20211027, 19:53  #1 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
16574_{8} Posts 
PRP on OBD candidates
Currently, it would be premature to attempt a PRP on a gigadigit Mersenne number with prime exponent.
Only one has been taken in TF to 91 bits, none to 92 bits, and none have been P1 factored to adequate bounds. Existing primality testing software either does not support such large exponents, does not support PRP, or does not support PRP proof generation. The primality testing effort per candidate is so huge that IMO a first attempt should not be attempted until proof generation is available at such large exponents and fft lengths, and has been well tested for the same software and version at lower exponents. An additional obstacle is achievable run time. To complete a PRP of an OBD in a year, the iteration benchmark would need to be under ~9.5 msec/iteration. 1 year / OBD PRP ~ 365 * 24 * 3600 seconds / (10^{9}/log_{10}2) iterations = 0.009,49 seconds / iteration. Versions of Mlucas available that can nominally handle PRP testing gigadigit candidates lack PRP proof generation. While it is likely timings on native Linux would be better, on Ubuntu atop WSL, Mlucas V20.x produces benchmark timings for the required 192M fft length of: Xeon Phi 7250 msec/iter = 1179.13 Xeon Phi 7210 msec/iter = 1156.88 i71165g7 msec/iter = 1153.63 dualXeone52690 msec/iter = 785.14 dualXeone52697v2 msec/iter = 404.89 The fastest of the above CPU msec/iter values corresponds to a run time of ~42.65 years. It's likely that they would do better on native Linux. But not likely two orders of magnitude better. Versions of gpuowl available that can nominally handle PRP testing gigadigit candidates lack PRP proof generation. (V6.584 to 6.11224) Run time on a Radeon VII would be around 50. msec/iter x 3.32E9 iterations ~ 5.3 years. Verification by doublecheck would take equally long as a first test, in the absence of PRP proof generation capability or certification software capable of handling gigadigit Mersennes. PRP proof generation space required will be considerable. Temporary space doubles for each increment of proof power and is proportional to exponent. Optimal proof power is an increasing function of exponent. Proof power 12 OBD temporary files would require ~ 1696. GiB each, judging by prime95 documentation. The resulting proof file would require ~5.4 GiB. Interim residue files are ~405. MiB each, as in Mlucas P1. Last fiddled with by kriesel on 20211027 at 19:56 
20221110, 17:29  #2  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{2}·3·17·37 Posts 
Still true:
Quote:
https://www.mersenne.ca/obd The rest of post one is still current as of today. Last fiddled with by kriesel on 20221110 at 17:30 

20230204, 22:39  #3 
Apr 2005
DFW, tx
5×7 Posts 
I'd love to test an OBD before I'm gone.
In theory, the LL double check would be faster as over the years it takes to run the test, newer hardware would be available to run the double check. Heck, as faster hardware becomes available it can be upgraded to during the test to speed along testing. 
20230205, 20:31  #4  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{2}×3×17×37 Posts 
Quote:
A leading candidate for OBD PRP with proof generation is a future release of Mlucas. Gpuowl extension is another possibility. Last fiddled with by kriesel on 20230205 at 20:47 

20230205, 20:43  #5  
Jan 2021
California
7^{2}×11 Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
P1 on OBD candidates  lavalamp  Operation Billion Digits  37  20230305 17:54 
A couple of 15e candidates  fivemack  NFS@Home  1  20141130 07:52 
No available candidates on server  japelprime  Prime Sierpinski Project  2  20111228 07:38 
Adding New Candidates  wblipp  Operation Billion Digits  6  20110410 17:45 
new candidates for M...46 and M48  cochet  Miscellaneous Math  4  20081024 14:33 