A158695 - OEIS

%I #6 Mar 07 2013 10:02:33

%S 1,-1,-1,1,1,-1,1,-1,-1,3,-1,1,10,1,-1,2,1,-1,8,-1,-1,15,1,1,4,1,-1,

%T 90,1,1,72,1,-1,33,1,-1,114,1,-1,15,1,1,37,-1,-1,516,1,1,301,1,-1,

%U 2029,-1,-1,54,1,-1,23,-1,-1,4756,-1,-1,65,1,1,696,1,-1,8503,-1,-1,3693,1,1

%N Table T(n,3) read by rows with T(n,1)=a,T(n,2)=b,T(n,3)=c and ((a*M(n))^3)*((a*M(n))^3+b)+c is prime for the least a with least b and c = -1 or 1 and M(n) = n-th Mersenne prime.

%C All primes certified.

%C For M(26), a(26)=4166, b(26)=1, c(26)=1.

%C For M(27), a(27)=5880, b(27)=-1, c(27)=-1.

%C For M(28), a(28)=3997, b(28)=-1, c(28)=-1; with the following expression being a certified prime ((3997*(2^86243-1))^3)*((3997*(2^86243-1))^3-1)-1.

%e ((1*(2^2-1))^3)*((1*(2^2-1))^3-1)-1=701 prime 2^2-1=M(1) a(1)=1 b(1)=-1 c(1)=-1

%e ((1*(2^3-1))^3)*((1*(2^3-1))^3+1)-1=117991 prime 2^3-1=M(2) a(2)=1 b(2)=1 c(2)=-1

%e ((1*(2^5-1))^3)*((1*(2^5-1))^3-1)-1=887473889 prime 2^5-1=M(3) a(3)=1 b(3)=-1 c(3)=-1

%K sign,tabf

%O 1,10

%A _Pierre CAMI_, Mar 24 2009