Share N+/-1 Primality Proofs

[chris2be8]

Originally Posted by chris2be8

Is anyone working on the PRP in post 204?

It's had a certificate submitted which factordb is processing. Thanks to whoever submitted if.

Chris

[Batalov]

Phi(5,-205*2^771)
Note that N-1 is divisible by 205*2^771 and by 205*2^771-1 which is prime.

Similar proofs are possible for Phi₇(n) and Phi₁₅(n) (with CHG and some extra factoring).
Maybe some Phi₁₁(n)...?

[chris2be8]

If anyone wants a challenge proving http://factorization.ath.cx/index.ph...00000260577719 (3747 digits) is prime will enable a N+1 proof for http://factorization.ath.cx/index.ph...00000295827426 (17^3564+16) (that's 4386 digits).

Chris

[Puzzle-Peter]

Originally Posted by chris2be8

If anyone wants a challenge proving http://factorization.ath.cx/index.ph...00000260577719 (3747 digits) is prime will enable a N+1 proof for http://factorization.ath.cx/index.ph...00000295827426 (17^3564+16) (that's 4386 digits).

Chris

Not a very big challenge. Even the single threaded windows version of primo will do this overnight.

[chris2be8]

Here's an easier case. Proving http://factorization.ath.cx/index.ph...00000762583206 (300 digits) should enable a N-1 proof for http://factorization.ath.cx/index.ph...00000439186872 ((316^1801-1)/315).

Chris

PS. What is the practical limit for PRIMO proofs?

[paulunderwood]

Originally Posted by chris2be8

PS. What is the practical limit for PRIMO proofs?

35k digits for the latest Linux implementation, running at O(log(n)^(4+eps)). 300 digits takes a minute or two on a multicore system I guess

[lorgix]

Originally Posted by paulunderwood

35k digits for the latest Linux implementation, running at O(log(n)^(4+eps)). 300 digits takes a minute or two on a multicore system I guess

IIRC a 300 digit PRP took a few seconds on a single core in Windows.

[ChristianB]

I'm usually downloading the lower PRPs (<= 1000 digits) in batches of 100 and give them to primo using 2 Threads on my 5 year old Athlon II X2 250. The smaller ones are done within seconds the larger ones take around 2 minutes or so. The only limitation here is primo which can't be automated to work with a script. So there is still some manual work required which usually stops me from working on the smaller PRPs.

[paulunderwood]

Originally Posted by ChristianB

I'm usually downloading the lower PRPs (<= 1000 digits) in batches of 100 and give them to primo using 2 Threads on my 5 year old Athlon II X2 250. The smaller ones are done within seconds the larger ones take around 2 minutes or so. The only limitation here is primo which can't be automated to work with a script. So there is still some manual work required which usually stops me from working on the smaller PRPs.

Marcel said he would make Primo command line driven once he has made stable his code.

[yoyo]

Originally Posted by paulunderwood

Marcel said he would make Primo command line driven once he has made stable his code.

Then I would like to run it in a Boinc project :)

[Puzzle-Peter]

Originally Posted by ChristianB

I'm usually downloading the lower PRPs (<= 1000 digits) in batches of 100 and give them to primo using 2 Threads on my 5 year old Athlon II X2 250. The smaller ones are done within seconds the larger ones take around 2 minutes or so. The only limitation here is primo which can't be automated to work with a script. So there is still some manual work required which usually stops me from working on the smaller PRPs.

I think the maximum number of tests you can start at once is 999, maybe that helps reducing the amount of manual work.