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Old 2013-01-26, 16:13   #34
Xyzzy
 
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Quote:
It would be very nice if the information about other work done on this new Mersenne prime exponent were not ereased from the database. I guess it would be nice for those who earlier did trial factoring on the exponent to notice this and get the feeling that they also contributed to the new discovery.
The Trolls are convinced they have the right exponent and have saved the relevant information. Or, they are smoking catnip again. Either way, the outcome will be interesting.
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Old 2013-01-26, 16:41   #35
ixfd64
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The chances of a false positive this time is almost nil. We all know Curtis Cooper is never wrong.
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Old 2013-01-26, 18:29   #36
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Quote:
Originally Posted by Xyzzy View Post
The Trolls are convinced they have the right exponent and have saved the relevant information. Or, they are smoking catnip again. Either way, the outcome will be interesting.
Thanks Xyzzy I am happy for that and looking forward to the publication of it as soon as the new Mersenne prime has been thoroughly confirmed and publically anounced.
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Old 2013-01-26, 18:49   #37
ixfd64
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Here are the most recent results from Curtis Cooper that were submitted before the purported prime was noticed:

Code:
curtisc              wd-102--03l      58917769  C        Jan 25 2013 11:38PM  71.1 130.8875  44DCF2B8559C18__
curtisc              jckl-4570        56183053  C        Jan 25 2013 11:03PM  44.6 119.0769  4A31AD9F0DDFF5__
curtisc              jckl-4591        59546191  C        Jan 25 2013 11:00PM  48.4 132.2835  CD350961C451D6__
curtisc              wcm220--03l      59061763  C        Jan 25 2013 10:45PM  65.1 131.2073  2FAD4B2069D2CF__
curtisc              wde2610-11l      49714487  C        Jan 25 2013 10:20PM  33.8  91.0742  321A0CF054A800__
curtisc              wde3107-17l      50137189  C        Jan 25 2013 10:12PM  41.8  91.8485  3AD1598A834E2C__
curtisc              wde2610-34l      59560279  C        Jan 25 2013  8:34PM  48.2 132.3148  1C873BE2C88102__
curtisc              jckl-4576        52055909  C        Jan 25 2013  8:02PM  38.8  99.7286  10E8BB5D808F74__
curtisc              jckl-ccd62l      56193461  C        Jan 25 2013  7:40PM  42.3 119.0989  6BB4AF9EFB70A6__
curtisc              wcm201--07l      60563023  C        Jan 25 2013  6:55PM  28.2 134.5424  3E018F00191A30__
curtisc              lov1130-22l      59135017  C        Jan 25 2013  6:11PM  53.9 131.3701  8C99457344B8E7__
curtisc              csc141-04s       58443731  C        Jan 25 2013  6:08PM  84.1 123.8682  E7C12B5A206607__
curtisc              grn016--17l      57161879  C        Jan 25 2013  5:53PM  48.4 121.1514  50639413919D04__
For the record, the previous fake residues were as follows:

Quote:
real M39: 13466917 0x5A4800136C936D__
real M40: 20996011 0xB6C80125A48000__
real M41: 24036583 0x7EC80125B6DB7E__
real M42: 25964951 0x7EC80136C8136C__
real M43: 30402457 0x92480137EC937F__
real M44: 32582657 0x663C8660956654__
real M45: 43112609 0x8691696D2BDA50__
real M46: 37156667 0x23F07D75BB426A__
real M47: 42643801 did not have a fake residue
fake M44: 29225803 0xB6C80136DB7FED__
fake M45: 20314069 0x5A480124936DA5__
fake M45: 43021553 0x1248125A492480__
fake M46: 32428427 0xB6C80137FEDB7E__
How the (old) fake residues were generated is described here and here.

Let the sleuthing begin!

Last fiddled with by ixfd64 on 2013-01-26 at 19:19
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Old 2013-01-26, 19:14   #38
ewmayer
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Quote:
Originally Posted by Prime95 View Post
I don't have the save file yet. Heck, the PC might be locked in some University Administrator's office until Monday morning. So, I'm letting flashjh start his CUDALucas run.

Ernst/Batalov are working on a multi-threaded Mlucas run.

Jeff Gilchrist has started a prime95 AVX run (the prime was found on an SSE2 Core2 machine).
Sergey, Mike (Xyzzy) and I were up late last night playing with our respective Mlucas builds and multithreaded timing tests. (Strictly SSE2 code in play). As I went to bed (not to be confused with "went to sleep", as I was far too wound up for that) around midnight, both were running at around 0.016 sec/iter, Sergey on 12 Xeon cores (scalability above 4-thread there was crap, but there were still modest speedups at 6 and 12 threads), Mike on 4 Sandy Bridge cores (where timings degraded above 4 threads). My SB quad is a tad slower than Mike's (0.020 sec), so I suggested to them to kick off separate verify runs.

Sergey continued to play with alternate (larger than default) FFT lengths and various thread counts this morning, and just a little while ago informed me he gets 0.011 sec/iter running @3328K (= 13*2^18 doubles) with 26 threads on a 32-core box. That is roughly what should be achievable using a mere 4 cores on Sandy/Ivy Bridge once the AVX code comes online, but for now we gotta run with what we got. :)

Last fiddled with by ewmayer on 2013-01-26 at 21:33 Reason: Wrap top sekrit stuff in der [spoiler] tags, ja
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Old 2013-01-26, 19:31   #39
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So it is about a week for a CPU based confirmation. How long for the GPU one?
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Old 2013-01-26, 20:07   #40
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Quote:
Originally Posted by ewmayer View Post
Sergey continued to play with alternate (larger than default) FFT lengths and various thread counts this morning, and just a little while ago informed me he gets 0.011 sec/iter running @3328K (= 13*2^18 doubles) with 26 threads on a 32-core box. That is roughly what should be achievable using a mere 4 cores on Sandy/Ivy Bridge once the AVX code comes online, but for now we gotta run with what we got. :)
Thanks for the update
Code:
else if( p >= 58050001 && p <= 62850000)    /* 3328K    */
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Old 2013-01-26, 20:21   #41
ATH
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Quote:
Originally Posted by ixfd64 View Post
Here are the most recent results from Curtis Cooper that were submitted before the purported prime was noticed
I already checked none of them follow the fake residue. The success popped up at midnight friday evening so should have been reported between 11pm and midnight. The fake residue haven't been used on primenet v5, I think the exponent is just hidden from all result lists :(


Quote:
Originally Posted by ewmayer View Post
Sergey continued to play with alternate (larger than default) FFT lengths and various thread counts this morning, and just a little while ago informed me he gets 0.011 sec/iter running @3328K
So FFT 3328K is larger than default which in Prime95 means the exponent is < ~ 61.2M where the crossover 3200K/3360K occurs (Prime95 doesn't seem to have 3328K). Crossovers are probably slightly different in Mlucas, I think the exponent is < 60M where most of the current work is done.

Quote:
Originally Posted by Ralf Recker View Post
Thanks for the update
Code:
else if( p >= 58050001 && p <= 62850000)    /* 3328K    */
Is that the crossover for Mlucas? That means the exponent is < 58050000.

Last fiddled with by ATH on 2013-01-26 at 20:25
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Old 2013-01-26, 20:40   #42
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That was taken from the (online) sources of v2.8x.

This is from the sources of v3.0x (comment at the end of get_fft_radices.c) (FFT size / maxP value)

Code:
  2816 K    53792328
  3072 K    58569855
  3328 K    63338470
  3584 K    68098867

Last fiddled with by Ralf Recker on 2013-01-26 at 20:43
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Old 2013-01-26, 20:42   #43
ewmayer
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Quote:
Originally Posted by ATH View Post
Is that the crossover for Mlucas? That means the exponent is < 58050000.
Not sure - it may be from an old version of my code, because my recent versions have used auto-computed thresholds based on the ROE model I developed in the F24 paper, which works very well for both Fermat and Mersenne-mod autoconvolution. My current code gives the exponent range for 3328 K as 58569855 - 63338470.
Code:
/*
For a given FFT length, estimate maximum exponent that can be tested.

This implements formula (8) in the F24 paper (Math Comp. 72 (243), pp.1555-1572,
December 2002) in order to estimate the maximum average wordsize for a given FFT length.
For roughly IEEE64-compliant arithmetic, an asymptotic constant of 0.6 (log2(C) in the
the paper, which recommends something around unity) seems to fit the observed data best.
*/
uint32 given_N_get_maxP(uint32 N)
{
	const double Bmant = 53;
	const double AsympConst = 0.6;
	const double ln2inv = 1.0/log(2.0);
	double ln_N, lnln_N, l2_N, lnl2_N, l2l2_N, lnlnln_N, l2lnln_N;
	double Wbits, maxExp2;

	ln_N     = log(1.0*N);
	lnln_N   = log(ln_N);
	l2_N     = ln2inv*ln_N;
	lnl2_N   = log(l2_N);
	l2l2_N   = ln2inv*lnl2_N;
	lnlnln_N = log(lnln_N);
	l2lnln_N = ln2inv*lnlnln_N;

	Wbits = 0.5*( Bmant - AsympConst - 0.5*(l2_N + l2l2_N) - 1.5*(l2lnln_N) );
	maxExp2 = Wbits*N;

	/* 3/10/05: Future versions will need to loosen this p < 2^32 restriction: */
	ASSERT(HERE, maxExp2 <= 1.0*0xffffffff,"given_N_get_maxP: maxExp2 <= 1.0*0xffffffff");
/*
	fprintf(stderr,"N = %8u K  maxP = %10u\n", N>>10, (uint32)maxExp2);
*/
	return (uint32)maxExp2;
}
/* Here a simple PARI 'script' to return maxExp for any desired

Bmant = 53.; AsympConst = 0.6; ln2inv = 1.0/log(2.0);
N = [enter FFT length in #doubles]
ln_N = log(1.0*N); lnln_N = log(ln_N); l2_N = ln2inv*ln_N; lnl2_N = log(l2_N); l2l2_N = ln2inv*lnl2_N; lnlnln_N = log(lnln_N); l2lnln_N = ln2inv*lnlnln_N;
Wbits = 0.5*( Bmant - AsympConst - 0.5*(l2_N + l2l2_N) - 1.5*(l2lnln_N) )
maxExp2 = Wbits*N */
=======================

On a separate note: Bad, wicked, naughty, evil Zoot Serge! Whatever would your mother think?
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Old 2013-01-26, 20:47   #44
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I've only just spotted this thread despite looking at the forum several times since it started. The title successfully put me off: I thought it was the crank thread in Misc. Math so I ignored it. Bet I'm not the only one who missed it for that reason.

Exciting stuff! This is what we're here for!
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