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Old 2015-03-09, 21:51   #89
wildrabbitt
 
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Default 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
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Old 2015-03-09, 21:53   #90
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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 non-Mersenne prime, but have no proofs yet are 99.999...999% sure to be prime.

Last fiddled with by paulunderwood on 2015-03-09 at 21:59
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Old 2015-03-10, 02:43   #91
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Thanks for that link. Great stuff.
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Old 2015-03-10, 03:04   #92
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Quote:
Originally Posted by paulunderwood View Post
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 non-Mersenne prime, but have no proofs yet are 99.999...999% sure to be prime.
By a nice coincidence, all three non-mersenne (primes/prps) are in the 13m bit (4m digit) range! Looks like there is a firewall there
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Old 2015-03-16, 17:07   #93
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Quote:
Originally Posted by axn View Post
By a nice coincidence, all three non-mersenne (primes/prps) are in the 13m bit (4m digit) range! Looks like there is a firewall there
Maybe a 4th now
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Old 2015-03-17, 22:16   #94
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Quote:
Originally Posted by paulunderwood View Post
Maybe a 4th now
Could this be a Seventeen or Bust find? Or would the BOINC project not qualify as a PrimeGrid undertaking?
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Old 2015-03-18, 03:00   #95
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Quote:
Originally Posted by philmoore View Post
Could this be a Seventeen or Bust find? Or would the BOINC project not qualify as a PrimeGrid undertaking?
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.
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Old 2015-03-19, 20:06   #96
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It turned out to be none of them -- a false alarm. However a "321" prime or Thabit number was found: 3*2^11731850-1 (3,531,640 decimal digits -- rank 12).
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Old 2015-03-19, 21:03   #97
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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.
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Old 2015-03-19, 21:32   #98
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I see your points. Getting matching residues on non-avx with the -a3 switch is crucial
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Old 2015-03-19, 21:46   #99
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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 N-1 (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 tie-breaker though is to run a 20-thread 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 2015-03-19 at 21:52
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