20201005, 17:58  #298 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3^{2}×23^{2} Posts 
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. Last fiddled with by kriesel on 20201005 at 17:59 
20201005, 22:43  #299 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
7×29^{2} Posts 
There is no point. It is a PRP test, so it can't prove primes.

20201005, 23:12  #300 
Sep 2006
Brussels, Belgium
3^{2}·181 Posts 
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 
20201006, 00:41  #301 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
7×1,277 Posts 
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.

20201006, 01:17  #302 
Mar 2019
7F_{16} Posts 

20201006, 01:26  #303 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
7·1,277 Posts 
No, it is a second 3 year old say "ooooo car" after the first one points it out.

20201006, 08:38  #304  
Feb 2008
Bray, Ireland
3·5^{2} Posts 
Quote:
CERT is like... the first 3yearold saving the residues of his neurons' calculations and the second 3year 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. 

20201006, 13:22  #305 
Random Account
Aug 2009
U.S.A.
2^{5}·53 Posts 
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...

20201006, 13:25  #306 
Einyen
Dec 2003
Denmark
2^{3}×373 Posts 
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. Last fiddled with by ATH on 20201006 at 13:27 
20201006, 14:09  #307  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·3·7·137 Posts 
Quote:
Given we have had falsepositive errors in the past, testing using multiple pieces of software makes sense. 

20201006, 14:38  #308  
Einyen
Dec 2003
Denmark
2984_{10} Posts 
Quote:
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. 

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