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-   -   (M48) NEW MERSENNE PRIME! LARGEST PRIME NUMBER DISCOVERED! (https://www.mersenneforum.org/showthread.php?t=17704)

Xyzzy 2013-01-26 16:13

[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. :smile:[/QUOTE]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.

ixfd64 2013-01-26 16:41

The chances of a false positive this time is almost nil. We all know Curtis Cooper [url=http://www.mersenneforum.org/showthread.php?t=10870]is never wrong[/url]. :smile:

aketilander 2013-01-26 18:29

[QUOTE=Xyzzy;325965]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.[/QUOTE]

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. :smile:

ixfd64 2013-01-26 18:49

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__
[/CODE]

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__
[/QUOTE]

How the (old) fake residues were generated is described [url=http://www.mersenneforum.org/showpost.php?p=139789&postcount=25]here[/url] and [url=http://www.hoegge.dk/mersenne/residue.txt]here[/url].

Let the sleuthing begin!

ewmayer 2013-01-26 19:14

[QUOTE=Prime95;325955]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).[/QUOTE]

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 @[spoiler]3328[/spoiler]K (= 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. :)

paulunderwood 2013-01-26 19:31

So it is about a week for a CPU based confirmation. How long for the GPU one?

Ralf Recker 2013-01-26 20:07

[QUOTE=ewmayer;325995]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. :)[/QUOTE]

Thanks for the update :smile:
[CODE]else if( p >= 58050001 && p <= 62850000) /* 3328K */[/CODE]

ATH 2013-01-26 20:21

[QUOTE=ixfd64;325994]Here are the most recent results from Curtis Cooper that were submitted before the purported prime was noticed[/QUOTE]

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=ewmayer;325995]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[/QUOTE]

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=Ralf Recker;326003]Thanks for the update :smile:
[CODE]else if( p >= 58050001 && p <= 62850000) /* 3328K */[/CODE][/QUOTE]

Is that the crossover for Mlucas? That means the exponent is < 58050000.

Ralf Recker 2013-01-26 20:40

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
[/CODE]

ewmayer 2013-01-26 20:42

[QUOTE=ATH;326004]Is that the crossover for Mlucas? That means the exponent is < 58050000.[/QUOTE]

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 F[sub]24[/sub] 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 */[/code]

=======================

On a separate note: Bad, wicked, naughty, evil [strike]Zoot[/strike] Serge! Whatever would your mother think?

Brian-E 2013-01-26 20:47

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!:smile:


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