Hello, again. As before, I'm replying to a bunch of different people. And I
have trouble thinking up decent subject lines as well. :-]
<<So, based on all of this, would there be some way write a program that used
these details to factor faster?>>
I don't think that elliptic curves are useful in the small trial factoring
that GIMPS does to weed out candidates, but I might be wrong.
<<OK. Then what about John Sweeney? Jason Kline? Crandall & Fagin?
How about the people that wrote factoring code?>>
Lucas's and Lehmer's heirs!
<<As others have noted, this is a big can of worms that's just
complicating things without really adding anything to the effort
itself.>>
Right on.
<<It's actually worse than this. I never intended to copyright any of
the code I distribute, in part because some of it is already covered
by copyright and/or patent for commercial purposes. Is trying to
claim the EFF prize a commercial purpose? Don't ask me; I'm not a
lawyer.>>
And it gets muckier. :-<
<<Just a quick note to praise the 'common-sense' posters on this list - I hope
we all know who they are - it's much appreciated when one of them puts a
stop to a thread which was getting way out of hand. Many thanks to STL for
this one... in particular>>
Thanks. :-)
****
>It's amazing what money will do to people. In
>a way, I almost wish that EFF had never come up with their prizes
I'll paraphrase another quote on this as well, "A *person* is intelligent.
*People* are irrational and dangerous". As individual human beings, we're
quite good at distinguishing what is important to us personally. The whole
EFF thing was supposedly to inspire advances in distributed computing - but
instead has encouraged mass mania and reduced the thing to a lottery. I'd
much rather the world factor the meager 200+ digits of 2^727-1, than find a
10M+ digit prime and fight over money. Isn't mathematics, science, human
knowledge in general above things such base and vile as money? Are we all
guilty of knowing the price of everything, but the value of nothing? Is
bigger necessarily better?
****
Mass mania is a very appropriate term. Or, rather, what _could_ happen if the
GIMPS project goes and sets up the very things I mentioned would be bad in my
last post/mail.
<<Otherwise, let's get some rationality in
here. We search on - and let's not let our areas of research and individual
interests be controlled by potential financial gain. Let's follow through
with STL's common-sense conclusions.
AND ABOVE ALL, LET'S KILL THIS THREAD.>> [Emphasis STL's]
Right on. Truer words were never spoken.
<<Well, the likelyhood that a failure occurs may be 1%, but the likelyhood
that a double check will not catch it is much lower. This is do to the
fact that (barring bugs), the likelyhood that the numbers produce the same
64-bit residue is very, very low. Probably somewhere between 2^-64 and
2^-128.>>
Ah, a product of my own brain drain. You're right, I stand corrected. So,
does the rate of needed triple-checks conform with what a 1% error rate per
test would indicate? (i.e. 1% * 1%, I think.)
<<Suppose the number you're testing is N. If we assume N is prime, then
quadratic reciprocity could be used to determine whether your base a is a
QNR. So pick your base a, do your test, which proves QNR and hence primality
(Proth's theorem basically states the Euler criterion for a QNR is necessary
*and* sufficient to prove primality). If you don't get what you expect from
the quadratic residue symbol, then it's composite. (Look up 'Kronecker
symbol' - basically, an excuse to use quadratic reciprocity whether or not
you know N is prime).>>
We need more talk like this (and maybe some that I understand better. :-D )
on the list and less of the evil thread.
<<what if they set some clear contractual conditions? Mumbo jumbo isn't
strictly needed. >>
My opinion is that anything legal/contractual is EVIL Jabibbian nonsense and
must be avoided at all costs.
<<No they won't, because the start-up marketing would be too difficult.
As
long as the GIMPS contractual terms are reasonable, there will be no
motivation
to compete.>>
"Marketing"? I wish that I never heard that word so much as spoken (typed?)
on this list.
****
> That would not be a good thing. It's amazing what money will do to people.
In
> a way, I almost wish that EFF had never come up with their prizes, so we
> could have avoided all of this unpleasantness.
what's unpleasant about speculative free speech?
****
The prize's effects are unpleasant. Not the rest of what EFF does.
<<points one and six seem contradictory.>>
We can't STOP the EFF from awarding money. But we can't and SHOULDN'T change
any way in which it's being done now, which includes dividing up money in
some Jabibbian manner. In my opinion, as long as _nothing_ changes with
what's being done now, GIMPS isn't really in danger. Jump-aheaders will not
be that much of a problem because testing that large will take a LONG time
with present computers - I think.
<<1) What is the approximate P-90 computing time to test for primality
for a 1, 10, 100 million (& 1 trillion!) digit Mersenne Primes?>>
Generally, a billion comes after 100 million, but I can't remember how the
British and other countries work with billions. And I don't think that many
people run P90s now for GIMPS.... I hope.
<<3) Assuming the continued (exponential?) growth of GIMPS, when will
GIMPS begin to assign work in each of these areas?>>
GIMPS's growth, sadly, doesn't _seem_ to be exponential, and the chart on
entropia.com STILL looks linear to me, though a parabolic curve is now fitted
to the data on the page. (A cubic curve would fit it even better, and a
quartic yet better! Fourier strikes again! Run for your lives!)
<<Of course I understand that there is a higher purpose to GIMPS than
the money - and that it would be better to "fill in the tables" of N
than just skip to the area that would yield prize money.>>
Yes.
<<I further suspect (perhaps someone agrees?) that GIMPS will run out of
steam when it starts reaching the values of N that might yield 10
million digit Mersenne primes... This is because the average home PC
will no longer be able to complete a primality test in a reasonable
amount of time.>>
Remember, computers seem to always be getting faster, and every once in a
while we get an algorithm improvement (much more sporadically than the
seemingly-dependable computer speed increases). Witness the steady
progression of 8086 - 80186 - 80286 - 80386 - 80486 - Pentium - Pentium Pro -
Pentium II - Pentium III.... When a large portion of GIMPSters are running
Intel McKinley 1.2GHz computers with 4GB of SLDRAM, testing a decamegadigit
Mersenne number will be a LOT quicker than on a pokey Pentium III 550Mhz.
<<Or perhaps people feel that home computers will catch up in power with
the added work of larger N's and won't be a problem in future years?>>
Moore's Law. Computers double in power approximately every 18 months. Has
worked for over a decade. Will _probably_ work for at least the next 5 years
and even up until 2020. At or around 2020, transistors hit the .01 micron
quantum limit, and "conventional" computing reaches its peak. Then, we break
out the Pentium XIV Quantum Computers, and proceed merrily on our way. :-)
Well, that's it. I don't think I need a summary this time. I think.
S.T.L.
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