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#1 |
May 2005
22×11×37 Posts |
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(2^1127239+2^563620+1)/5 is 3-PRP!, which AFAIK is the largest GQ so far
![]() The question I have now is, how to prove it is, or it is not a prime ![]() BTW: I don't consider using PRIMO or other ECPP based software for this purpose as it would take more than my life to complete ![]() |
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#2 |
Nov 2003
1110001001102 Posts |
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There is no way to prove it prime, AFAIK. Primo distributed version (not publicly available) takes months on 20k digit numbers, and yours has more than 300k digits!
What you can do is the following, all using pfgw: test that it's PRP in another 2-3 bases, for example in base 7 run: pfgw -b7 -q(2^1127239+2^563620+1)/5 as other two bases select a prime between 10 and 30 and one larger than 100. And finally run the "-tc" test pfgw -tc -q... it will do some extra tests to show that it is "Fermat and Lucas PRP". You can submit it to the list of largest PRPs maintained by Henri Lifchitz currently, it will be the largest one. Congratulations! ![]() |
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#4 |
Sep 2002
Database er0rr
24×281 Posts |
![]() ![]() However, congrats for finding, by far, the world's largest known "probable prime" ![]() Last fiddled with by paulunderwood on 2006-11-17 at 20:59 |
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#5 |
Sep 2002
Database er0rr
106208 Posts |
![]() ![]() Congrats for largest PRP is retracted by me ![]() Command: /home/caldwell/client/pfgw -tc -q"(2^1127239+2^563620+1)/5" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^1127239+2^563620+1)/5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(131072,20) to FFT(131072,19) Reduced from FFT(131072,19) to FFT(131072,18) 2254482 bit request FFT size=(131072,18) Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(131072,20) to FFT(131072,19) Reduced from FFT(131072,19) to FFT(131072,18) 2254482 bit request FFT size=(131072,18) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(131072,20) to FFT(131072,19) Reduced from FFT(131072,19) to FFT(131072,18) 2254490 bit request FFT size=(131072,18) (2^1127239+2^563620+1)/5 is composite (-1716.3205s+0.0000s) [Ellapsed time: 94132 seconds] |
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#6 |
Nov 2003
E2616 Posts |
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Sorry to hear that
![]() There are several possibilities: 1) It's really 3-PRP but composite. That's entirely possible and that's the reason to try several more bases, and show that it's 7-PRP, 13-PRP etc. Check some entries on the largest PRP list, for example Jean-Louis Charton [Congrats Jean!] who holds the record tested as many as 7 bases on 4^341233-3^341233 (205443 digits). 2) There is a bug in LLR. That's also possible because GQ feature is a new one, much less tested than the mean-stream k*2^n-1 one. 3) Your hardware problem. Therefore, please run "pfgw -q(2^1127239+2^563620+1)/5", base=3 implied, on a stable hardware, if it's PRP mistery solved, if not than more tests will be required to find out what really happened. BTW, the PRP test will take much less time than the tc test which took 26 hrs on a Top-5000 machine, not more than 3 hrs on a 3GHz P-4 I think. |
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#7 |
Sep 2002
Database er0rr
24·281 Posts |
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I confirmed Cruelty's 3-PRP with llr (for linux) and am now running PFGW PRP test with base 137, and then I will check with base-3 and maybe too I will test with PFGW -tc. But I am only using 3.4Ghz Pentium 4
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#8 |
May 2005
162810 Posts |
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Strange, I have tested it with PFGW to find that:
(2^1127239+2^563620+1)/5 is 3-PRP! (6992.4544s+0.0010s) (2^1127239+2^563620+1)/5 is 7-PRP! (22176.6766s+0.0022s) (2^1127239+2^563620+1)/5 is 13-PRP! (22235.2301s+0.0018s) I will run "-tc" command over weekend. |
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#9 |
Sep 2002
Database er0rr
449610 Posts |
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Cruelty, what version of PFGW did you uses? 1.2.0?
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#10 | |
Jun 2003
2·2,719 Posts |
![]() Quote:
![]() Last fiddled with by axn on 2006-11-18 at 07:27 |
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#11 | |
Sep 2002
Database er0rr
449610 Posts |
![]() Quote:
I reinstate my congratulations for Cruelty for the ~50% improvement of the PRP record (even though it was naughty of him to submit it to UTM without first verifying it as a prime.) Lastly, great work Jean and Citrix (and Jim and George!) ![]() Last fiddled with by paulunderwood on 2006-11-18 at 09:57 |
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