Report top-5000 primes for all k<=1001

[Luminescence]

Added 135795 : 421*2^2324375-1 (699710 digits)

[gd_barnes]

Max found:
909*2^2056937-1 is prime

[kar_bon]

909*2^2056937-1 seems composite but verification status is PRP.

[gd_barnes]

Originally Posted by kar_bon

909*2^2056937-1 seems composite but verification status is PRP.

I just now double-checked it. LLR version 3.8.23 says otherwise:

909*2^2056937-1 is prime! (619203 decimal digits) Time : 1299.213 sec.

Max's machines have been quite stable. He just now found another prime and I also verified that it is prime. I'll report it in the next post.

The new top-5000 site appears to be wrong! They need to work on their verification process. It takes many hours for the tests to start, it takes too long to run the test (over an hour for this one), and now it outputs the wrong result.

Anyone else care to test this?

Edit: I just now used their "let us know if anything isn't working" process to Email them about the problem.

[gd_barnes]

Max found:
813*2^2060392-1 is prime

Double-checked by LLR 3.8.23.

[JeppeSN]

Originally Posted by gd_barnes

I just now double-checked it. LLR version 3.8.23 says otherwise:

909*2^2056937-1 is prime! (619203 decimal digits) Time : 1299.213 sec.

Max's machines have been quite stable. He just now found another prime and I also verified that it is prime. I'll report it in the next post.

The new top-5000 site appears to be wrong! They need to work on their verification process. It takes many hours for the tests to start, it takes too long to run the test (over an hour for this one), and now it outputs the wrong result.

Anyone else care to test this?

Edit: I just now used their "let us know if anything isn't working" process to Email them about the problem.

Could be a hardware glitch on the Digital Ocean cloud ressource used by the new t5k.org. The prime is most likely good. Administrators of t5k.org are aware and have up to now prevented the deletion of the entry.

Note that a proof of such c=-1 candidate with Lucas-Lehmer-Riesel does not allow Gerbicz checks to catch hardware glitches. So the best way to prove primality seems to be to repeat the run on several different reliable machines.

/JeppeSN

[gd_barnes]

Originally Posted by JeppeSN

Could be a hardware glitch on the Digital Ocean cloud ressource used by the new t5k.org. The prime is most likely good. Administrators of t5k.org are aware and have up to now prevented the deletion of the entry.

Note that a proof of such c=-1 candidate with Lucas-Lehmer-Riesel does not allow Gerbicz checks to catch hardware glitches. So the best way to prove primality seems to be to repeat the run on several different reliable machines.

/JeppeSN

Thanks for the update and info!

[odicin]

Originally Posted by gd_barnes

I just now double-checked it. LLR version 3.8.23 says otherwise:

909*2^2056937-1 is prime! (619203 decimal digits) Time : 1299.213 sec.

Anyone else care to test this?

I also verified it.

C:\prpnet\prpclient-4>cllr64.exe -v
LLR Program - Version 3.8.23, using Gwnum Library Version 29.8

C:\prpnet\prpclient-4>cllr64.exe -t4 -d -q"909*2^2056937-1"
Starting Lucas Lehmer Riesel prime test of 909*2^2056937-1
Using AVX FFT length 140K, Pass1=448, Pass2=320, clm=1, 4 threads
V1 = 3 ; Computing U0...done.
909*2^2056937-1 is prime! (619203 decimal digits) Time : 1001.568 sec.

Regards Odi

[Happy5214]

I ran it using my copy of PFGW (which appears to be the same version as T5K), and I got a bunch of round-off errors:

$ ./pfgw -tp -q"909*2^2056937-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 909*2^2056937-1 [N+1, Brillhart-Lehmer-Selfridge]                                    
Running N+1 test using discriminant 5, base 1+sqrt(5)                                    
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate                                    
Iteration: 18/2056948 ERROR: ROUND OFF 0.5>0.45                                    
(Test aborted, try again using the -a1 switch)                                    
Running N+1 test using discriminant 5, base 1+sqrt(5)                                    
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate                                    
Iteration: 19/2056948 ERROR: ROUND OFF 0.5>0.45                                    
(Test aborted, try again using the -a2 (or possibly -a0) switch)                                    
Running N+1 test using discriminant 5, base 1+sqrt(5)                                    
^C1: 909*2^2056937-1 5000/2056948 mro=0.5
Ctrl-C detected, shutting down the program.

I re-ran with -a2:

$ ./pfgw -tp -q"909*2^2056937-1" -a2
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 909*2^2056937-1 [N+1, Brillhart-Lehmer-Selfridge]                                    
Running N+1 test using discriminant 5, base 1+sqrt(5)                                    
909*2^2056937-1 is prime! (3940.2488s+0.0006s)

[JeppeSN]

The bad result on t5k.org is reproducible, so not a random hardware glitch.

Thought to be related to the version of GWNUM used, on hardware where the AVX-512 instructions are available.

If someone with some version of PFGW can test on AVX-512-capable hardware, with -tp -q"909*2^2056937-1" -V where the -V seems to give info about choices made by GWNUM.

/JeppeSN

[kruoli]

$ ./pfgw64 -tp -q"909*2^2056937-1" -V
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]

Primality testing 909*2^2056937-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 144K, Pass1=192, Pass2=768, clm=1 on 909*2^2056937-1
909*2^2056937-1 is prime! (1746.6204s+0.0004s)