The Next Big Development for GIMPS

[kriesel]

Is there enough utility to PRP proof/cert of known Mersenne primes to be worth running them? (Or whichever weren't already run during recent development?)
For just a little more confidence in the conclusions of primality. Radeon VII or AVX512 should make short work of them.

[retina]

Originally Posted by kriesel

Is there enough utility to PRP proof/cert of known Mersenne primes to be worth running them? (Or whichever weren't already run during recent development?)
For just a little more confidence in the conclusions of primality.

There is no point. It is a PRP test, so it can't prove primes.

[S485122]

Originally Posted by retina

There is no point. It is a PRP test, so it can't prove primes.

Agreed ... but it is new ! And it would mean that real, but ancient, proofs should be discarded : a probabilistic test; is better !
Sarcasm put aside, a new prime found by PRP with or without certificates will not be confirmed until a few matching LL tests (or until another primality proof has given the same reult.

Jacob

[Uncwilly]

The PRP is a bit like having a 3 year old say something is a car. The LL is like having a qualified mechanic tell you it is a 1972 Rolls Royce.

[mathwiz]

Originally Posted by Uncwilly

The PRP is a bit like having a 3 year old say something is a car. The LL is like having a qualified mechanic tell you it is a 1972 Rolls Royce.

Does that make the CERT after PRP like the 3 year old giving you a powerpoint presentation as to why it's a car?

[Uncwilly]

No, it is a second 3 year old say "ooooo car" after the first one points it out.

[ZFR]

Originally Posted by Uncwilly

No, it is a second 3 year old say "ooooo car" after the first one points it out.

That's closer to a DC analogy.

CERT is like... the first 3-year-old saving the residues of his neurons' calculations and the second 3-year old using them to verify that the thought process that lead the first one to identify the object as a car were done corretly without external interference or the first child purposely faking.

[storm5510]

Originally Posted by retina

There is no point. It is a PRP test, so it can't prove primes.

PRP cannot prove primes! I was under the impression this is what all the Prime95 and mprime major revisions were for. It neither cannot provide residues to compare then I do not see the point an any of it...

[ATH]

PRP tests proves composites (compositeness?), which is all we need in >99.99% of the exponents.

Then only if the PRP tests fails to shows composites, and shows a probable prime, do we need to run at least 2 x LL tests to prove it is prime.

[henryzz]

Originally Posted by ATH

PRP tests proves composites (compositeness?), which is all we need in >99.99% of the exponents.

Then only if the PRP tests fails to shows composites, and shows a probable prime, do we need to run at least 2 x LL tests to prove it is prime.

We don't although for a Mersenne prime we have a tradition of multiple tests. I think the EFF might have required it back when we were going for the 10M digit prize.
Given we have had false-positive errors in the past, testing using multiple pieces of software makes sense.

[ATH]

Originally Posted by storm5510

PRP cannot prove primes! I was under the impression this is what all the Prime95 and mprime major revisions were for. It neither cannot provide residues to compare then I do not see the point an any of it...

PRP test = probable prime test, so if positive (zero residue) it is "probably" prime.
Lucas Lehmer test (LL) proves it is prime if you get a zero residue. Both tests are in Prime95/mprime, but we only need LL test if a PRP test is positive.

We switched from LL to PRP tests in the last ~2 years because of the increased (Gerbicz) error checking in PRP tests and now because of the certificates.