Thread: Prime gap records View Single Post
2022-04-18, 20:55   #93
MJansen

Jan 2018

2·5·11 Posts

Quote:
 Originally Posted by ATH Code: 29*479909#/9699690-3531714+0 is 2-PRP! (1377.0026s+0.2389s) 29*479909#/9699690-3531714+0 is 31-PRP! (1406.6504s+0.2672s) 29*479909#/9699690-3531714+0 is 61-PRP! (1324.6448s+0.3519s) 29*479909#/9699690-3531714+0 is 89-PRP! (1351.6884s+0.1892s) 29*479909#/9699690-3531714+0 is 107-PRP! (1337.2569s+0.2194s) 29*479909#/9699690-3531714+0 is 127-PRP! (1295.6427s+0.2666s) 29*479909#/9699690-3531714+0 is Lucas PRP! (5028.9635s+0.3283s) 29*479909#/9699690-3531714+7186572 is 2-PRP! (1398.9850s+0.2509s) 29*479909#/9699690-3531714+7186572 is 31-PRP! (1325.3246s+0.2589s) 29*479909#/9699690-3531714+7186572 is 61-PRP! (1257.9103s+0.2403s) 29*479909#/9699690-3531714+7186572 is 89-PRP! (1253.9708s+0.2486s) 29*479909#/9699690-3531714+7186572 is 107-PRP! (1253.6129s+0.1967s) 29*479909#/9699690-3531714+7186572 is 127-PRP! (1316.4862s+0.3536s) 29*479909#/9699690-3531714+7186572 is Lucas PRP! (6843.9628s+0.2712s) Congratulations again on another record. Sorry, I'm not going to double check this gap just after finishing the other one. In the future I think it would be beneficial to start the sieving longer time before you want to use all the cores on the PRP tests and then let sieving run longer. Each PRP test takes 10-20 min on 1 core depending on the CPU, and I'm pretty sure sieving finds more than 6 factors per hour after 1e12, it is probably beneficial to 2e12 or even longer. Since the sieving is single threaded it is just a matter of starting it on 1 core like 1-2 weeks before you want to use lots of cores for all the PRP tests.
Thnx Andreas! No worries about not running the gap again, the classification should at least be PRP after you verified the gap ends.

I did sieve multiple gaps before I started PRP-ing them. After that I PRP-d 6 different gaps for 2 weeks and the ones that did not had any end points found, I searched seperately later, among this one.

I did not sieve the interval further because of the dimininishing returns, i.e. the number of composites found decreased fairly fast already, not sure how much sieving till 2*10^12 would save ...
After 70*10^10 the number of (new) composites that is found is around 0,0006% (6/1.000.000th) of the total candidates. Say 162 candidates for the primes between 69-70 * 10^10, in an interval of 25.306.551 candidates for a primorial of the first 42.000 primes. So extending the presieving till 10^12 is already a bit superfluous imho, doubling that till 2*10^12 seems excessive at the moment, but if (big if!) I will do another mega gap search I will keep this in mind.

This record can be improved very easily if :
a. there is a bignum library for the GPU
b. a gpu is used for sieving and PRP-ing. If for instance the speed of a GPU core is half that of a cpu core, the number of available cores (1.000 - 10.000+) makes that job so much easier ...

Note I still have not been able to get the GPU to run a gap search, I installed the necessairy programs under Ubuntu, but for the life of me I do not know how to tell the gapsearch program where they can be found ...