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?
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My lucky number is 6219*2^3374198+1

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

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. :)
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1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000