Quote:
Originally Posted by primus
Maybe someone on this forum can prove or disprove this conjecture .

This isn't a new test. This is just the LLtest, disguised by using a polynomial which combines 3 iterations of LL into 1. It is only faster because of the interpreted nature of your implementation. I'm betting that the plain version will be faster for larger p (because 3 iterations of s^22 should be faster than the deg8 poly).
EDIT:
Code:
LL1(p)={my(s=Mod(4,2^p1)); for(i=1,p2, s=s^22); s==0}
LL2(p)={my(s=Mod(4,2^p1)); for(i=1,(p2)/3, s=s^88*s^6+20*s^416*s^2+2); s==0}
LL3(p)={my(s=Mod(4,2^p1)); for(i=1,(p2)/3, s=((s^22)^22)^22); s==0}
LL1(9689)
time = 1,280 ms.
LL2(9689)
time = 3,511 ms.
LL3(9689)
time = 1,276 ms.
In PARI/GP, your version is nearly 3 times slower.