(may be) stupid idea for speed of mersenne-LLT

[Random_zh]

Hi all. I have an idea how to may be speed or slow down LL test. I just dont know how FFT multiplication behaves with even larger numbers.

you could test 2 or more numbers at same time:

example for the iterations with 3 exponents p,q,r:
S(0) = 4
S(n+1) = S(n)^2-2 mod (2^p-1 * 2^q-1 * 2^p-1)
test p,q,r like always:
S(p-2) mod (2^p-1)
S(q-2) mod (2^q-1)
S(r-2) mod (2^r-1)

hmm i guess it will cost more time with larger numbers, but since i'm not sure... :)

[akruppa]

It would be slower. The time for doing a multiplication grows faster than the size of the input number, O(n log(n) loglog(n)) for FFT multiplication, so testing two numbers at once would take more than twice as long as testing a single one. Also, the DWT will probably not work.

Alex