20200510, 20:14  #1 
May 2003
243_{10} Posts 
PRP testing
This appears to be a new step in the GIMPS process.
What exactly is it, and how does the math work? 
20200510, 20:37  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
19×443 Posts 
PRP is a different way of checking if a number is prime or not. It is not conclusive, but is good enough in most cases. It takes about the same time to do as LL testing. But, with the error checking that has been applied, it is less likely that we will miss a prime during first time checking. It is also less likely that an exponent will need a triple check.
https://en.wikipedia.org/wiki/Probable_prime If a number passes the PRP test, then the normal LL checks will be done to prove that the number is prime. I believe that Prime95 uses a version of the MillerRabin test https://www.rieselprime.de/ziki/Mill...primality_test 
20200510, 23:37  #3 
May 2003
3^{5} Posts 
Does that mean we only do LL on exponents that pass PRP?

20200511, 00:10  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
19·443 Posts 
Any exponent that had a First Time check doing LL should have an LL DC. Other than that, the rule of thumb is to use PRP for all new First Time checks and to DC those that have PRP for a first time check.
TLDR; Yes. It is preferred. 
20200511, 01:18  #5 
"Curtis"
Feb 2005
Riverside, CA
4,243 Posts 
Right! If the prp test shows composite, there is no reason to do an LL test.
If the prp test shows probable prime, we do an LL test to confirm the discovery we do not expect to ever find a mersenne candidate that is prp but not actually prime. 
20200511, 15:12  #6 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}·23^{2} Posts 
Ideally yes, since the PRP test is protected by the excellent Gerbicz error check But many systems have not been switched over from the traditional LL test (protected by the 50% error detection rate Jacobi symbol check in prime95, mprime, mlucas, but not in cudalucas or recent versions of gpuowl). LL tests are much more prone to needing triplechecks because of their approximately 2% error rate. PRP tests are backed up a bit and retried when a error is detected by the Gerbicz check, so PRP final results are almost guaranteed to be correct the first time. Almost.
Last time I checked, the LL/PRP first test mix was about 5050. Last fiddled with by kriesel on 20200511 at 15:13 
20200511, 16:23  #7 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}×23^{2} Posts 
The PRP/LL ratio was checked 6 months ago and described at https://www.mersenneforum.org/showpo...9&postcount=14

20200514, 07:22  #8  
"Oliver"
Sep 2017
Porta Westfalica, DE
FB_{16} Posts 
Quote:
http://mersenneforum.org/showthread....22471&p=465431 

20200516, 07:30  #9 
Romulan Interpreter
Jun 2011
Thailand
5·11·157 Posts 
In fact, finding a mersenne PSP (pseudoprime, i.e. it is PRP, but composite) will make a lot more sensation and bring you more fame than finding a new prime, even if that is only base 3. We know few dozens mersenne primes, but no PSP yet...

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