Factoring paper is wrong
James Harris
had a dumb mistake in it, as in a key place while I properly had h_1
h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
how I got what looked to me like a spectacular result.
The error is non-fixable in terms of that approach.
The factoring method itself does work, but so far I haven't gotten it
to work well for decent bitlengths as so far at best it works for
bitlengths of 40 and under, so it's useless at this point for even
approaching RSA.
The problem is determining s, so at this point, my approach of using
surrogate factoring is just a curiousity.
James Harris
Uncle Al
>
> My apologies but the paper that I thought solved the factoring problem
> had a dumb mistake in it, as in a key place while I properly had h_1
> h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
> how I got what looked to me like a spectacular result.
>
> The error is non-fixable in terms of that approach.
Harris, you are an idiot. Here, do something more productive with
your time
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
oğin
Good James, you are being honest, which is better than many others! Keep
working at it though. You never know what might turn up...
Also, I am now sorry for my recent post where I was teasing you...
oğin
Michael Varney
"James Harris" <jst...@msn.com> wrote in message
news:3c65f87.04061...@posting.google.com...
> My apologies
Your apologies do not come close to making up for the shit you have
subjected sci.math for the last several years, Crackpot.
David Eather
Ditto.
MorituriMax
>> The problem is determining s...
>
> Good James, you are being honest, which is better than many others! Keep
> working at it though. You never know what might turn up...
If he were really honest he would have had several people proof read his paper
before he posted it.
Robert J. Kolker
MorituriMax wrote:
>
>
> If he were really honest he would have had several people proof read his paper
> before he posted it.
Has James -ever- been right?
Bob Kolker
>
>
Bryan Olson
> My apologies but the paper that I thought solved the factoring problem
> had a dumb mistake in it
[...]
> The factoring method itself does work, but so far I haven't gotten it
> to work well for decent bitlengths as so far at best it works for
> bitlengths of 40 and under, so it's useless at this point for even
> approaching RSA.
Specifically, in the special cases where the method has worked,
it was because reducing j to lowest terms stumbled across a
proper factor of m.
As I reported in sci.crypt, if one does *not* reduce j = b/a to
lowest terms, but simply leaves a = f2 - f1, then the two GCD's
at the end will always yield m, not a proper factor. (Proof
available upon request by anyone who's actually serious.)
--
--Bryan
Gary Shannon
"Uncle Al" <Uncl...@hate.spam.net> wrote in message
news:40CCEB63...@hate.spam.net...
> James Harris wrote:
> >
> > My apologies but the paper that I thought solved the factoring problem
> > had a dumb mistake in it, as in a key place while I properly had h_1
> > h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
> > how I got what looked to me like a spectacular result.
> >
> > The error is non-fixable in terms of that approach.
>
> Harris, you are an idiot. Here, do something more productive with
> your time
What could possibly be more productive than learning by doing.
I applaud Mr. Harris for his interest, effort, and honesty.
--gary
The Ghost In The Machine
<Uncl...@hate.spam.net>
wrote
on Sun, 13 Jun 2004 17:03:47 -0700
<40CCEB63...@hate.spam.net>:
> James Harris wrote:
>>
>> My apologies but the paper that I thought solved the factoring problem
>> had a dumb mistake in it, as in a key place while I properly had h_1
>> h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
>> how I got what looked to me like a spectacular result.
>>
>> The error is non-fixable in terms of that approach.
>
> Harris, you are an idiot. Here, do something more productive with
> your time
>
> http://www.kingstroker.com/
>
One of the few games that does *not* play well with a trackball... :-)
--
#191, ewi...@earthlink.net
It's still legal to go .sigless.
Sam Wormley
Xaonon
Shannon <ga...@fiziwig.com> teithant i thiw hin:
> "Uncle Al" <Uncl...@hate.spam.net> wrote in message
> news:40CCEB63...@hate.spam.net...
>
> > James Harris wrote:
> >
> > > My apologies but the paper that I thought solved the factoring problem
> > > had a dumb mistake in it, as in a key place while I properly had h_1
> > > h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
> > > how I got what looked to me like a spectacular result.
> > >
> > > The error is non-fixable in terms of that approach.
> >
> > Harris, you are an idiot. Here, do something more productive with
> > your time
>
> What could possibly be more productive than learning by doing.
Oh, Harris is full of doing. It's the learning part that seems to escape him.
--
Xaonon, EAC Chief of Mad Scientists and informal BAAWA, aa #1821, Kibo #: 1
http://xaonon.dyndns.org/ Guaranteed content-free since 1999. No refunds.
"Why should I perspire to death on the subway, when I could be flying around
in Dick Cheney's invisible nuclear helicopter or whatever?" -- mnftiu.cc
Joe Peschel
news:Tm7zc.26612$KL2....@fe2.texas.rr.com:
> If he were really honest he would have had several people proof read
> his paper before he posted it.
>
Proofreading the paper would have made little difference.
J
--
__________________________________________
When will Bush come to his senses?
Joe Peschel
D.O.E. SysWorks
http://members.aol.com/jpeschel/index.htm
__________________________________________
Michael Varney
"Gary Shannon" <ga...@fiziwig.com> wrote in message
news:d0a69e600e93e69d...@news.teranews.com...
You are a clueless idiot.
Douglas A. Gwyn
> If he were really honest he would have had several people proof read his paper
> before he posted it.
That's more a matter of maturity and wisdom than honesty.
Even acknowledged top-flight mathematicians have been
known to make errors. Peer review is an attempt to
catch ones that can readily be spotted by colleagues
(among other functions), and it seems to work fairly
well for that, but it doesn't catch them all. The most
famous example is probably Kempe's proof of the four-
color theorem.
Tim Smith
> What could possibly be more productive than learning by doing.
> I applaud Mr. Harris for his interest, effort, and honesty.
New in town?
--
--Tim Smith
Franz Heymann
problem
> had a dumb mistake in it,
As has every single contribution you have made on this topic over the
months.
Why don't you just go and count your toes instead?
Franz
José Carlos Santos
> Has James -ever- been right?
Sure he has! As when he wrote that he suffered from Narcissistic
Personality Disorder. :-)
Best regards,
Jose Carlos Santos
James Harris
> MorituriMax wrote:
> > If he were really honest he would have had several people proof read his paper
> > before he posted it.
>
> That's more a matter of maturity and wisdom than honesty.
It's also something I try to do.
I *did* send my paper to several mathematicians and tried to talk
about it with various people you might say are in my circle before I
started talking about it publicly.
No one pointed out the error though I don't blame them.
It was just such a silly, dumb error.
>
> Even acknowledged top-flight mathematicians have been
> known to make errors. Peer review is an attempt to
> catch ones that can readily be spotted by colleagues
> (among other functions), and it seems to work fairly
> well for that, but it doesn't catch them all. The most
> famous example is probably Kempe's proof of the four-
> color theorem.
The problem is that sometimes you just REALLY WANT SOMETHING to be
true, and you can convince yourself of things.
In looking back I find it hard to believe that some part of me didn't
know that I was screwing up and using h_1 h_2 = T instead of h_1 h_2 =
T^4, and there were other signs as well.
Still I prefer to talk out my ideas, which is why I end up on Usenet,
despite knowing its limitations and facing a HUGE amount of abuse.
I have few outlets where I can talk math. So it's my curse that
Usenet is one of them and so many on Usenet feel a need to work hard
against me.
There aren't a lot of mathematicians out there to just chat things up
with, for me, and when I come to Usenet...well, you can see what
happens.
Regardless of any of that there's NEVER any reason to hold on to a
false result in mathematics as it's just stupid and silly.
After all, the math will never change.
Mathematics is an absolute. What's true is true, and what's not is
not.
My apologies again for the error. The research in this area continues
though at this point there's not a lot of progress.
It is a new way to factor, but so far it doesn't seem to be very
practical.
So, it seems, once again, I'm stuck doing "pure math", and once again,
you can see how mathematicians REALLY react to "pure math" when it
suits them.
Oh well.
James Harris
James Harris
> James Harris wrote:
>
> > My apologies but the paper that I thought solved the factoring problem
> > had a dumb mistake in it
> [...]
> > The factoring method itself does work, but so far I haven't gotten it
> > to work well for decent bitlengths as so far at best it works for
> > bitlengths of 40 and under, so it's useless at this point for even
> > approaching RSA.
>
> Specifically, in the special cases where the method has worked,
> it was because reducing j to lowest terms stumbled across a
> proper factor of m.
That's not true.
> As I reported in sci.crypt, if one does *not* reduce j = b/a to
> lowest terms, but simply leaves a = f2 - f1, then the two GCD's
> at the end will always yield m, not a proper factor. (Proof
> available upon request by anyone who's actually serious.)
You have a point there, but that's why the reduction is important.
The theory is just more complicated than you wish to give it credit
for, which I'm not surprised at seeing as yes, you're a Usenet poster.
The behavior is *extremely* complex at this point, and no one,
including myself, completely understands it.
Here's an example for you to test your ideas as I can factor
34699508649151
with this method.
So why don't you see what the probability is of just stumbling across
its two prime factors are and report back?
James Harris
Robert J. Kolker
Douglas A. Gwyn wrote:
>
> Even acknowledged top-flight mathematicians have been
> known to make errors. Peer review is an attempt to
> catch ones that can readily be spotted by colleagues
> (among other functions), and it seems to work fairly
> well for that, but it doesn't catch them all. The most
> famous example is probably Kempe's proof of the four-
> color theorem.
That was caught eventually. Some errors are very subtle.
Bob Kolker
>
Robert J. Kolker
James Harris wrote:
>
> 34699508649151
>
So what? Does it work for all numbers?
Bob Kolker
oğin
> Mathematics is an absolute. What's true is true, and what's not is
> not.
How do you know that? Do you have a proof that mathematics is an absolute?
I am guessing at what you mean by "absolute", but I figure that you are
wrong about that. For one thing, Gödel had some interesting proof that math
is not absolute (i.e. self contained systems of reasoning cannot be
perfect). Also, math is never absolute in another sense... it is always
relative to the axioms that you start with, which are arbitrary. Again, I am
guessing at what you mean by "absolute", but I figure that math has way too
much "relativity" and "arbitrariness" to agree with you.
Mok-Kong Shen
oðin wrote:
In a different vein, most 'proofs' are in one way or other
shortened/simplified for human reading and human errors
could happen (a post of Gwyn mentioned an example of an
error slipped through the scrutiny of professional reviewers).
One could employ software aids in the verification, I suppose.
But then the software itself would need verification and one
could thus get into a vicious circle, I am afraid.
M. K. Shen
Richard Tobin
Robert J. Kolker <robert...@hotmail.com> wrote:
>> 34699508649151
>
>So what? Does it work for all numbers?
You're missing James's point. Bryan Olson claimed that James's
algorithm only worked in cases with a particular property. James is
(if I understand correctly) claiming that 34699508649151 is a number
that he can factor that doesn't have that property.
-- Richard
Mok-Kong Shen
Sebastian Gottschalk wrote:
> oğin schrieb:
>
>>>After all, the math will never change.
>>
>>>Mathematics is an absolute. What's true is true, and what's not is
>>
>>>not.
>>
>>How do you know that? Do you have a proof that mathematics is an absolute?
>
> Well, it is absolute when reduced to a formulation in predicative logic,
> which itself is absolute in not taking any non-provable asumtations.
Maybe that depends on the semantics of the term 'absolute'.
He meant Goedel's imcompleteness result implies 'non-absoluteness'
(in his sense), I guess.
M. K. Shen
Wayne Brown
>
>
> What could possibly be more productive than learning by doing.
> I applaud Mr. Harris for his interest, effort, and honesty.
Did you notice that he originally presented his factoring "efforts"
by prefacing them with a prediction that mathematicians would try to
(dishonestly) discredit and suppress his results? Did you also notice
that his "honesty" in admitting he was wrong did *not* include even a
*hint* of an apology for that false accusation? (He apologized only for
being wrong about his factoring method, not for his accusations.) If he
remains true to his own history, he will forget all about being wrong
in this instance, and will bring this up in some future discussion as
an example of how "mainstream mathematicians" refused to accept his work.
--
Wayne Brown (HPCC #1104) | "When your tail's in a crack, you improvise
fwb...@bellsouth.net | if you're good enough. Otherwise you give
| your pelt to the trapper."
"e^(i*pi) = -1" -- Euler | -- John Myers Myers, "Silverlock"
Mok-Kong Shen
Sebastian Gottschalk wrote:
> Mok-Kong Shen schrieb:
>
>>Maybe that depends on the semantics of the term 'absolute'.
>>He meant Goedel's imcompleteness result implies 'non-absoluteness'
>>(in his sense), I guess.
>
> Maybe that depends that predicative logic cannot tell much about the
> semantics at all. Due to Goedel we also know that predicative logic with
> two- or more-term symbols is indeed incomplete. It all goes about the
> semantics, but I'm pretty sure there is no big probability that even a
> complete different kind of society will produce results that violate our
> very well believed results as for example the incompleteness results.
Well, the incompleteness theorem itself seems to be indeed
universally true and would in this sense be 'absolute', in fact.
M. K. Shen
MorituriMax
> Has James -ever- been right?
I could say, no, but then I might be being dishonest. Since I haven't kept
track of everything he has published. Heh..
James Harris
Here's some data which also shows that what I have is STILL a
curiousity, but at least the facts about my current curiousity can be
correct!
T=17349754321448
S=17349754327703
It took the program 3128 iterations to find that T and S.
Factors: 15077087, 2301473
S1()=15077087
S2()=2301473
Incoming is 34699508649151
Number of digits: 14
bitLength=45
Total time: 20999
And it took it nearly 21 seconds to show you how freaking slow the
damn thing still is!!!!!!!!!
The behavior resists explanation, and yes there is more than one S
that will work, as there's some pattern to the S's which is yet
another unknown.
James Harris
Chairman of the Ozzy Osbourne Appreciation Society
Sebastian Gottschalk wrote:
> Mok-Kong Shen schrieb:
>
>
>>Well, the incompleteness theorem itself seems to be indeed
>>universally true and would in this sense be 'absolute', in fact.
>
>
> What about formal independency? Everything which has been shown to be
> formally independent is obviously true to me, as the selection problem, the
> continuum hypothesis and the P-NP-problem is, where there's no evidence on
> counterexamples.
AFAIK the P=NP problem hasn't been determined to be independent of
ZFC?
> This is also very interesting because the continuum hyptothesis partially
> depends on predicative logic, at least the decision problem.
> (Proof is simple. If f is a function where s^f=w if s \iselem R, f
> otherwise, then f is an interpretation. Now reduce it to the Herbrand
> interpretation f', which has the same characteristics. As a herbrand
> interpretation f' is countable, but R is not, so such an f cannot exist.)
Douglas A. Gwyn
> ... Also, math is never absolute in another sense... it is always
> relative to the axioms that you start with, which are arbitrary.
That is one school of thought, but by no means the only one.
Brian Quincy Hutchings
do most "arbitrarily chosen numbers" have only two factors,
as opposed to being prime (or even more composited) ??
ric...@cogsci.ed.ac.uk (Richard Tobin) wrote in message news:<cakd67$2r8a$2...@pc-news.cogsci.ed.ac.uk>...
> (if I understand correctly) claiming that 34699508649151 is a number
> that he can factor that doesn't have that property.
--ils duces d'Enron!
http://tarpley.net/bush7.htm
Dik T. Winter
(about 34699508649151)
> how did he happen to choose that number?...
> do most "arbitrarily chosen numbers" have only two factors,
> as opposed to being prime (or even more composited) ??
Most numbers are composite with more than two factors, so I have no idea
how he came at that number. Perhaps he started with two primes and
multiplied them together. However, JSH already mentioned that his method
ws horribly slow. 20 seconds on that number. Straight-forward trial
division by odd numbers gives the factors in 0.40 seconds on the (not so
very fast) machine I am using.
About 25 years ago I already found that for numbers of less than 48
bits trial division was comparable in speed or better than other methods.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Douglas A. Gwyn
> Most numbers are composite with more than two factors, ...
This reminds me that this thread got me thinking about
just how much information is embodied in the knowledge
that a given 1000-bit (for example) positive integer
has precisely two prime factors, assuming that nothing
else is known about the number a priori. Or we could
be more specific and say that we know that each prime
factor has 500 bits, which is even more information.
(There is a slight complication in that case, because
not all products of 500-bit numbers has a 1000-bit
result.) We know that the chance of a random integer
N being prime is about 1/ln(N), but that doesn't seem
to help answer the question.
It would be interesting if that information amounts
to something like 100 bits..
Gib Bogle
Tom Potter
> h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
> how I got what looked to me like a spectacular result.
>
> The error is non-fixable in terms of that approach.
>
> The factoring method itself does work, but so far I haven't gotten it
> to work well for decent bitlengths as so far at best it works for
> bitlengths of 40 and under, so it's useless at this point for even
> approaching RSA.
>
> surrogate factoring is just a curiousity.
It looks like James Harris
wants to keep all the RSA money for himself.
--
Tom Potter http://home.earthlink.net/~tdp
Bryan Olson
> Bryan Olson schrieb:
>
>
>>As I reported in sci.crypt, if one does *not* reduce j = b/a to
>>lowest terms, but simply leaves a = f2 - f1, then the two GCD's
>>at the end will always yield m, not a proper factor. (Proof
>>available upon request by anyone who's actually serious.)
>
> No, as with my example given you get gcf(b+k,M)=factor of M and
> gcd(b-k,M)=M, so your proof must also be wrong.
Ah, right. My assertion is true for one square root but not the
other.
Are gcf(b+k,M) and gcd(b-k,M)=M really what Harris uses? I see
where he takes
gcf(M, b +/- sqrt(b^2 + a^2(s^2 - T^2)))
Does k reduce to the square root part?
> I'm more interested in the cases where you actually reduce j=b/a and
still
> just getting M - because the reduction step just takes polynomial
time and
> wouldn't prove it wrong in terms of running time.
Given M, let:
u * v be the factorization of record for T;
g be gcf(a, b), or whatever we divide out of (f1^4 - f2^4) to get 'a',
the denominator of j.
Then according to my algebra, and my reading of Harris, the
gcf's at the end are:
gcf(M, (uv + s) (u^2 - v^2)^2 / g)
gcf(M, (uv - s) (u^2 + v^2)^2 / g)
In the former, (uv + s) *is* M, so the gcf can be a proper
factor of M only if g is not relatively prime to M. Given how g
is derived, we might as well check whether GCD(M, u^4 - v^4) is
a proper factor, then forget the first gcf and g.
In the latter, (uv - s) and (u^2 + v^2) could share a proper
factor with M, but since u and v are, at this point, arbitrary,
the terms have no more chance of sharing a proper factor with M
than any other arbitrarily chosen integers.
I therefore think the following scheme dominates Harris's
method:
Given an integer M, choose two integers u and v.
Check whether any of:
GCD(M, u^4 - v^4),
GCD(M, 2uv - M),
GCD(M, u^2 + v^2),
is strictly between 1 and M. If so, return such a GCD as a
factor, otherwise report failure for this choice of
parameters.
Possibly I have misunderstood Harris's method, or made a math
error. I'd be interested to see a worked-through example where
Harris's method works and my version does not (well, interested
enough to check it).
If the scheme above does work whenever Harris's method works
with corresponding parameters, please do not name it after me.
--
--Bryan
Gary Shannon
Intriguing thought. But I suspect all we know from this information is that
we don't need to try divisors smaller than some limit. That's not really
much help.
--gary
Bryan Olson
> You have a point there, but that's why the reduction is important.
>
> The theory is just more complicated than you wish to give it credit
> for, which I'm not surprised at seeing as yes, you're a Usenet poster.
>
> The behavior is *extremely* complex at this point, and no one,
> including myself, completely understands it.
See my reply to Sebastian Gottschalk, less than an hour ago; it
might complete the theory.
> Here's an example for you to test your ideas as I can factor
>
> 34699508649151
>
> with this method.
>
> So why don't you see what the probability is of just stumbling across
> its two prime factors are and report back?
Obviously 34699508649151 is trivial to factor, but I see you
already spent 21 machine seconds to find them with your method.
If you'll tell me what a and b you used, and how you got the
final working GCD, I'll see if my theory corresponds to your
method.
--
--Bryan
Bryan Olson
> You're missing James's point. Bryan Olson claimed that James's
> algorithm only worked in cases with a particular property. James is
> (if I understand correctly) claiming that 34699508649151 is a number
> that he can factor that doesn't have that property.
Fair enough. I did miss that I had only considered one of the
two chances James Harris's algorithm has to factor M. I believe
I've corrected that in my latest follow-up to Sebastian
Gottschalk.
I've not confirmed the properties of this new example. I need
to see the rest of the parameters, and preferably the method
worked out.
Possibly I mis-read the method, and possibly I made a mistake in
my math. If so, I'll correct my work again. For now I believe
that the method amounts to checking the GCD of M with some
arbitrary integers.
--
--Bryan
Simon Johnson
> My apologies but the paper that I thought solved the factoring problem
> had a dumb mistake in it
I'll invoke the fundamental theorem of mathematicians:
"The quality of a mathematician is inversely proportional to the
number of incorrect proofs they produce."
That makes you decidably amateur. Not that that's a bad thing. I'm an
amateur but don't have delusions of grandeur. You lack the requisite
skill to create an efficient factoring algorithm.
There are only a handful of people in the world with the knowledge to
significantly advance the state of the art and you're not one of them.
Simon.
Aatu Koskensilta
> What about formal independency? Everything which has been shown to be
> formally independent is obviously true to me, as the selection problem, the
> continuum hypothesis and the P-NP-problem is, where there's no evidence on
> counterexamples.
The inconsistency of ZFC is independent of ZFC (assuming it's
consistent). Do you think ZFC is obviously inconsistent?
--
Aatu Koskensilta (aatu.kos...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Peter Fairbrother
trying to say. I wasn't willing to spend the time to sort it out. It wasn't
presented like the usual paper - perhaps you should read some papers, and
imitate their style next time. Try to write a paper on something a bit more
ordinary as well.
Research it. Write it, rewrite it, revise it, research the details that came
up and rewrite it again. You want to make your explanation as simple and
clear as you can. I usually rewrite/revise a paper at least 5 times before I
ask anyone to look at it, another 10 times before submission, and then
another 5 or so times before it is presented and published. That's about 20
revisions/rewrites per paper, at least 5 will be full rewrites. YMMV, but
that is what I do.
Explain what you are doing, and how it works, in English. You will probably
need to put your result in equations as well, so people can use the
equations to resolve any ambiguities in the English version, and use the
notation to discuss points, but even the best mathematicians will usually
skip over the equations at first reading, looking for an explanation in
English.
Keep the math to a minimum. Use the most generally accepted notation in your
field, do not invent new notation. Ever. On pain of death.
Make sure the grammar and spelling is correct. If I have two papers of
similar apparent worth and only time to read or space to publish one, the
one with good grammar and spelling will get read or published. The other
will get left on a train or rejected.
Making sure it is as correct and well-explained as you can before asking
people to read it is only polite. We are busy people, and we do not have
time to read everything in detail, especially if it is not clearly
explained.
Plus, note that we are people too. If you are impolite to us, we will ignore
you and diss you and publicly or privately floccinaucinihilipilificate your
work just because you were rude. Real people do things like that.
Many of us are geniuses, so don't try throwing your genius at us - genius is
expected, it doesn't impress. Be polite, and do it in the accepted way. That
impresses. Not a lot, but we are hard to impress at all.
To be more accurate, it soothes us, and makes us think the author might know
what he is talking about. We are busy, and quite capable of discarding a
paper unread if something about it annoys us or if we suspect it is garbage.
When properly gruntled, we read with a kindlier and more accepting eye.
In crypto, LaTeX with Springer styles is the most gruntling look, and it
changes over time so you can date a paper just by it's look. Which is nice.
It's a free download or two, and a day or two learning to use it, although
no matter how good you get at LaTeX someone will always kindly point out
that you could have done it in a better way.
A quick post telling us that you have done something is all that is needed
to let people here know. Excessive raving on about how good your paper turns
people off, and makes them less likely to read your papers in a soothed
state.
Also, if you get a reputation for excessive raving, people will not read
your next papers at all.
--
Peter Fairbrother
James Harris wrote:
> My apologies but the paper that I thought solved the factoring problem
> had a dumb mistake in it, as in a key place while I properly had h_1
> h_2 = T^4, in my derivation I was actually using h_1 h_2 = T, which is
> how I got what looked to me like a spectacular result.
>
> The error is non-fixable in terms of that approach.
>
> The factoring method itself does work, but so far I haven't gotten it
> to work well for decent bitlengths as so far at best it works for
> bitlengths of 40 and under, so it's useless at this point for even
> approaching RSA.
>
> The problem is determining s, so at this point, my approach of using
> surrogate factoring is just a curiousity.
>
>
> James Harris
James Harris
Why act like it's some major freaking conspiracy? I multiply together
primes and then see how the factorization works with them!
There is something really, truly wrong with you people.
I've seen it time and time again over a period of years where some of
you will work very hard to shadow a particular person and use
insinuation, innuendo and anything else you can to always push the
idea that they are just wrong.
There was someone who posted in one of thse threads asking if I ever
had anything right!!!
Yet I have my prime counting function which was smeared but at least
no one can say it doesn't work, but wait! There was a Usenet poster
who went on and on for a while claiming it didn't!!!
There's something wrong with you people on Usenet.
And you don't even care that if your behavior were rational you'd at
least wander away and do something else, as some of you have been
doing this for YEARS.
For years you have been shadowing my posts repeatedly posting in a way
clearly meant to try and distract other people from anything I'm
saying.
So now in testing out a factorization technique actually multiplying
prime numbers together and then seeing if it can factor them is so
strange.
Oh, and I *do* have a math paper that passed peer review, and when
word that it was to be published went out, what happened?
Usenet posters from sci.math harrassed the journal claiming it was
wrong by email, and the chief editor Ioannis Argyros personally yanked
it the NEXT DAY, and told me afterwards claiming that one of the
Usenet posters was a reviewer!!!
That paper is at ANOTHER JOURNAL YOU LOSERS and once again it is UNDER
PEER REVIEW and the journal it's at doesn't have a single weak editor
like Argyros that you rage filled people can bully.
And when that paper comes out then the trial of Usenet can really
begin, and when the regulations come down and the laws and when your
words here are used against you, I'm sure that there will be hollering
all over Usenet.
But you brought it on yourselves.
James Harris
Michael Varney
"Peter Fairbrother" <zenad...@zen.co.uk> wrote in message
news:BCF491EA.5080F%zenad...@zen.co.uk...
<SNIP>
>
> Also, if you get a reputation for excessive raving, people will not read
> your next papers at all.
Too late... by years.
Richard Tobin
Douglas A. Gwyn <DAG...@null.net> wrote:
>This reminds me that this thread got me thinking about
>just how much information is embodied in the knowledge
>that a given 1000-bit (for example) positive integer
>has precisely two prime factors, assuming that nothing
>else is known about the number a priori. Or we could
>be more specific and say that we know that each prime
>factor has 500 bits, which is even more information.
>(There is a slight complication in that case, because
>not all products of 500-bit numbers has a 1000-bit
>result.) We know that the chance of a random integer
>N being prime is about 1/ln(N), but that doesn't seem
>to help answer the question.
Well, there are 2^499 500-bit numbers. The chance of one being
prime is about 1/ln(1.5 * 2^498) = 1 / ln(1.5 * e ^ 345) =
1 / 345.5.
So there about 2^499 / 345.5 500-bit primes, and about 2^998 / 120,000
pairs of them. So there are about 2^(998-17) products of two 500-bit
primes.
These products are 998- and 999-bit numbers, of which there are about
2^999.
So knowing that a 998- or 999- bit number is the product of two
500-bit primes gives you about 18 bits of information.
-- Richard
Douglas A. Gwyn
> So there about 2^499 / 345.5 500-bit primes, and about 2^998 / 120,000
> pairs of them. So there are about 2^(998-17) products of two 500-bit
> primes.
Dividing by two since the order doesn't matter.
> So knowing that a 998- or 999- bit number is the product of two
> 500-bit primes gives you about 18 bits of information.
Thanks.
Richard Tobin
Douglas A. Gwyn <DAG...@null.net> wrote:
>Dividing by two since the order doesn't matter.
Oops, yes of course.
-- Richard
James Harris
Well now that everyone knows how simple it is...well humor aside, what
I have is a new way to factor which at this point appears to be a
curiosity.
In my method you use difference of squares but don't go looking for
perfect squares as you always have them, if you have the factorization
of a surrogate number I call T, and it's kind of odd in a way that it
ever works.
But it does sometimes work, and the open research question is, can it
be made to ALWAYS work, and if so, just like that it becomes the most
efficient factoring algorithm ever, despite your protestations or
delusions that it is all so simple.
Convincing yourself that you have the world figured out can be
comforting, but often the world decides to just do its own thing no
matter how cleverly you think you have it worked out:
> "The quality of a mathematician is inversely proportional to the
> number of incorrect proofs they produce."
That may seem like a perfect and beautiful rule to you, but to me that
makes you an amateur, unlikely to be able to adequately critique work
that challenges you, and shows you are narrowminded with a need to
simplify the world to a level where it's easy for you.
James Harris
Douglas A. Gwyn
> But it does sometimes work, and the open research question is, can it
Which is purely speculation at this point.
Of course, we know a simple factoring algorithm that
does always work in principle, but it's not practical
for large input.
Nobody was saying that efficient factoring was simple;
to the contrary, so far as we (yourself included)
actually *know*, it remains a hard problem.
Will Twentyman
> Well now that everyone knows how simple it is...well humor aside, what
> I have is a new way to factor which at this point appears to be a
> curiosity.
>
> In my method you use difference of squares but don't go looking for
> perfect squares as you always have them, if you have the factorization
> of a surrogate number I call T, and it's kind of odd in a way that it
> ever works.
A great many things work *sometimes*. That should not be impressive.
> But it does sometimes work, and the open research question is, can it
> be made to ALWAYS work, and if so, just like that it becomes the most
> efficient factoring algorithm ever, despite your protestations or
> delusions that it is all so simple.
If it always works, there will still be an issue as to whether it is
actually efficient, much less most efficient. Until you get the form
for which it always works, calculating its efficiency will be a bit
tricky. As it stands, I see no particular reason to believe it will be
significantly better than brute-force testing by division by odd integers.
> Convincing yourself that you have the world figured out can be
> comforting, but often the world decides to just do its own thing no
> matter how cleverly you think you have it worked out:
Convincing yourself should be inspiring. I don't really feel comfort
until someone else has looked over my results and confirmed them.
Otherwise, I could be overlooking something simple that destroys my result.
--
Will Twentyman
email: wtwentyman at copper dot net
gowan
<snip>
> That paper is at ANOTHER JOURNAL YOU LOSERS and once again it is UNDER
> PEER REVIEW and the journal it's at doesn't have a single weak editor
> like Argyros that you rage filled people can bully.
>
<snip>
The results in that paper are WRONG and that won't change just because
some journal publishes it. Merely publishing a paper in a peer
reviewed journal does not mean the results are correct or even worthy
of publication. Since the paper's results are incorrect, once it is
made known, any editor worth his salt would reject the paper. No
bullying necessary.
James Harris
Not exactly but I think you've given the fairest and most on-point
critique, yet.
I finally looked carefully at results where it does factor and noticed
that in every case the gcd found in a key place equals one of the
factors of M.
So basically I agree with you, and so I didn't come up with some grand
new way to factor. It was curious to play with for a while though.
I think I was just desperate after that paper of mine got yanked
because those sci.math assholes harassed the journal and intimidated
the chief editor, and I figured that I could get past them if only I
could come up with a dramatic result that no one could ignore.
My pure math results are too easy to fight, so I desperately tried to
find some way to break through, and ended up just convincing myself
something worked when it didn't.
Pure math is a sick joke. Mathematicians can and will ignore any
result they don't like, even if you manage to get it past peer review.
The "purer" it is, the more easily they ignore it.
My other work has been fought out over YEARS. It took YEARS before I
had that paper and the paper was at a journal for NINE MONTHS, but
sci.math posters destroyed my efforts in a couple of days, and no one
really cared.
I need to break something to get the world's attention. If I could
design a weapon or anything, something concrete. Pure math is a waste
of time.
You can't win with pure math. Mathematicians have a political game,
and you can't win with pure math.
It doesn't matter what you discover, how important it is, if it
doesn't come down to dollars and cents.
If practical matters are not involved mathematicians can and will
ignore your results, like they have with all of mine.
I'm impotent in the face of it, having foolishly dependend on a system
that can't be trusted, now stuck with only the hope of finding some
way, any way to force the world to notice what mathematicians have
done.
And here I failed. No new way to factor. Still no way out.
James Harris
Tom St Denis
>> Possibly I mis-read the method, and possibly I made a mistake in
>> my math. If so, I'll correct my work again. For now I believe
>> that the method amounts to checking the GCD of M with some
>> arbitrary integers.
>
> Not exactly but I think you've given the fairest and most on-point
> critique, yet.
>
> I finally looked carefully at results where it does factor and noticed
> that in every case the gcd found in a key place equals one of the
> factors of M.
>
> So basically I agree with you, and so I didn't come up with some grand
> new way to factor. It was curious to play with for a while though.
Ok. *Now* do you see why people scorn you for your "This is all trivial,
why haven't you solved this yet? My Math-fu is strong!" attitude?
Clearly you made a mistake. That isn't a big deal. Everyone makes
mistakes.
But please, please, learn from this instance. Be more humble. Be less
hostile and for the love of all that is holy on Earth use some modesty when
posting results.
By all means try to prove people wrong. Show that factoring is easy. I'd
personally love to see that result. Just go about it the right way.
Measure twice, post once [to borrow from an old saying].
Please reflect on what you have learned and good luck in your future
endeavours.
Tom
Douglas A. Gwyn
> Pure math is a sick joke. Mathematicians can and will ignore any
> result they don't like, even if you manage to get it past peer review.
> The "purer" it is, the more easily they ignore it.
I've followed "pure math" research for decades now, and
I don't think your comments are correct, except perhaps
in that mathematicians "don't like" incorrect results.
> You can't win with pure math. Mathematicians have a political game,
> and you can't win with pure math.
There are "politics" in all fields. What you have to
hope for is that truth will win out in the long run.
> It doesn't matter what you discover, how important it is, if it
> doesn't come down to dollars and cents.
There aren't many dollars and cents in pure math!
I suggest that you simply keep working on research
and keep trying to publish what you have *proven*
according to usual professional mathematical
standards. You may have to take time out to study
what those standards are before you can mimic them.
bubba
[snip]
> I need to break something to get the world's attention.
A counter example disproving Fermat's Last Theorem would do.
Rob Warnock
+---------------
| A great many things work *sometimes*. That should not be impressive.
(*cough*) Uh... Yes, indeed. Reminds me of the old joke about
an engineer "proving" that all odd numbers are prime:
"Let's see... 3 is prime, 5's prime, 7's prime, 9... we'll throw that
out due to experimental error, 11's prime, 13's prime. Looking good..."
-Rob
-----
Rob Warnock <rp...@rpw3.org>
627 26th Avenue <URL:http://rpw3.org/>
San Mateo, CA 94403 (650)572-2607
Douglas A. Gwyn
> (*cough*) Uh... Yes, indeed. Reminds me of the old joke ...
Or the skit in Manifold involving a math grad student
and his advisor trying to figure out if Goldbach-like
conjecture might be a theorem.
Tim Smith
>> If he were really honest he would have had several people proof read his
>> paper before he posted it.
>
> Has James -ever- been right?
Yes. His prime counting function seems to be correct.
--
--Tim Smith
David C. Ullrich
>[...]
>
>My pure math results are too easy to fight,
That's very curious. Nobody's ever had any success trying to
fight any of _my_ pure math results...
************************
David C. Ullrich
David Kastrup
> On 15 Jun 2004 17:53:38 -0700, jst...@msn.com (James Harris) wrote:
>
> >[...]
> >
> >My pure math results are too easy to fight,
>
> That's very curious. Nobody's ever had any success trying to
> fight any of _my_ pure math results...
Except when they were just able to swat them (typos, thinkos etc).
That is, the quality of your contributions is not unimodal. As a
result, there would be little temptation for you to argue something
from one mode into the other: much too high threshold. A quantum
barrier not easy to tunnel.
James is unimodal, so arguing has much more value for him.
You know the famous put-down from Pauli to some findings or whatever
he had looked over?
"This is not right. It is not even wrong."
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
David C. Ullrich
>David C. Ullrich <ull...@math.okstate.edu> writes:
>
>> On 15 Jun 2004 17:53:38 -0700, jst...@msn.com (James Harris) wrote:
>>
>> >[...]
>> >
>> >My pure math results are too easy to fight,
>>
>> That's very curious. Nobody's ever had any success trying to
>> fight any of _my_ pure math results...
>
>Except when they were just able to swat them (typos, thinkos etc).
Well, right, if we're talking about usenet posts - I wouldn't
call the posts I make here "my results", I was referring to
the things that I've actually discovered and published.
>That is, the quality of your contributions is not unimodal. As a
>result, there would be little temptation for you to argue something
>from one mode into the other: much too high threshold. A quantum
>barrier not easy to tunnel.
>
>James is unimodal, so arguing has much more value for him.
>
>You know the famous put-down from Pauli to some findings or whatever
>he had looked over?
>
>"This is not right. It is not even wrong."
Heh.
************************
David C. Ullrich
The Ghost In The Machine
<reply_i...@mouse-potato.com>
wrote
on Wed, 16 Jun 2004 09:01:17 GMT
<x%Tzc.880$bs4...@newsread3.news.atl.earthlink.net>:
It was correct. Slow, but correct.
<plug mode="blatant">
http://home.earthlink.net/~ewill3/math/primecounters/index.html
</plug>
--
#191, ewi...@earthlink.net
It's still legal to go .sigless.
Daryl McCullough
polynomials.
James Harris
No one cares about your results Ullrich. Why don't you name them and
see?
I'm fighting a dedicated cabal of sci.math posters, some of whom are
mathematicians like Ullrich, who you can see make it their business to
track my postings and keep up a propaganda attack.
My paper faced a coordinated assault from these people.
No sane person would expect that simple dislike or animosity could
drive so many people!
Use your brains. This is far beyond just some posters after some
"crank" or "crackpot" and these people are playing for keeps. Use
your brains.
James Harris
Tim Smith
wrote:
> It was correct. Slow, but correct.
Note that being slow doesn't necessarily mean that it is useless.
A slow formula--so slow that it is completely worthless for anyone who
actually needs to count primes up to a specific number--could still be of
great use if it is in a form that makes theoretical analysis easier.
--
--Tim Smith
Will Twentyman
> David C. Ullrich <ull...@math.okstate.edu> wrote in message news:<vt80d0h1kbqn4t0nt...@4ax.com>...
>
>>On 15 Jun 2004 17:53:38 -0700, jst...@msn.com (James Harris) wrote:
>>
>>
>>>[...]
>>>
>>>My pure math results are too easy to fight,
>>
>>That's very curious. Nobody's ever had any success trying to
>>fight any of _my_ pure math results...
>>
>>************************
>>
>>David C. Ullrich
>
> No one cares about your results Ullrich. Why don't you name them and
> see?
I suspect his work on Harmonic Functions is of great interest to a
number of people.
Uncle Al
How many slide rules do you see around these days? Better is the
eternal lethal enemy of merely OK.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
oğin
> > A slow formula--so slow that it is completely worthless for anyone who
> > actually needs to count primes up to a specific number--could still be
of
> > great use if it is in a form that makes theoretical analysis easier.
>
> How many slide rules do you see around these days? Better is the
> eternal lethal enemy of merely OK.
You missed the point.
For example taylor series are slow to converge, and are thus not used in
calculating trig functions in calculators. But, taylor series make many
proofs simple.
Michael Varney
"James Harris" <jst...@msn.com> wrote in message
news:3c65f87.04061...@posting.google.com...
Hey Harris, remember when you tried to get me fired from NIST? Do you
recall attempting to get various people in trouble with their employers,
David included?
Quit whining about having your crap paper attacked... you have done far
worse.
David C. Ullrich
>David C. Ullrich <ull...@math.okstate.edu> wrote in message news:<vt80d0h1kbqn4t0nt...@4ax.com>...
>> On 15 Jun 2004 17:53:38 -0700, jst...@msn.com (James Harris) wrote:
>>
>> >[...]
>> >
>> >My pure math results are too easy to fight,
>>
>> That's very curious. Nobody's ever had any success trying to
>> fight any of _my_ pure math results...
>>
>>
>>
>>
>> ************************
>>
>> David C. Ullrich
>
>No one cares about your results Ullrich. Why don't you name them and
>see?
I didn't _say_ anyone cared about my results! I said that nobody
had ever had any success in "fighting" them.
Why don't _you_ try to fight one of them? You can find references
to quite a few by finding a university library and looking for
my name in the index of Mathematical Reviews (probably looking
in the annual indexes from the 80's and early 90's would be best).
Here's one that hasn't been published yet - it's probably wrong,
since it hasn't "passed peer review": If X is a Besov space on the
line then either X contains a nowhere-differentiable function
or every function in X is locally absolutely continuous.
You can find a proof, or what I _think_ is a proof, at
http://www.math.okstate.edu/~ullrich/besov/nd.pdf
.
>I'm fighting a dedicated cabal of sci.math posters, some of whom are
>mathematicians like Ullrich, who you can see make it their business to
>track my postings and keep up a propaganda attack.
So fight back already. Explain to the world exactly what's wrong
with the proof in that pdf.
>My paper faced a coordinated assault from these people.
>
>No sane person would expect that simple dislike or animosity could
>drive so many people!
>
>Use your brains. This is far beyond just some posters after some
>"crank" or "crackpot" and these people are playing for keeps. Use
>your brains.
>
>
>James Harris
************************
David C. Ullrich
Randy Poe
> Will Twentyman <wtwen...@read.my.sig> wrote:
> +---------------
> | A great many things work *sometimes*. That should not be impressive.
> +---------------
>
> (*cough*) Uh... Yes, indeed. Reminds me of the old joke about
> an engineer "proving" that all odd numbers are prime:
>
> "Let's see... 3 is prime, 5's prime, 7's prime, 9... we'll throw that
> out due to experimental error, 11's prime, 13's prime. Looking good..."
No, no, that's the physicist's proof. The engineer's proof is:
3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime...
... yep, all odd numbers are prime.
- Randy
David Kastrup
And the computer scientist's was
1 is prime, 1 is prime, 1 is prime, 1 is prime...
Andrew Swallow
news:df76407e.04061...@posting.google.com...
3 is prime, 5 is prime, 7 is prime
11 prime, 17 prime, even bigger 113 prime
All test numbers were prime so yep, all odd numbers prime.
Andrew Swallow
James Harris
Really? Why?
James Harris
Will Twentyman
Because, if he is working with Harmonic Functions related to PDEs, they
could be useful in providing solutions to physics and engineering
problems. As I recall, electromagnetic waves and waves in fluids deal
with these, in particular. If his contributions have simplified the
formulas for these, or given the tools for extending their analysis, he
has provided the world with tools to extend our knowledge of the
physical sciences.
David, please correct me if I made an error in any of the above.
David Moran
Are you really that naive? I'd think Harmonic Functions would come up in
physics, which you claim to have a degree in (not sure if I believe that).
Dave
Brian Quincy Hutchings
why don't you?
you know, Ullrich teaches math at a university, and
they can be pretty snooty, but that doesn't mean that
you can just pretend that they're completely full of it.
you could just be televizing, dood!
anyway, I couldn't see the abstracts for those papers, but
i susppect I'd have a hard time of reading them.
jst...@msn.com (James Harris) wrote in message news:<3c65f87.04061...@posting.google.com>...
> > I suspect his work on Harmonic Functions is of great interest to a
> > number of people.
> >
> > http://www.aimath.org/library/library.cgi?database=reprints;mode=display;BrowseTitle=Ullrich,%20David%20C.
>
>
> Really? Why?
--Give Earth a Trickier Dick Cheeny -- out of office, after gigayears!
http://larouchepub.com/pr/2004/040505missouri_testim.html
http://larouchepub.com/other/2004/3107repeal_hava.html
http://larouchepub.com/pr/2004/040505MISSOURI_testim.html
http://larouchepub.com/lar/2004/3121cmpgn_v_racism.html
http://larouchepub.com/pr/2004/040505missouri_testim.html
http://larouchepub.com/other/2004/3104elect_voting.html
http://larouchepub.com/other/2003/3045dems_dive_SOROS.html
http://tarpley.net/bush12.htm
http://www.benfranklinbooks.com/
http://members.tripod.com/~american_almanac
http://www.wlym.com/pdf/iclc/HowTheNation.PDF
http://larouchepub.com/other/2003/3048iraq_58_const.html
http://www.rand.org/publications/randreview/issues/rr.12.00/
http://www.rwgrayprojects.com/synergetics/plates/figs/plate02.html
Dik T. Winter
> rp...@rpw3.org (Rob Warnock) wrote in message news:<vvadnU_K1qV...@speakeasy.net>...
> > an engineer "proving" that all odd numbers are prime:
> >
> > "Let's see... 3 is prime, 5's prime, 7's prime, 9... we'll throw that
> > out due to experimental error, 11's prime, 13's prime. Looking good..."
>
> No, no, that's the physicist's proof. The engineer's proof is:
>
> 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime...
> ... yep, all odd numbers are prime.
And the computer scientist:
3 is prime, 3 is prime, 3 is prime, ...
Oh, something got stuck, but all odd numbers are prime.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Jose Sanchez
> result they don't like, even if you manage to get it past peer review.
> The "purer" it is, the more easily they ignore it.
>
> My other work has been fought out over YEARS. It took YEARS before I
> had that paper and the paper was at a journal for NINE MONTHS, but
> sci.math posters destroyed my efforts in a couple of days, and no one
> really cared.
>
> I need to break something to get the world's attention. If I could
> design a weapon or anything, something concrete. Pure math is a waste
> of time.
>
> You can't win with pure math. Mathematicians have a political game,
> and you can't win with pure math.
>
> It doesn't matter what you discover, how important it is, if it
> doesn't come down to dollars and cents.
>
> If practical matters are not involved mathematicians can and will
> ignore your results, like they have with all of mine.
>
> I'm impotent in the face of it, having foolishly dependend on a system
> that can't be trusted, now stuck with only the hope of finding some
> way, any way to force the world to notice what mathematicians have
> done.
>
> And here I failed. No new way to factor. Still no way out.
>
>
> James Harris
Here you go:
.-. _,,,,,_ .-.
( , ' : : ' , )
/ : : \
; 0.---.0 ;
\ / _ \ /
\ | (_) | /
." `\ -'- /` ".
/ `"""""` \
/ .' .-== '. \
/ / .-=='\ \
( / \ )
'-;`. .';-'
/_ `-.______ .-` __\
/` `\ / `\ / `\
\ | / \ | /
`'--'` `'--'`
This is Teddy. Keep Teddy close at all times and everything will be alright!
No reason to cry and whine any more, now that you have your very own Teddy!
Jose
Stewart Robert Hinsley
<am.sw...@eatspam.btinternet.com> writes
>Not quite, an engineer would probably do it
> 3 is prime, 5 is prime, 7 is prime
> now try some bigger numbers
> 11 prime, 17 prime, even bigger 113 prime
>
>All test numbers were prime so yep, all odd numbers prime.
>
statistician's proof.
--
Stewart Robert Hinsley
James Harris
> Richard Tobin wrote:
> > You're missing James's point. Bryan Olson claimed that James's
> > algorithm only worked in cases with a particular property. James is
> > (if I understand correctly) claiming that 34699508649151 is a number
> > that he can factor that doesn't have that property.
>
> Fair enough. I did miss that I had only considered one of the
> two chances James Harris's algorithm has to factor M. I believe
> I've corrected that in my latest follow-up to Sebastian
> Gottschalk.
>
> I've not confirmed the properties of this new example. I need
> to see the rest of the parameters, and preferably the method
> worked out.
>
> Possibly I mis-read the method, and possibly I made a mistake in
> my math. If so, I'll correct my work again. For now I believe
> that the method amounts to checking the GCD of M with some
> arbitrary integers.
Yup. You were *exactly* right Bryan, and I want to thank you for
noticing that and for repeatedly pointing it out.
Thank you.
James Harris
Simon Johnson
> I have is a new way to factor which at this point appears to be a
> curiosity.
>
> In my method you use difference of squares but don't go looking for
> perfect squares as you always have them, if you have the factorization
> of a surrogate number I call T, and it's kind of odd in a way that it
> ever works.
> But it does sometimes work, and the open research question is, can it
> be made to ALWAYS work, and if so, just like that it becomes the most
> efficient factoring algorithm ever, despite your protestations or
> delusions that it is all so simple.
The algorithm might be simple but it's not efficient. I have a
"simple" algorithm for obtaining a factor of n.
1. Pick a random integer 'x' such that n>x>1.
2. Divide n by x and set y equal to the result.
3. If y is an integer then we have two factors. Halt.
4. Goto 1.
That algorithm has a best case complexity of exactly one iteration.
This algorithm always works it's just slow in the average case. Your
algorithm has shown to be quicker than this god awful design. I don't
think there's any conclusive result on how quick the algorithm is yet.
I expect it to be no quicker than pollard-rho.
> Convincing yourself that you have the world figured out can be
> comforting, but often the world decides to just do its own thing no
> matter how cleverly you think you have it worked out:
I believe nothing of the sort. I admire people who adopt the
scientific method if that's what you mean. You of all people know that
you can't have a half baked idea in mathematics. A single fault in a
single lemma of a complicated proof (as shown recently in the 'proof'
of the twin prime conjecture) can bring an entire approach crashing to
the ground.
The fact that you haven't even met the basic standard of presentation
of an idea for the standard peer review process for an idea that is
meant to be a revolution in it's field is what makes me pretty cynical
towards you.
There's no formal description of the algorithm. There's limited theory
as to why the algorithm should work. There's no average case time
estimate of the algorithm. You can't expect people to do the work for
you. The entry bar to the peer review process is quite demanding.
> > "The quality of a mathematician is inversely proportional to the
> > number of incorrect proofs they produce."
>
> That may seem like a perfect and beautiful rule to you, but to me that
> makes you an amateur, unlikely to be able to adequately critique work
> that challenges you, and shows you are narrowminded with a need to
> simplify the world to a level where it's easy for you.
It's not a theorem. There are counter examples but that's not the
point. It's beautiful in the sense that it that it sorts cranks from
mathematicians with high probability.
I like the fact you use amateur as some sort of slur on my character.
I quite enjoy being an amateur because it's nice to have cryptography
as a hobby. It's always there for me as a quiet retreat from the
hastle of every day life. It doesn't pay my bills and I wouldn't have
it any other way.
Most of that paragraph is true but the tone is all wrong. There's no
way I could peer-review a typical factoring paper so you're right in
that limited sense in that I can't "adequately critique" a work that
challenges me. What I don't see is how this makes me narrow-minded.
I'm aware of my limitations to make a statement in a particular field
and this is where you and I differ.
Frankly, that last line is a bit silly aswell. Any person's view of
the world is simplified to the level of the viewer. An attack on a
person for displaying that characteristic is baseless since it's an
attack on humanity itself.
Simon.
James Harris
Well, it turns out that he wasn't exactly correct, as the method I've
found works better than chance. It's not a random search.
James Harris
Bryan Olson
> James Harris wrote:
>
>>Bryan Olson wrote:
[...]
>>> For now I believe
>>>that the method amounts to checking the GCD of M with some
>>>arbitrary integers.
>>
>>Yup. You were *exactly* right Bryan, and I want to thank you for
>>noticing that and for repeatedly pointing it out.
>>
>>Thank you.
>
> Well, it turns out that he wasn't exactly correct, as the method I've
> found works better than chance. It's not a random search.
If you can show that in a theorem, it might gain some interest.
I find it hard to fathom, since there was no guidance at all on
choosing the parameters for any given number to be factored.
My own algebraic reductions suggested that the method might be
*worse* than random trial-GCD. Of the two integers with which
GCD might be tried, one had a square as a factor, and the other
required the common factor to be in both a numerator and a
denominator.
--
--Bryan