k=22544089918041953*E(130) generates 216 known primes - Page 4

Jean Penné · 2013-08-15, 19:09

Quote:

Originally Posted by Thomas11

What do you mean by "reliable"?

Due to the size of k we run a PRP test first instead of a more demanding primality test (Brillhart-Lehmer-Selfridge). For a positive PRP test the BLS test is done manually afterwards. If it turns out prime, then it should be as "reliable" as if it would have been done by any other primality testing software (like LLR, Proth, Prime95, even if the latter are unable to test those numbers).

It is not true that LLR cannot test these numbers : Indeed, it cannot process the input file in ABC format, but it can process it in Newpgen format (k*2^n-1 whith k fixed) with k as a digit string, not in factorized form :

1:M:1:2:2
1480472640274704456611717878515654164205 1
1480472640274704456611717878515654164205 2
1480472640274704456611717878515654164205 11
1480472640274704456611717878515654164205 14
1480472640274704456611717878515654164205 16
1480472640274704456611717878515654164205 36
....................................................................
....................................................................
1480472640274704456611717878515654164205 498496
1480472640274704456611717878515654164205 531133
1480472640274704456611717878515654164205 608207
1480472640274704456611717878515654164205 608462
1480472640274704456611717878515654164205 639888

I am presently verifying successfully your prime results with LLR
Regards,
Jean

Thomas11 · 2013-08-15, 19:37

Quote:

Originally Posted by Jean Penné

It is not true that LLR cannot test these numbers : Indeed, it cannot process the input file in ABC format, but it can process it in Newpgen format (k*2^n-1 whith k fixed) with k as a digit string, not in factorized form : ...

I am presently verifying successfully your prime results with LLR
Regards,
Jean

Thanks for this information, Jean! This is really good news!

Many years ago I tried larger k in LLR and noticed that there was some limitation (maybe k<2^53, I can't remember).

What is the current size limit for k in LLR?

Thomas11 · 2013-08-15, 19:50

Here is for convenience the input file in NewPGen format needed for LLR. Please help yourself to cut out your ranges.

It would be nice if some of you could post some comparative timings for LLR and PFGW (PRP test).

BTW.: I'm already running a new sieve for the candidates up to n=1M (I've completely underestimated your interest and machinery in this sub-project). The new sieve file will be ready for testing around Monday next week.

Batalov · 2013-08-15, 20:42

22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^716611-1 is prime

Batalov · 2013-08-15, 21:01

Taking 720-730.

pepi37 · 2013-08-15, 21:24

Quote:

Originally Posted by Thomas11

Here is for convenience the input file in NewPGen format needed for LLR. Please help yourself to cut out your ranges.

It would be nice if some of you could post some comparative timings for LLR and PFGW (PRP test).

BTW.: I'm already running a new sieve for the candidates up to n=1M (I've completely underestimated your interest and machinery in this sub-project). The new sieve file will be ready for testing around Monday next week.

Starting Lucas Lehmer Riesel prime test of 1480472640274704456611717878515654164205*2^498496-1
Using generic reduction AVX FFT length 48K, Pass1=256, Pass2=192
V1 = 5 ; Computing U0...done.

1480472640274704456611717878515654164205*2^498496-1 is prime! Time : 395.696 sec.

I7-2700K at 4 GHz

Batalov · 2013-08-15, 23:58

All done. (Attached)

Jean Penné · 2013-08-16, 06:12

Quote:

Originally Posted by Thomas11

Thanks for this information, Jean! This is really good news!

Many years ago I tried larger k in LLR and noticed that there was some limitation (maybe k<2^53, I can't remember).

What is the current size limit for k in LLR?

For k > 2^53, the use of generic modular reduction is required, so the calculus becomes 3 times slower, but it is due do the gwnum library usage, and PFGW has the same limitation!

Regards,
Jean

Kosmaj · 2013-08-16, 07:29

My LLR ver. 3.8.8 on a 64bit Mac was crashing on these numbers, but ver. 3.8.9 works fine.

Exe times:
n=498496, 424 sec
n=730004, 965 sec (FFT len = 72k)

The CPU is I5 at 2.7GHz (only one LLR client running on a 4-core machine)

robert44444uk · 2013-08-16, 09:29

Good to see LLR can be used..here are my comparative times:

pfgw:

22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^612375-1 is composite: RES64: [29838CC7648D40C8] (930.6872s+0.1715s)

LLR:
1480472640274704456611717878515654164205*2^612377-1 is not prime. LLR Res64: 1B0F6C3C8C558D4F Time : 800.448 sec

Well done Batalov on doing a huge chunk of work, and a prime to boot. 210!!!

Kosmaj · 2013-08-16, 11:40

Taking 730-732.

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2013-08-15, 20:42	#37
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 13×773 Posts	2254408991804195335111319293753596167831011071312^716611-1 is prime

2013-08-15, 21:01	#38
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 13·773 Posts	Taking 720-730.

2013-08-16, 07:29	#42
Kosmaj Nov 2003 2×1,811 Posts	My LLR ver. 3.8.8 on a 64bit Mac was crashing on these numbers, but ver. 3.8.9 works fine. Exe times: n=498496, 424 sec n=730004, 965 sec (FFT len = 72k) The CPU is I5 at 2.7GHz (only one LLR client running on a 4-core machine)

2013-08-16, 09:29	#43
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	Good to see LLR can be used..here are my comparative times: pfgw: 2254408991804195335111319293753596167831011071312^612375-1 is composite: RES64: [29838CC7648D40C8] (930.6872s+0.1715s) LLR: 1480472640274704456611717878515654164205*2^612377-1 is not prime. LLR Res64: 1B0F6C3C8C558D4F Time : 800.448 sec Well done Batalov on doing a huge chunk of work, and a prime to boot. 210!!!

2013-08-16, 11:40	#44
Kosmaj Nov 2003 2×1,811 Posts	Taking 730-732.