20150309, 21:51  #89 
Jul 2014
3·149 Posts 
largest non Mersenne prime
Hi,
just wondering. Does anyone know what the largest known prime number is that isn't a Merseene prime? Would be nice to know. William 
20150309, 21:53  #90 
Sep 2002
Database er0rr
3,853 Posts 
http://primes.utm.edu/primes/lists/all.txt
http://www.primenumbers.net/prptop/prptop.php shows 2 PRPs that are bigger than the largest known nonMersenne prime, but have no proofs yet are 99.999...999% sure to be prime. Last fiddled with by paulunderwood on 20150309 at 21:59 
20150310, 02:43  #91 
Jul 2014
3×149 Posts 
Thanks for that link. Great stuff.

20150310, 03:04  #92  
Jun 2003
53·97 Posts 
Quote:


20150318, 03:00  #95 
Jun 2003
1415_{16} Posts 
Based on the size hints, it is either a Woodall, Prime Sierpinski or GF(20,b) (aka GFN short). In fact, based on the uncertainity in the wording, I am currently leaning towards GFN.

20150319, 20:06  #96 
Sep 2002
Database er0rr
3,853 Posts 
It turned out to be none of them  a false alarm. However a "321" prime or Thabit number was found: 3*2^117318501 (3,531,640 decimal digits  rank 12).

20150319, 21:03  #97 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×7×683 Posts 
I am not entirely convinced that this is definitely a false alarm. Presented evidence ("Two computers returned matching results with the same residue. That's enough to be considered conclusive" and I quote literally) is weak, but strangely consistent with the way the do their things (for example, they seem to insist on absolutely necessity to sieve twice with their left hand, and then run LLR only once with their right hand).
But it's theirs to throw away. So let them. They have not shown any tests similar to George's. At least Prime95, if being run twice, does provide additional evidence (there is a bit shift specifically implemented for that). They simply ran the same LLR test for the second time: but as you know, there is no shift, and the FFT size is likely the same; of course the result will be the same if the bug is in the code and not in hardware. I am much more worried that many primes because of the bug return two matching residues and are not even noticed ever on anyone's radar. That's what I am worried about. But am I worried about it enough to drop my day job and fix the code that I know only partially at best? Hmm, ...no. 
20150319, 21:32  #98 
Sep 2002
Database er0rr
3,853 Posts 
I see your points. Getting matching residues on nonavx with the a3 switch is crucial

20150319, 21:46  #99 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
255A_{16} Posts 
Don't I know it. ;)
With different test bases, too! ...but there's a catch: unlike with a PRP test, you cannot simply force PFGW to use another base for N1 (or N+1 as the case may be). You can though, if you know what you are doing and care to change the code and properly recompile the whole product (which sadly is not a walk in the park for a new user.) You can instruct LLR to use another "FermatBase" (that's the name of the parameter to change in llr.ini or from command line, but there's also FBase parameter; it's best to set both in llr.ini) The fastest tiebreaker though is to run a 20thread PRP test using Prime95 and use various PRPBase=... in prime.txt (if you have a 20 CPU comp). This quick validation method also is unaffected by the bug even at default FFT size and with AVX (don't ask me why*). _______________ *as a footnote: this is what makes debugging the bug difficult. George (rightly) says: there is no bug in my code  I can run your debug case just fine. Jean and Mark say the bug must be in the lib, because otherwise why does the test fail for both; both tools are written differently. I think the bug is on the interface somewhere between the lib and how LLR and PFGW are using it. Last fiddled with by Batalov on 20150319 at 21:52 
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