## Other

drummers-lowrise

Message boards : 321 Prime Search : Task Length

 Subscribe SortOldest firstNewest firstHighest rated posts first
Author Message
dannyridel
Volunteer tester

Joined: 3 Feb 19
Posts: 994
ID: 1097922
Credit: 81,717,656
RAC: 13,464

Message 151729 - Posted: 10 Oct 2021 | 2:58:27 UTC

Is there some sort of mathematical explanation to why 321 tasks are so much faster than other tasks of similar length/smaller length like ESP? Is it due to the uniquely small k size?
____________
My lucky number is 6219*2^3374198+1

Vato
Volunteer tester

Joined: 2 Feb 08
Posts: 841
ID: 18447
Credit: 645,137,585
RAC: 556,383

Message 151732 - Posted: 10 Oct 2021 | 14:45:35 UTC - in response to Message 151729.

pretty much, yes.
not only that the number being tested is a little smaller at the same n, but i believe that small k can also be more efficient in gwnum as well? or is it just a smaller FFT?
____________

dannyridel
Volunteer tester

Joined: 3 Feb 19
Posts: 994
ID: 1097922
Credit: 81,717,656
RAC: 13,464

Message 151737 - Posted: 10 Oct 2021 | 23:52:35 UTC - in response to Message 151732.

Ah ok, I'm still not so sure about how it actually happens that it is faster though...
____________
My lucky number is 6219*2^3374198+1

Bur
Volunteer tester

Joined: 25 Feb 20
Posts: 515
ID: 1241833
Credit: 414,155,367
RAC: 40,410

Message 151738 - Posted: 11 Oct 2021 | 6:16:05 UTC - in response to Message 151737.

The prime test takes a specific amount of iterations that is proportional to the log of the tested number (i.e. the exponent). However, each iteration takes longer if the FFT size is large as in that case more multiplication steps are required per iteration. If you run llr2 manually you'll see it prints a "time per iteration", that increases with increasing FFT size.

The FFT size depends on both the size of the number and the size of k. And k=3 is the smallest one can get. You'll see that computation times for the different k's in the conjecture subprojects vary strongly depending on the respective k.

A short and more mathematical explanation can be found here:

Prime scores

As to why a large FFT requires more multiplications per iteration, I have no idea. Maybe some of the more knowledgeable members can explain that. :)
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Message boards : 321 Prime Search : Task Length