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2008-02-26, 17:06   #166
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by davieddy To get back on topic, if we take for granted the accuracy of "expected number of Mersenne primes" (=m) within a specified range of exponents, is it not true that the probaility of finding x primes within that range is given very precisely by the Poisson distribution: P(x)=e^(-m)*m^x/x!
It is *conjectured* that they are Poisson distributed. There is no proof.

And we can NOT "take for granted the accuracy". The conjectures
about the distribution of M_p *ONLY* apply as p-->oo. We have
no idea how accurate estimates might be for ranges now being studied.
Do not use words like "very precisely" when dealing with ASYMPTOTIC
estimates as applied to small numbers.

2008-02-27, 05:38   #167
jasong

"Jason Goatcher"
Mar 2005

3·7·167 Posts

Quote:
 Originally Posted by retina So which is it? I didn't see anywhere that you mention it being a "gross approximation". You suddenly pull that out from nowhere hoping we all won't notice? "Fairly close" != 'gross approximation". BTW: is the method purely a linear or exponential speed up? If it is only linear then it's affect will be limited, and we still wouldn't be seeing 100M digit primes very soon. What is the time complexity (that's the 'Big O' thing)? Simply stating X number of times speed up gives no meaningful idea of how much improvement is really there.
I thought I mentioned in a post after the one you just quoted that it's closer to a minute for every day it takes now. So, taken literally, that would be a 1440 speedup. I'm not going to go back to check, but I intended to say that it's closer to a 1440 times speedup than a 10,000 or 1,000,000 time speedup.

Sorry I wasn't clearer.

Btw, the man in question hasn't been in irc for about 4 days according to my chat client. The pounce is still set up though. :)

Btw, to R.D. Silverman, nice to see your claws come out. :)

2008-02-28, 11:02   #168
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by R.D. Silverman It is *conjectured* that they are Poisson distributed. There is no proof. And we can NOT "take for granted the accuracy". The conjectures about the distribution of M_p *ONLY* apply as p-->oo. We have no idea how accurate estimates might be for ranges now being studied. Do not use words like "very precisely" when dealing with ASYMPTOTIC estimates as applied to small numbers.
What I wanted confirming was the applicability of the formula
given that the (small) probabilities involved are varying.
If justified, the formula helps interpret what "expected number
of primes" means in terms of predicting M45.

David

 2008-03-03, 01:38 #169 jasong     "Jason Goatcher" Mar 2005 350710 Posts Just heard from "the dude" now. He says the double-check will finish in the next few weeks, meaning it will almost certainly be finished in the next 3 weeks, probably no more than two weeks, and possibly in 1 week or less.
2008-03-03, 01:58   #170
jasong

"Jason Goatcher"
Mar 2005

3·7·167 Posts

from my friend:
Quote:
 07:44:48 PM) NAME WITHHELD: when you get back, please add that I read your post, and asked you to post, on my behalf, the number is being verified on 4 architectures with 4 different configurations and independent of existing X86 platforms to eliminate the potential for errors/false positive results.... Also the results (as I quoted 2 weeks) will complete the computation in a few days, but we are going to take a few more days to verify the output confirmation results, he (07:45:00 PM) NAME WITHHELD: you may quote this, except for my name. (07:46:09 PM) NAME WITHHELD: also, forgot to mention this has already passed human review of (4 of 5) so far, and waiting for the 5th to 'sign off' on the proof before submitting to all for public review and verification/validation. (07:51:56 PM) NAME WITHHELD: FWIW, the current method is valid to 'minimally' 100 megadigits. Some existing conjectures will fall and some will be fortified by this find. (07:54:39 PM) NAME WITHHELD: you may also add (and quote this).... @ 66 mhz iPod (yes, iPOD) fixed bit, montgomery math extended precision multiply technique is faster (at least 40x) than today's P4 machines at 2.4-2.8 Ghz. It does it because less data is moved OUTSIDE the L1 cache and registers of the CPU. And for iPod coders reference.... The ARM-7 is not the computational engine. (07:56:07 PM) NAME WITHHELD: the iPod Gen 5 is capable of 100 Mhz operation, but run @ 66 to synchronize with the HD and conserve power (as all know). Now, how was it done????? the answer is more simple than the letters FFT. :)

2008-03-06, 14:18   #171
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

22·11·97 Posts

Quote:
 Originally Posted by jasong from my friend:
Is he just pointing out that an iPod with his new idea is faster than LLR on P4, or is it only run on an iPod? If so, why can't it run on a x86? What about the iPod's architecture would make it so good for prime-finding? Does it play a musical tone relating to the number and see if it sounds prime?

 2008-03-06, 23:28 #172 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 96D16 Posts I had a dream last night that someone found M45. Too bad I woke up.
2008-03-24, 11:22   #173
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

22×11×97 Posts

Quote:
 Originally Posted by jasong Just heard from "the dude" now. He says the double-check will finish in the next few weeks, meaning it will almost certainly be finished in the next 3 weeks, probably no more than two weeks, and possibly in 1 week or less.
Quote:
 Originally Posted by jasong from my friend:
These indicate 3 weeks at the very most, and your friend seems to say a week or so. Is the double check complete yet? If so, what are the results? If not, what's the ETA for it finishing?

2008-03-29, 02:10   #174
nngs

Jun 2004

22×3×5 Posts

Quote:
 Originally Posted by Ethan (EO) ... The resulting chart is somewhat suggestive! There is fairly high power in periodicity around 1 cycle per 20 Mersennes, assuming we really know M40..M44. ...
This makes me to think to use more complicated function to
fit $\log_2(\log_2(M_{\rm n}))$ instead of the simple linear function used in http://primes.utm.edu/notes/faq/NextMersenne.html

I used a function like this:

$A+B\times n+C\sin(D\times n+E)$

and the best fit is:
A=1.0591955
B=0.55569804
C=0.62716836
D=0.29018205
E=-3.1763649

use this result to predict the next Mx exponent should be around
57971335,
the one sigma range of this prediction is
45441065 < Mx < 73956798

Attached figure shows all 44 known exponents with the best fit curve (dotted lines indicate the 1-sigma range)
Attached Thumbnails

Last fiddled with by nngs on 2008-03-29 at 02:16

2008-03-29, 03:08   #175
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

628610 Posts

Quote:
 Originally Posted by Mini-Geek These indicate 3 weeks at the very most, and your friend seems to say a week or so. Is the double check complete yet? If so, what are the results? If not, what's the ETA for it finishing?
I think it is clear that it is all a mistake. I'm sure we would have seen it in the news by now if it was successful.

2008-03-29, 03:13   #176
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

22×11×97 Posts

Quote:
 Originally Posted by retina I think it is clear that it is all a mistake. I'm sure we would have seen it in the news by now if it was successful.
Well, sure, but I'd like to hear a confirmed "no" than a "well, I haven't heard a 'yes' yet, so it's probably 'no'".

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