20141012, 09:10  #1 
Jul 2014
Montenegro
32_{8} Posts 
Conjectured Primality Test for Specific Class of Mersenne Numbers
Conjecture
Let such that is prime and Let with , then is prime iff Maxima Implementations LL Test Code:
p:9689; (s:4,M:2^p1, for i from 1 thru (p2) do (s:mod(s^22,M)))$ (if(s=0) then print("prime") else print("composite")); Code:
p:9689; (s:4,M:2^p1, for i from 1 thru (p2)/3 do (s:mod(s^88*s^6+20*s^416*s^2+2,M)))$ (if(s=0) then print("prime") else print("composite")); Maybe someone on this forum can prove or disprove this conjecture . 
20141012, 09:25  #2  
Jun 2003
2^{2}×3^{2}×151 Posts 
Quote:
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. Last fiddled with by axn on 20141012 at 09:31 

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