
Here is a better example with a smaller number:
Number to factor n = 9090287
9090287 is a 24 bit number, the product of two 12 bit primes that I created as an example.
In base 2 the number 9090287 is 1000 1010 1011 0100 1110 1111.
This is 24 bits.
Using the new rsa challenge number notation they would call it an RSA24 length 24 in base 2.
Under the old rsa challenge number notation they would call it an RSA7 length 7 in base 10.
The range of all 12 bit odd numbers is 2049-4095.
2049 is 100000000001 in base 2, the lowest 12 bit odd number
4095 is 111111111111 in base 2, the highest 12 bit odd number
9090287/2049 = 4436.4504636 2049 is the lowest 12 bit odd number
4436 in base 2 is 1 0001 0101 0100 that's 13 bits it's too big.
9090287/4095 = 2219.8503052 4095 is the highest 12 bit odd number
2219 in base 2 is 1000 1010 1011 that's 12 bits so it's ok.
4095 is the highest 12 bit odd number so it's ok.
So the highest possible ratio of two 12 bit factors of 9090287 is approximately:
4095/2219 1.8454258675078864353312302839117
Because the range of all 12 bit odd numbers is 2049-4095 the maximum ratio of two 12 bit
factors is 4095/2049 or 1.9985358711566617862371888726208.
and others forgive me if I've dumbed this down too much.
Here is a better example with a smaller number:
Number to factor n = 9090287
9090287 is a 24 bit number, the product of two 12 bit primes that I created as an example.
In base 2 the number 9090287 is 1000 1010 1011 0100 1110 1111.
This is 24 bits.
Using the new rsa challenge number notation they would call it an RSA24 length 24 in base 2.
Under the old rsa challenge number notation they would call it an RSA7 length 7 in base 10.
The range of all 12 bit odd numbers is 2049-4095.
2049 is 100000000001 in base 2, the lowest 12 bit odd number
4095 is 111111111111 in base 2, the highest 12 bit odd number
9090287/2049 = 4436.4504636 2049 is the lowest 12 bit odd number
4436 in base 2 is 1 0001 0101 0100 that's 13 bits it's too big.
9090287/4095 = 2219.8503052 4095 is the highest 12 bit odd number
2219 in base 2 is 1000 1010 1011 that's 12 bits so it's ok.
4095 is the highest 12 bit odd number so it's ok.
So the highest possible ratio of two 12 bit factors of 9090287 is approximately:
4095/2219 1.8454258675078864353312302839117
Because the range of all 12 bit odd numbers is 2049-4095 the maximum ratio of two 12 bit
factors is 4095/2049 or 1.9985358711566617862371888726208.
Professor Gavin
Nov 14, 2014, 2:43:07 PM11/14/14
to
Looking at Numbers is good.
Sequences and Series.
Integrals.
The association between a particular Integral
and the relevant Sequence, Series. (Factorials).
Otherwise, a certain formula (transformation) comes to mind.
Transformations.
Spatial Transformations.
Sequences and Series.
Integrals.
The association between a particular Integral
and the relevant Sequence, Series. (Factorials).
Otherwise, a certain formula (transformation) comes to mind.
Transformations.
Spatial Transformations.
djoyce099
Nov 14, 2014, 7:15:51 PM11/14/14
to
early example.
Also, if true, I could narrow my search on creating simple ratios of rsa2048
(surrogate) that fall @ or below the ratio you show for rsa2048. Thus creating
these polynomial primes and then exclude all those primes also.
What if one prime factor has one or more digit then the other.
That would rule all this out no?
If true, this is huge.
Have you tested it on other large factored RSA semi-prime?
Dan
Pubkeybreaker
Nov 14, 2014, 7:26:37 PM11/14/14
to
On Friday, November 14, 2014 7:15:51 PM UTC-5, djoyce099 wrote:
> On Friday, November 14, 2014 2:21:12 PM UTC-5, someg...@gmail.com wrote:
> > Dan,
> > and others forgive me if I've dumbed this down too much.
> >
<snip>
> On Friday, November 14, 2014 2:21:12 PM UTC-5, someg...@gmail.com wrote:
> > Dan,
> > and others forgive me if I've dumbed this down too much.
> >
>
> If this is true it eliminates a huge block of primes in rsa2048 as in your
> early example.
I generated the data.
> Also, if true, I could narrow my search on creating simple ratios of rsa2048
is meaningless babble.
> (surrogate) that fall @ or below the ratio you show for rsa2048. Thus creating
> these polynomial primes
do you refer to as in "these" polynomial primes. Learn to write
intelligently, damn it! What you write is a meaningless jumble of words
and undefined phrases.
>
> What if one prime factor has one or more digit then the other.
> That would rule all this out no?
been told that rsa2048 is the product of two 1024 bits primes. I will
guarantee that the ratio of these two primes is NOT close to the ratio
of two small integers.
>
> If true, this is huge.
> Have you tested it on other large factored RSA semi-prime?
What is "it"?
> If true, this is huge.
> Have you tested it on other large factored RSA semi-prime?
As I have said multiple times in this forum and on other forums:
The RSA challenge numbers are each the product of primes of equal
bit size and the moduli themselves are immune to Fermat's Method,
Lehman's Method, P-1, P+1.
>
> Dan
djoyce099
Nov 14, 2014, 8:29:53 PM11/14/14
to
Otherwise it would have been factored long ago.
Is the last poster right in his upper limit of the ratio of these two primes
of rsa2048?
The Polynomial primes I will attempt to explain in my next presentation.
djoyce099
Nov 14, 2014, 8:37:36 PM11/14/14
to
On Friday, November 14, 2014 12:23:46 PM UTC-5, someg...@gmail.com wrote:
and < sqrt(2048) are the only valid prime search for
the smallest factor of rsa2048.
1.40156893226316019479941913178154838500579327255238570308793069224221043369965345420238159408957846541060211337829719038702472867618892249030920162793512241163098202969181707748101088039185275764903132489458774572096493080532401749911948298368988797295937403570532973780536850201617755923795627266649798201067e+308
The largest factor < integer below and > sqrt(rsa2048) are the
only valid prime search for the largest factor.
1.79769313486231590772930519078902303305164860630362159898956915271139886133137415654346438626577626587143429435298604917652827561804024108691087064488722332192846150488595112257083051393403651070142940926593058646159555446325170764516376590632807009992846153681499806368482144990936609603508591852480352354475e+308
It looks like you have eliminated more then half of all the primes
in this range below where --
It is > e+308 as always remaining 1024 bit number
and
It is < sqrt(rsa2048) for locating the smallest prime.
It is <
2.51959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590957000973304597488084284017974291006424586918171951187461215151726546322822168699873e+308
and
It is > sqrt(rsa2048) for locating the largest prime.
Fantastic if true.
Dan
someg...@gmail.com
Nov 15, 2014, 11:13:50 AM11/15/14
to
> RSA2048 is the product of two 1024 bit primes. I have direct knowledge.
> I generated the data.
>
You are the one at RSA labs who ran the software to generate RSA2048 for the RSA Factoring Challenge all those years ago?
> I generated the data.
>
Well, you know this is the internet where anyone can fake an identity. I have to tease you about that.
It doesn't matter whether you are or not because you have demonstrated deep knowledge of the topic.
Pubkeybreaker
Nov 15, 2014, 12:54:46 PM11/15/14
to
someg...@gmail.com
Nov 15, 2014, 1:01:32 PM11/15/14
to
> So what you are saying is all primes > then integer below
> and < sqrt(2048) are the only valid prime search for
> the smallest factor of rsa2048.
>
> 1.40156893226316019479941913178154838500579327255238570308793069224221043369965345420238159408957846541060211337829719038702472867618892249030920162793512241163098202969181707748101088039185275764903132489458774572096493080532401749911948298368988797295937403570532973780536850201617755923795627266649798201067e+308
>
> The largest factor < integer below and > sqrt(rsa2048) are the
> only valid prime search for the largest factor.
>
> 1.79769313486231590772930519078902303305164860630362159898956915271139886133137415654346438626577626587143429435298604917652827561804024108691087064488722332192846150488595112257083051393403651070142940926593058646159555446325170764516376590632807009992846153681499806368482144990936609603508591852480352354475e+308
>
> It looks like you have eliminated more then half of all the primes
> in this range below where --
>
> It is > e+308 as always remaining 1024 bit number
> and
> It is < sqrt(rsa2048) for locating the smallest prime.
>
>
> It is <
> 2.51959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590957000973304597488084284017974291006424586918171951187461215151726546322822168699873e+308
> and
> It is > sqrt(rsa2048) for locating the largest prime.
>
> Fantastic if true.
>
> Dan
Yes, the min and max factors you mention above are approximately the same as what I calculate. The difference is probably because of rounding error.(number of digits precision. I think I used 255 decimal digits precision)
> and < sqrt(2048) are the only valid prime search for
> the smallest factor of rsa2048.
>
> 1.40156893226316019479941913178154838500579327255238570308793069224221043369965345420238159408957846541060211337829719038702472867618892249030920162793512241163098202969181707748101088039185275764903132489458774572096493080532401749911948298368988797295937403570532973780536850201617755923795627266649798201067e+308
>
> The largest factor < integer below and > sqrt(rsa2048) are the
> only valid prime search for the largest factor.
>
> 1.79769313486231590772930519078902303305164860630362159898956915271139886133137415654346438626577626587143429435298604917652827561804024108691087064488722332192846150488595112257083051393403651070142940926593058646159555446325170764516376590632807009992846153681499806368482144990936609603508591852480352354475e+308
>
> It looks like you have eliminated more then half of all the primes
> in this range below where --
>
> It is > e+308 as always remaining 1024 bit number
> and
> It is < sqrt(rsa2048) for locating the smallest prime.
>
>
> It is <
> 2.51959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590957000973304597488084284017974291006424586918171951187461215151726546322822168699873e+308
> and
> It is > sqrt(rsa2048) for locating the largest prime.
>
> Fantastic if true.
>
> Dan
It is true. One easy way to check your answer is to pick many random 1024 bit integers.
Pick a random 1024 bit integer p, doesn't have to be prime.
Find q = RSA2048/p
If p and q are both 1024 bits show the ratio p/q if p is larger or q/p if q is larger.
If you don't have a bitlength function available you can calculate
bitlength(n) = ceiling(log(n)/log(2)).
You do have your work cut out for you because the previous poster is right about
Lehman's and other factoring algorithms are just too slow to work on RSA2048.
The most respected experts in the field agree that the only algorithm effective for factoring numbers the size of RSA2048 is the GNFS algorithm. And they can prove it mathematically.
The reason it is so effective is because it eliminates absolutely huge blocks of primes as possible candidates. If GNFS were a sieve for gold it would find a speck of gold in a mountain of dirt immediately.
djoyce099
Nov 15, 2014, 4:05:28 PM11/15/14
to
where up front it can remove,as far as rsa2048 is concerned, more then half
of all primes in the range we discussed above.
My method also removes many large blocks of primes but no where near as
effective as this method. So employing both methods could be a possibility
working within the above range of this method?
I use 2011 digit precision normally.
Thanks for your imput, I will give this method a try.
Dan
Pubkeybreaker
Nov 15, 2014, 4:19:09 PM11/15/14
to
On Saturday, November 15, 2014 4:05:28 PM UTC-5, djoyce099 wrote:
> On Saturday, November 15, 2014 1:01:32 PM UTC-5, someg...@gmail.com wrote:
> > > So what you are saying is all primes > then integer below
> > > and < sqrt(2048) are the only valid prime search for
> > > the smallest factor of rsa2048.
> >
> On Saturday, November 15, 2014 1:01:32 PM UTC-5, someg...@gmail.com wrote:
> > > So what you are saying is all primes > then integer below
> > > and < sqrt(2048) are the only valid prime search for
> > > the smallest factor of rsa2048.
> >
> > The most respected experts in the field agree that the only algorithm effective for factoring numbers the size of RSA2048 is the GNFS algorithm. And they can prove it mathematically.
> >
> > The reason it is so effective is because it eliminates absolutely huge blocks >of primes as possible candidates.
This is complete nonsense. GNFS does not "eliminate blocks of primes"
> >
> > The reason it is so effective is because it eliminates absolutely huge blocks >of primes as possible candidates.
as possible candidates. GNFS will factor any number regardless of any
special properties of its factors. Its run time depends ONLY on the
size of the composite.
> So GNFS does employ this method.
Thus, the phrase "this method" is totally meaningless.
No wonder it is used on large semi-primes
> where up front it can remove,as far as rsa2048 is concerned, more then half
> of all primes in the range we discussed above.
two factors. If N is the product of three or more factors, each iteration
can split N into A*B, where A and B do not have to be prime.
Why don't you try READING about these algorithms??? You do know how to read,
I assume?
>
> My method also removes many large blocks of primes but no where near as
> effective as this method. So employing both methods could be a possibility
> working within the above range of this method?
>
> I use 2011 digit precision normally.
>
> Thanks for your imput, I will give this method a try.
hope of factoring rsa2048.
djoyce099
Nov 15, 2014, 4:54:59 PM11/15/14
to
someg...@gmail.com
Nov 15, 2014, 5:00:18 PM11/15/14
to
>GNFS does not "remove" primes. One iteration splits a composite integer N into
>two factors. If N is the product of three or more factors, each iteration
>can split N into A*B, where A and B do not have to be prime.
Yes, you are correct, I misspoke. It doesn't rule out blocks of primes as possible factors directly. I was trying to make an analogy that didn't work.
>two factors. If N is the product of three or more factors, each iteration
>can split N into A*B, where A and B do not have to be prime.
No GNFS is not similar to any method that I mentioned in any post. Understanding GNFS requires understanding the advanced math and there is no simple English explanation that would do it justice.
djoyce099
Nov 15, 2014, 5:16:08 PM11/15/14
to
It is way over my head.
Your bit method is still an interesting concept if it works.
Dan
Professor Gavin
Nov 16, 2014, 3:07:47 AM11/16/14
to
Prime numbers are good.
How does this relate to $40,000
Prime numbers are or can be complex.
Style in writing is important.
What is a prime number.
Not easily divisible.
Understanding this in terms of number space.
Overlap through number sets.
Eliminating "sames" and allowing only new combinations.
Tom Cruise coudl do this.
Missing numbers could be the subject of a Black Hole
or so.
Pubkeybreaker
Nov 17, 2014, 7:33:57 AM11/17/14
to
The mathematics does not go beyond the undergraduate level.
Pick up some books and learn the math.
Ignorance is curable.
Willful ignorance is not.
Phil Carmody
Nov 17, 2014, 12:54:55 PM11/17/14
to
his real name to Pubkeybreaker, probably close to a decade ago.
But when posting under his real name, at least for a while,
the domain was "rsa.com".
Phil
--
The best part of re-inventing the wheel is that you get to pick how
many sides the new one has. -- egcagrac0 on SoylentNews
Pubkeybreaker
Nov 17, 2014, 3:22:02 PM11/17/14
to
On Monday, November 17, 2014 12:54:55 PM UTC-5, Phil Carmody wrote:
> someg...@gmail.com writes:
> > > RSA2048 is the product of two 1024 bit primes. I have direct knowledge.
> > > I generated the data.
> >
> > You are the one at RSA labs who ran the software to generate RSA2048 for the RSA Factoring Challenge all those years ago?
> >
> > Well, you know this is the internet where anyone can fake an identity. I have to tease you about that.
> >
> > It doesn't matter whether you are or not because you have demonstrated deep knowledge of the topic.
>
> He's the real deal, no BS. Not quite sure when he transitioned from
> his real name to Pubkeybreaker, probably close to a decade ago.
> But when posting under his real name, at least for a while,
> the domain was "rsa.com".
>
> Phil
Actually, I used to be BS. For 10 years I was b...@mitre.org
> someg...@gmail.com writes:
> > > RSA2048 is the product of two 1024 bit primes. I have direct knowledge.
> > > I generated the data.
> >
> > You are the one at RSA labs who ran the software to generate RSA2048 for the RSA Factoring Challenge all those years ago?
> >
> > Well, you know this is the internet where anyone can fake an identity. I have to tease you about that.
> >
> > It doesn't matter whether you are or not because you have demonstrated deep knowledge of the topic.
>
> He's the real deal, no BS. Not quite sure when he transitioned from
> his real name to Pubkeybreaker, probably close to a decade ago.
> But when posting under his real name, at least for a while,
> the domain was "rsa.com".
>
> Phil
Phil Carmody
Nov 18, 2014, 4:52:24 PM11/18/14
to
my line lengths give it away that it was a bit of an after-
thought.)
djoyce099
Jan 20, 2015, 4:21:18 PM1/20/15
to
A question about your entry of rsa240 closest neighbor challenge does the
above procedure have anything to do with your results?
I find quasis' entry facinating that beats both are entries and also
the rsa2048 entry that beats the pants off of my closest gap for rsa2048
but am still intrigued with your results because of its' complex ratio
between factors.
Dan
fas
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