20061116, 21:57  #1 
May 2005
2^{3}·7·29 Posts 
(2^1127239+2^563620+1)/5 is 3PRP!, 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 
20061116, 22:59  #2 
Nov 2003
2·1,811 Posts 
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 23 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! 
20061117, 20:56  #4 
Sep 2002
Database er0rr
3×1,231 Posts 
Cruelty  and this goes for all who submit to the top5000 primes list  please check before your submissions to the top5000 primes that your numbers are indeed proven prime. Why did you submit it? Did you think some magic would happen?
However, congrats for finding, by far, the world's largest known "probable prime" Last fiddled with by paulunderwood on 20061117 at 20:59 
20061118, 01:11  #5 
Sep 2002
Database er0rr
3·1,231 Posts 
the number is composite: http://primes.utm.edu/primes/page.php?id=78860
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 [N1/N+1, BrillhartLehmerSelfridge] Running N1 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 N1 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] 
20061118, 02:58  #6 
Nov 2003
2×1,811 Posts 
Sorry to hear that
There are several possibilities: 1) It's really 3PRP but composite. That's entirely possible and that's the reason to try several more bases, and show that it's 7PRP, 13PRP etc. Check some entries on the largest PRP list, for example JeanLouis Charton [Congrats Jean!] who holds the record tested as many as 7 bases on 4^3412333^341233 (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 meanstream k*2^n1 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 Top5000 machine, not more than 3 hrs on a 3GHz P4 I think. 
20061118, 05:47  #7 
Sep 2002
Database er0rr
7155_{8} Posts 
I confirmed Cruelty's 3PRP with llr (for linux) and am now running PFGW PRP test with base 137, and then I will check with base3 and maybe too I will test with PFGW tc. But I am only using 3.4Ghz Pentium 4

20061118, 06:00  #8 
May 2005
2^{3}·7·29 Posts 
Strange, I have tested it with PFGW to find that:
(2^1127239+2^563620+1)/5 is 3PRP! (6992.4544s+0.0010s) (2^1127239+2^563620+1)/5 is 7PRP! (22176.6766s+0.0022s) (2^1127239+2^563620+1)/5 is 13PRP! (22235.2301s+0.0018s) I will run "tc" command over weekend. 
20061118, 06:14  #9 
Sep 2002
Database er0rr
111001101101_{2} Posts 
Cruelty, what version of PFGW did you uses? 1.2.0?

20061118, 07:27  #10  
Jun 2003
3×1,669 Posts 
Quote:
Last fiddled with by axn on 20061118 at 07:27 

20061118, 09:54  #11  
Sep 2002
Database er0rr
3693_{10} 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 20061118 at 09:57 
