mersenneforum.org > News Merry Christmas and a prime! (M50 related)
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2017-12-30, 22:10   #166
ATH
Einyen

Dec 2003
Denmark

3·17·59 Posts

MLucas 4608K FFT run has finished as well:

[Dec 30 21:52:55] M7xxxxxxx Iter# = 7xxxxxxx [100.00% complete] clocks = 00:01:40.200 [ 0.0030 sec/iter] Res64: 0000000000000000. AvgMaxErr = 0.013612168. MaxErr = 0.019531250.
M7xxxxxxx is a new MERSENNE PRIME!!!

Now we have verification using 4 different programs:
Prime95, gpuOwl, CUDALucas and MLucas

and using 3 different types of hardware:
Intel CPU, AMD Vega GPU, Titan Black GPU

and using 3 different FFT lengths:
4096K, 4320K, 4608K.

Quote:
 Originally Posted by Batalov I suppose you will get the s0 = 10 value as well, no doubt. As for s0 = 2/3, I am curious to learn if the Penultimate LL value is proven to be a simple function of p ...or only conjectured? Anyone?
I'm working on both the s0=10 and s0=2/3.

Last fiddled with by ATH on 2017-12-30 at 22:10

 2017-12-30, 22:15 #167 pacionet     Oct 2005 Italy 33910 Posts So ... how many other verifications left before the announcement ?
2017-12-30, 22:25   #168
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×3×1,543 Posts

Quote:
 Originally Posted by ATH I'm working on both the s0=10 and s0=2/3.
But the s0=2/3 pen.residue will be simply + if p%4==1 and - if p%4==3, won't it?

2017-12-30, 22:27   #169
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

9,187 Posts

Quote:
 Originally Posted by pacionet So ... how many other verifications left before the announcement ?
Because it is the weekend and the end of the year, I would say the announcement will be on Jan 2 or 3.

2017-12-30, 22:28   #170
chalsall
If I May

"Chris Halsall"
Sep 2002

100100101110102 Posts

Quote:
 Originally Posted by pacionet So ... how many other verifications left before the announcement ?
The new prime is now known to be true, with high confidence.

It is now up to George et al to decide on the timing (as is their right). Somewhere around 2018.01.03 is likely.

2017-12-30, 22:47   #171
ATH
Einyen

Dec 2003
Denmark

3·17·59 Posts

Quote:
 Originally Posted by Batalov But the s0=2/3 pen.residue will be simply + if p%4==1 and - if p%4==3, won't it?
I have not heard that conjecture / theorem, but it fits the data except for M3 = 2^5-1 = 31.

S0 = 2/3 (mod 31) = 11 (mod 31)
S1 = 26 (mod 31)
S2 = 23 (mod 31) = - 2^(p+1)/2
S3 = 0 (mod 31)

It seems like too much of a coincidence that it fits all the other 47 values for it not to be true....

Last fiddled with by ATH on 2017-12-30 at 22:51

 2017-12-30, 22:48 #172 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 22×587 Posts I seem to recall George saying that Tuesdays are best in terms of press exposure.
 2017-12-30, 22:50 #173 bgbeuning   Dec 2014 22×32×7 Posts Congrats everyone! Thanks to everyone on that 1023 long e-mail list who coordinate our efforts.
2017-12-30, 22:59   #174
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×3×1,543 Posts

Quote:
 Originally Posted by ATH I have not heard that conjecture / theorem, but it fits the data except for M3 = 2^5-1 = 31.
p=5 is a known, specifically listed, counterexample (I didn't mention it because we are talking about M"50"). This statement (with p!=5 in it) is there on the first page of the Jansen paper; I don't have the rest (the old link leads nowhere), that's why I was asking - does he end up proving it or not in his work.

P.S. Archive.org kept it! - https://web.archive.org/web/20160131.../PhDJansen.pdf

P.P.S. Yes, it is proven (S.Y. Gebre-Egziabher). No need to compute those for s0 = 2/3.

Last fiddled with by Batalov on 2017-12-30 at 23:36

2017-12-30, 23:11   #175
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

7×283 Posts

Quote:
 Originally Posted by Batalov P.S. Archive.org kept it! - https://web.archive.org/web/20160131.../PhDJansen.pdf

I hope you are aware that their crawls have been terminated probably by a robots.txt or something on this site.

2017-12-30, 23:12   #176
The Carnivore

Jun 2010

E516 Posts

Quote:
 Originally Posted by preda Congrats all! there was a rather surprisingly large hole between M48 at 57'885'161) and the [ex] M49 at 74'207'281.
As of today, M49 still appears to be M49, not M50. From what was posted in this thread, the exponent of the new Mersenne prime appears to be greater than 74207281.

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