Searching for Wagstaff PRP

[lalera]

hi,
i did this range with llr v3.8.21/3.8.23 and i do not have a json file
i read here in the forum that the programmer of llr will
integrate gerbicz error checking but it will need some time

[paulunderwood]

Originally Posted by lalera

hi,
i did this range with llr v3.8.21/3.8.23 and i do not have a json file
i read here in the forum that the programmer of llr will
integrate gerbicz error checking but it will need some time

You can use Prime95/mprime to crunch these numbers and get the desirable output.

[GP2]

I don't think there's any advantage to using LLR. It uses the same underlying gwnum library as mprime. Maybe it can test some extra forms, but for plain old k*b^n+c PRP-3 I don't think there's any reason not to use mprime (the latest version, namely 29.8 b5).

LLR added the capability to do "Vrba-Reix" residues, but those are unproven. I don't know if there was speed advantage to using them, compared to PRP-3 ?

The LLR output in your file shows 64-bit "RES64" and "OLD64" values, I'm not sure how these differ, or if the first one is indeed a PRP-3 residue.

The range is 20.19M to 20.20M ... did you do 20.0M to 20.19M ? I think I saw only a bunch of trial-factoring results from you in the 20M ranges.

[lalera]

hi,
here are the results for W2147483647

no factor for W2147483647 from 2^84 to 2^85 [mfaktc 0.21 barrett87_mul32_gs]
no factor for W2147483647 from 2^85 to 2^86 [mfaktc 0.21 barrett87_mul32_gs]

W2147483647 released

[lalera]

Originally Posted by GP2

I don't think there's any advantage to using LLR. It uses the same underlying gwnum library as mprime. Maybe it can test some extra forms, but for plain old k*b^n+c PRP-3 I don't think there's any reason not to use mprime (the latest version, namely 29.8 b5).

LLR added the capability to do "Vrba-Reix" residues, but those are unproven. I don't know if there was speed advantage to using them, compared to PRP-3 ?

The LLR output in your file shows 64-bit "RES64" and "OLD64" values, I'm not sure how these differ, or if the first one is indeed a PRP-3 residue.

The range is 20.19M to 20.20M ... did you do 20.0M to 20.19M ? I think I saw only a bunch of trial-factoring results from you in the 20M ranges.

hi,
i do use sometimes a prpnet server that cannot use prime95/mprime

[GP2]

Originally Posted by GP2

The LLR output in your file shows 64-bit "RES64" and "OLD64" values, I'm not sure how these differ, or if the first one is indeed a PRP-3 residue.

Originally Posted by lalera

i do use sometimes a prpnet server that cannot use prime95/mprime

I did a quick check of the first exponent you did, 20190017. Neither of the Res64 values that LLR produced (RES64 and OLD64) is a type-5 PRP-3 residue.

Perhaps one of them is a type-1 PRP-3 residue, I'm not sure. Gerbicz testing for Wagstaff numbers only works with type-5 residues, not type-1.

Can you do a quick check with your LLR executable of a small exponent like 999983 ? Then we could compare the results with mprime and see if the residues really are type-1 PRP-3.

So anyways I think we can conclude that the 20.19M subrange almost certainly doesn't contain a Wagstaff prime. But the numerical residue values can't be added directly to my little database because that stores 2048-bit type-5 residues.

[lalera]

Originally Posted by GP2

I did a quick check of the first exponent you did, 20190017. Neither of the Res64 values that LLR produced (RES64 and OLD64) is a type-5 PRP-3 residue.

Perhaps one of them is a type-1 PRP-3 residue, I'm not sure. Gerbicz testing for Wagstaff numbers only works with type-5 residues, not type-1.

Can you do a quick check with your LLR executable of a small exponent like 999983 ? Then we could compare the results with mprime and see if the residues really are type-1 PRP-3.

So anyways I think we can conclude that the 20.19M subrange almost certainly doesn't contain a Wagstaff prime. But the numerical residue values can't be added directly to my little database because that stores 2048-bit type-5 residues.

hi,
with llr v3.8.23

(2^999983+1)/3 is not prime. RES64: 4C43A8FD104EC89D. OLD64: 607828060DA47DC2 Time : 303.538 sec.

[GP2]

Originally Posted by lalera

hi,
with llr v3.8.23

(2^999983+1)/3 is not prime. RES64: 4C43A8FD104EC89D. OLD64: 607828060DA47DC2 Time : 303.538 sec.

For this exponent mprime gave "res64":"23A646DAB9B2B3C1", "residue-type":1

So LLR is producing neither type-1 PRP-3 nor type-5 PRP-3 residues.

[lalera]

hi,
here are the results for wagstaff numbers
n=11980k to 12000k

[diep]

Originally Posted by GP2

For this exponent mprime gave "res64":"23A646DAB9B2B3C1", "residue-type":1

So LLR is producing neither type-1 PRP-3 nor type-5 PRP-3 residues.

How about composite-27 type residue?

[diep]

Originally Posted by lalera

hi,
here are the results for wagstaff numbers
n=11980k to 12000k

Thanks for your fanatism Lalera - but why do you already checked range by Propper? You want to double check?

Why not factor exponent+1 and then the factorisation exponent+1 giving for example the strongest primes and having a Mersenne or Wagstaff known prime exponent als one of its factors - try search those exponents at say range 19M-59M and hope you are so lucky?