factoring request
master1729
(46^46 - 1) /( (46+1)*(46-1))
(58^58 - 1) /( (58+1)*(58-1))
(82^82 - 1) /( (82+1)*(82-1))
(106^106 - 1) /( (106+1)*(106-1))
thank you.
regards
tommy1729
master1729
I said PLZ.
Virgil
<1699063352.149909.1257...@gallium.mathforum.org>,
master1729 <tomm...@gmail.com> wrote:
(46^46 - 1) /( (46+1)*(46-1)) factors into
[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46^23 + 1)]
And similarly for the others.
master1729
> In article
> <1699063352.149909.1257108152590.JavaMail.root@gallium
sigh.
im tired of these jokes.
you people know darn well that
1) i was aware of the above trivial factorization
or should i say : " what is intended " since the above is actually wrong :
quote :
(46^46 - 1) /( (46+1)*(46-1)) factors into
[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46^23 + 1)]
/
wow a number factors into a smaller number !!??!!
yes smaller because (46^23 + 1) / (46^23 + 1) = 1
so that joke is even wrong and pathetic.
2) im not a beginner at factoring , otherwise i could not have known that (46^46 - 1) /( (46+1)*(46-1)) is actually an integer.
3) thus i wanted - as you darn well know - a full factorization. and a correct one !
4) if you will reply with jokes , mistakes , nonsense and irrelevant stuff , i will too and say here : axiom of choice is wrong.
regards - assuming and hoping you will give a better reply now -
tommy1729
since this reply of virgil was rediculous ( didnt say virgil is ) , i feel the urge to quote an idiot :)
" sd354fq35f13e4f115fsd search the people " musatov.
master1729
(46^23 + 1) / 47 = prime.
tommy1729
Pubkeybreaker
> Plz factor the following 4 numbers :
>
> (46^46 - 1) /( (46+1)*(46-1))
>
> (58^58 - 1) /( (58+1)*(58-1))
>
> (82^82 - 1) /( (82+1)*(82-1))
>
> (106^106 - 1) /( (106+1)*(106-1))
(1) Each of the numerators is the difference of two
squares.
Their factorization is trivial.
(2) You can find the full facorizations at Richard
Brent's website.
Martin M. Musatov
master1729
>
>
>
shut up musatov , you retarded son of a german whore who married a bad smelling pokemon.
go ' search the people '
master1729
thanks.
i will look at R Brents website.
i already factored 3 out of 4.
but that last one is tricky , better use his website.
maybe it will lead to a nice conjecture.
regards
tommy1729
master1729
i have trouble with .gz files for some reason.
didnt find an online program to factor , did i overlook ?
master1729
did it :)
Virgil
<968439331.150126.12571...@gallium.mathforum.org>,
master1729 <tomm...@gmail.com> wrote:
My poor proof reading, sorry.
Should have been
[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46+ 1)]
Which is a factorization. though apparently not the COMPLETE
factorization that OP did not actually specify he wanted.
>
> wow a number factors into a smaller number !!??!!
>
> yes smaller because (46^23 + 1) / (46^23 + 1) = 1
>
> so that joke is even wrong and pathetic.
>
> 2) im not a beginner at factoring , otherwise i could not have known that
> (46^46 - 1) /( (46+1)*(46-1)) is actually an integer.
>
> 3) thus i wanted - as you darn well know - a full factorization. and a
> correct one !
If you want a FULL (or more properly, a complete) factorization, it is
not that much more difficult to say so.
Martin M. Musatov
dan73
More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e+111.
Dan
Pubkeybreaker
> > Plz factor the following 4 numbers :
>
> > (46^46 - 1) /( (46+1)*(46-1))
>
> > (58^58 - 1) /( (58+1)*(58-1))
>
> > (82^82 - 1) /( (82+1)*(82-1))
>
> > (106^106 - 1) /( (106+1)*(106-1))
>
> > thank you.
>
> > regards
>
> > tommy1729
>
> More of a challenge --
> The 3 + the first 111 decimal digits of pi changed
> to an integer.
>
>
> Dan- Hide quoted text -
>
> - Show quoted text -
Not much of a challenge. A few days computing on a single PC using
GNFS. Even less if one can
pull out a small factor or two with ECM.
dan73
>> The 3 + the first 111 decimal digits of pi changed
>> to an integer.
>
> 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e+111.
>
>> Dan- Hide quoted text -
>
> - Show quoted text -
>Not much of a challenge. A few days computing on a >single PC using
>GNFS. Even less if one can
>pull out a small factor or two with ECM.
You are probably right, I have only run it on ECM
for a few hours and @ curve 750 it appears this
composite has at most three factors but maybe
only two.
master1729
nice problem.
i think its not so hard if you use a computerprogram.
but perhaps we can do without computers and use some math tricks !?
for instance the many formula's concerning sin , arcsin etc and products ?
maybe that is too optimistic. or not.
i bet on q-sine ...
regards
tommy1729
master1729
> In article
> <968439331.150126.1257112893522.JavaMail.root@gallium.
still wrong !!
lol
regards
tommy1729
dan73
> >The 3 + the first 111 decimal digits of pi changed
> >to an integer.
>
> >3.1415926535897932384626433832795028841971693993751058
> >209749445923078164062862089986280348253421170679821480
> >86513e+111.
>
> >Dan
>nice problem.
>i think its not so hard if you use a computerprogram.
>but perhaps we can do without computers and use some math tricks !?
>for instance the many formula's concerning sin , arcsin etc and products ?
>maybe that is too optimistic. or not.
>i bet on q-sine ...
>regards
>tommy1729
I was trying to use Darios' ECM and my python triangle
sum program simultaneously but the memory over head was
just to great.
So I opted to use only the ECM because it is much
faster, like probably 100 times faster!
Although in some limited instances of certain composites
my python triangle summing program beats the pants off
of the ECM.
Here is where it stands now with no factors yet --
Factoring 3141 592653 589793 238462 643383 279502 884197
169399 375105 820974 944592 307816 406286 208998 628034
825342 117067 982148 086513 (112 digits)
Limit (B1=1000000; B2=100000000) Curve 1036
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability:----------100% 100% 100% 99% 34% 5%
About 10 hours worth.
It would be nice if someone could pickup on curve 1200.
After finishing my run of 1012 too 1199 I could jump
too 1400 and the other party could jump from 1399 to 1600
and so on!
Generally speaking, if there are just 2 factors that are
close to equal digit length then this may take about 5
or 6 days to factor on one computer.
If there are just 3 factors the factoring time
would be much less, more like what pubkeybreaker
is saying. Or 2 factors much different in length by
about 10 or more digits the factoring time would be
much less than the 5 of 6 day factoring time.
Dan
dan73
>More of a challenge --
>The 3 + the first 111 decimal digits of pi changed
>to an integer.
>3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e+111.
>Dan
The latest update on factoring floor(10^111 * pi)
The ECM after 5 days factoring =
Factoring 3141 592653 589793 238462 643383 279502 884197 169399 375105 820974
944592 307816 406286 208998 628034 825342 117067 982148 086513 (112 digits)
Limit (B1=11000000; B2=1100000000) Curve 2450
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability:------- 100% 100% 100% 100% 97% 33%
It now appears that there are just two factors.
I was wrong on this one. It is more of a challenge
than I first thought, on the high side it could
take years to factor.
Dan
Pubkeybreaker
> tommy1729 wrote:
> >> Plz factor the following 4 numbers :
>
> >> (46^46 - 1) /( (46+1)*(46-1))
>
> >> (58^58 - 1) /( (58+1)*(58-1))
>
> >> (82^82 - 1) /( (82+1)*(82-1))
>
> >> (106^106 - 1) /( (106+1)*(106-1))
>
> >> thank you.
>
> >> regards
>
> >> tommy1729
> >More of a challenge --
> >The 3 + the first 111 decimal digits of pi changed
> >to an integer.
> >Dan
>
> The latest update on factoring floor(10^111 * pi)
>
> The ECM after 5 days factoring =
>
> Factoring 3141 592653 589793 238462 643383 279502 884197 169399 375105 820974
> 944592 307816 406286 208998 628034 825342 117067 982148 086513 (112 digits)
> Limit (B1=11000000; B2=1100000000) Curve 2450
> Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
> Probability:------- 100% 100% 100% 100% 97% 33%
>
> It now appears that there are just two factors.
> I was wrong on this one. It is more of a challenge
> than I first thought, on the high side it could
> take years to factor.
Sigh. People simply do not read.
As I said:
It will take only a few days on any modern PC using GNFS.
dan73
Pubkeybreaker wrote:
>Sigh. People simply do not read.
>As I said:
>It will take only a few days on any modern PC using >GNFS.
Yea I did read and used ECM, but it has chugged
for 5+days.
Will GNFS give quicker results?
Dan
master1729
Dan , which part of
"It will take only a few days on any modern PC using
GNFS."
didnt you understand ? x)
lol
tommy1729
dan73
>"It will take only a few days on any modern PC using
>GNFS."
>didn't you understand ? x)
>lol
>tommy1729
I had it wrong also, even with GNFS it is going
to take more than just a few days!
It is still chugging along on the ECM
after 6 + days but if GNFS is more than
twice as fast as ECM, it is possible GNFS could
factor it in a few days.
I never used that algorithm (GNFS) but it
is better to use on larger composites like this
one rather than ECM or so I have read!
Is there any free GNFS software for the Python
language out there?
Dan
factorboy13
> to take more than just a few days!
I don't think it will take more than a couple of hours to factor it with ggnfs (only 112 decimal digits).
I will do try it now and will post the factors here
factorboy13
3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513 (112 digits)
prp43 factor: 1215666422974078739455530964256912318288897
prp70 factor: 2584255511395974781222544726762221278238062155282351848420786629580529
elapsed time 00:03:10
dan73
>31415926535897932384626433832795028841971693993751058209>74944592307816406286208998628034825342117067982148086513 (112 digits)
>prp43 factor: >1215666422974078739455530964256912318288897
>prp70 factor: >25842555113959747812225447267622212782380621552823518484>20786629580529
>elapsed time 00:03:10
This was allready factored ---
See "more on factoring floor(pi*(10^111))
posted on 16th nov.
Dan
factorboy13
>
> See "more on factoring floor(pi*(10^111))
> posted on 16th nov.
> Dan
Ah ok. You took a significant time but is normal with ECM when a factor is of this size.
dan73
I guess so, 3.10 sec. against 14 days.
I must live in the dinosaur age.
It would probably be much faster with ECM if
my cp was a duo core processor and I downloaded
the ECM software instead of doing it online!
Probably more like 10 days.
Even at that, 3.10 sec. really makes that look sick.
What are the bench-marks with 60-80 digit composites
with GGNFS and ECM when the two factors are of equal
length in these composites.
Dan
Dan
factorboy13
> I guess so, 3.10 sec. against 14 days.
> I must live in the dinosaur age.
>
Well, not 3.10 sec, actually 3 hours and 10 minutes :(
And I did it with a i7 860 working with 8 threads!
> What are the bench-marks with 60-80 digit composites
> with GGNFS and ECM when the two factors are of equal
> length in these composites.
GGNFS is not the best for factors up to 100 digits, probably SIQS is better when factors are about equal size and ECM can not find fast a factor up to 30 digits
dan73
> I must live in the dinosaur age.
>
>Well, not 3.10 sec, actually 3 hours and 10 minutes :(
>And I did it with a i7 860 working with 8 threads!
>> What are the bench-marks with 60-80 digit composites
>> with GGNFS and ECM when the two factors are of equal
>> length in these composites.
>GGNFS is not the best to factor numbers with up to 100 >decimal digits, probably SIQS is better when factors >are about equal size and ECM can not find fast a factor >up to 30 to 35 digits
What does that mean in real time for just one computer
factoring floor(pi*(10^111))because when I see
8 threads does that mean you had 8 other processors
as help?
I like to experiment with different factoring methods
but to be quite honest a lot of these factoring
algorithms are way over my head.
Thanks for the info!
Dan
factorboy13
Since ggnfs+msieve allow to allocate CPUs and Threads to a job then i was running at full speed (near 100% CPU utilization).
My operating system is Windows 7 64-bit and have used the 64-bit binaries of the software.
A Pentium 4 3.0 would probably be much slower, at least 1 day to factor that number with the same software.
Pubkeybreaker
> I like to experiment with different factoring methods
> but to be quite honest a lot of these factoring
> algorithms are way over my head.
Ignorance is a curable disease.
Run, don't walk, and get a copy of:
Crandall & Pomerance, Prime Numbers, A computational Perspective.
Read it. It will teach you all about modern factoring methods.
It is an excellent book.
dan73
Thanks for the explanation.
The latest in hardware and software is surely
far beyond what I have.
That is about the time frame I came up with for a
pentium 4. Still a lot faster than 14 days for ECM.
Thanks,
Dan
dan73
>> but to be quite honest a lot of these factoring
>> algorithms are way over my head.
>Ignorance is a curable disease.
>Run, don't walk, and get a copy of:
>Crandall & Pomerance, Prime Numbers, A computational >Perspective.
>Read it. It will teach you all about modern factoring >methods.
>It is an excellent book.
Thanks!
Dan
Phil Carmody
> On Dec 1, 8:32�am, dan73 <fasttrac...@att.net> wrote:
> > I like to experiment with different factoring methods
> > but to be quite honest a lot of these factoring
> > algorithms are way over my head.
>
> Ignorance is a curable disease.
>
> Run, don't walk, and get a copy of:
>
> Crandall & Pomerance, Prime Numbers, A computational Perspective.
If, due to its popularity, it's checked out of your local library,
then Hans Riesel's Prime Numbers and Computer Methods for Factorisation
is almost as good. It doesn't cover as much as PNaCP, but the places
it falls short are not the ones that you will need to worry about until
you're familiar enough with the field to be able to resort to primary
source material rather than PNaCP.
> Read it. It will teach you all about modern factoring methods.
> It is an excellent book.
My above paragraph might appear to say the contrary, but it doesn't.
PNaCP is a stunning book. It was one of the books that needed to be
written.
Phil
--
Any true emperor never needs to wear clothes. -- Devany on r.a.s.f1
Tim Little
> i7 processors are quad-core but each core can run 2 threads. This
> makes it sort of eight-core.
Usually quite poorly, as there are plenty of internal bottlenecks
preventing full-speed execution of two threads. It's probably more
like 4.5 cores in the best case, but could even be less than 4 as
hyperthreading tends to evict cache faster and can stall both threads
more often.
- Tim
factorboy13
> wrote:
>
> Usually quite poorly, as there are plenty of internal
> bottlenecks
> preventing full-speed execution of two threads. It's
> probably more
> like 4.5 cores in the best case, but could even be
> less than 4 as
Well, I run factorization tests both on it and on an old Core2 2600 (2 cores/2threads) and the I7 (4cores/8threads) is more than 3x faster.
Also ran factorizations with a dual CPU Xeon 3.0 that does hiperthreading (then 4 threads), but this one is much slower than the Core2, probably the sole reason is that it running 32-bit binaries (cannot support 64-bit OS).
I can only be happy with the i7
Tim Little
> Well, I run factorization tests both on it and on an old Core2 2600
> (2 cores/2threads) and the I7 (4cores/8threads) is more than 3x
> faster. Also ran factorizations with a dual CPU Xeon 3.0 that does
> hiperthreading (then 4 threads), but this one is much slower than
> the Core2, probably the sole reason is that it running 32-bit
> binaries (cannot support 64-bit OS). I can only be happy with the i7
I'm not trying to imply that the i7 is poor, just that use of its
hyperthreading capability has mixed performance impact depending upon
type of workload and fine details of algorithm implementation. The
appropriate comparison is to see how the same i7 performs with
hyperthreading turned on, vs turned off.
- Tim
factorboy13
I have not made any test with HT disabled.
With the HT enabled what I see is that CPU utilization is proporcional to the number of threads in use. For example if I run a single-threaded console application CPU utilization is about 12.5% and for every instance I add CPU utilization increases by another 12.5%. When 8 applications like that are running at full spead CPU utilization is near 100%.
I really don't know if each application was going to run at more than double speed if I was going to run with HT disabled. Probably i will have to make a test sometime.