20210224, 23:12  #12  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3^{2}·557 Posts 
Quote:
Mihai Preda had an unreliable gpu and wrote a variant of early gpuowl that did segments of the LL sequence twice and compared them (which IIRC he called "supersafe"). Forum user Error identified the Jacobi symbol check for the LL sequence. Because of its high cost it's done only rarely and it has a ~50% chance of detecting that an error has occurred. This I believe led some to search for more reliable / definitive error checks. Its implementation was quick and added ~0.3% to run times. Robert Gerbicz identified a way to provide a superior check (GEC, Gerbicz Error Check) that applies to the probably prime test but not to the LL sequence, detecting essentially 100% of errors, which enables reliable retreat after a failed GEC to the most recent saved state that passed a GEC. At this point there was a debate over whether full double checks of PRP results were necessary. Most of the major GIMPS primality testing software also quickly adopted the PRP/GEC rather quickly (Gpuowl, prime95, mprime, Mlucas) https://www.mersenne.org/ describes the effect of the third piece of progress, the VDF applied to the whole PRP primality test. See also https://mersenneforum.org/showthread.php?t=25638 This was added last year to Gpuowl, prime95, mprime, and is planned for Mlucas.The PrimeNet server was modified too, to accept new format PRP result records and proof files from client software, and issue certification assignments to mprime/prime95 and accept certification results, keep track of new work types and the computing credit for them, etc. More recently, some of the error checking has been applied to P1 factoring also. Partly by combining stage 1 P1 with early PRP iterations protected by the GEC, and partly by applying the Jacobi check, in gpuowl v7.x, along with other older techniques, such as detecting zeroedresidue. Last fiddled with by kriesel on 20210224 at 23:12 

20210225, 01:15  #13 
"Curtis"
Feb 2005
Riverside, CA
11172_{8} Posts 

20210225, 01:20  #14  
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Quote:
Edit: nice mega Pidgeot Last fiddled with by Primeinator on 20210225 at 01:32 

20210225, 02:24  #15 
Jan 2021
79 Posts 
I don't want to hijack this thread, but can anyone tell me if the PRP test conclusively proves a number is prime, or only that it is probably prime, as the name suggests? If it is only probably, what is the probability of an exponent around 120,000,000 or 330,000,000 being detected as prime, when in fact is is not?
I believe the LucasLemar test gives a definitive prime/composite answer. I'm ignoring hardware or software errors. Last fiddled with by drkirkby on 20210225 at 02:26 
20210225, 03:14  #16  
"Kyle"
Feb 2005
Somewhere near M52..
915_{10} Posts 
Quote:
Last fiddled with by Primeinator on 20210225 at 03:15 

20210225, 03:24  #17 
"Curtis"
Feb 2005
Riverside, CA
11172_{8} Posts 
A mersenne prp is 99.999+% likely to be prime. It would be a much more important discovery to find a mersenne prp that isn't actually prime than it would be to find a new mersenne prime.
LL testing at 100M+ exponents is about 2% likely to have an error. Prp testing is more than 100 times less likely to have an error. So, "ignoring hardware or software errors" is, unfortunately, where all the chance of "not actually prime" occurs. The prp test has checks for errors, which is why it's the only test we use going forward. 
20210225, 03:44  #18  
Einyen
Dec 2003
Denmark
2^{2}×13×59 Posts 
Quote:
This has not happened yet, since all Mersenne Primes has been found by LL tests so far, before PRP test became the most common test. 

20210225, 05:20  #19 
Romulan Interpreter
Jun 2011
Thailand
2·4,679 Posts 
.
Offtopic, about thread title. There is nothing "moronic" about asking, and we (engineers, math/technical guys, geeks, etc.) love humble questions and love the people who sincerely want to learn. Having less knowledge about some subject is not wrong or despicable. Nobody in the world knows all about everything. Having the courage to ask questions and learn is commendable. What's bad is repeating the same mistakes forever, and refusing to learn from them. We hate those people who are ignorant, arrogant, and stubborn to stay ignorant, in the same time. Therefore, I changed the thread title to get rid of the "moronic" words. I don't know if OP posted it like that from the start (I call myself bad words when I am angry on my own stupidity, which actually happens quite often), or some funny moderator changed it, but if the later, then it was a bad joke. Sorry for offtopic, I only read the first few posts, I continue reading and I may post something which is not offtopic, if the other posters didn't already say everything I could comment about the subject. . Last fiddled with by LaurV on 20210225 at 05:36 
20210225, 14:39  #20  
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Quote:
I sincerely appreciate the responses from people on this forum so far to my question on PRP testing. I need to work with the examples provided so try and make the leap from applying the binomial theorem to the PRP test. I do wish to understand the "why" and "how" of the PRP test but it takes me longer to understand the mathematics than for most other people on this form. While I enjoy math it was never my strongest subject and my field of expertise is very different (biology/medicine). 

20210225, 15:01  #21 
6809 > 6502
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Aug 2003
101×103 Posts
2·7·677 Posts 

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