20141012, 09:10  #1 
Jul 2014
Montenegro
2·13 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
1010100011101_{2} 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 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Lucasian Pseudoprimality Hypothesis for Specific Class of k 2^n1  primus  Miscellaneous Math  14  20150704 15:42 
Pseudoprimality Hypothesis for Specific Class of Generalized Fermat Numbers  primus  Miscellaneous Math  1  20150325 22:18 
Disproven Primality Test for Specific Class of kb^n1  primus  Computer Science & Computational Number Theory  8  20140821 15:16 
Conjectured Primality Test for Specific Class of k6^n1  primus  Computer Science & Computational Number Theory  16  20140815 01:15 
Conjectured Primality Test for 2^p1, (2^p+1)/3 and (2^2^n+1)  T.Rex  Math  75  20070904 07:53 