login
Residues of the Lucas - Lehmer primality test for M(23) = 8388607.
8

%I #9 Oct 11 2019 16:11:39

%S 4,14,194,37634,7031978,7033660,1176429,7643358,3179743,2694768,

%T 763525,4182158,7004001,1531454,5888805,1140622,4321431,7041324,

%U 2756392,1280050,6563009,6107895

%N Residues of the Lucas - Lehmer primality test for M(23) = 8388607.

%C Since a(21) > 0, M(23) = 8388607 is composite. Mersenne numbers are only prime if a(p-2) = 0.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lucas-LehmerTest.html">Lucas Lehmer Test</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucas-Lehmer_primality_test">Lucas Lehmer Primality Test</a>.

%F a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

%e a(21) = 6563009^2 - 2 mod 8388607 = 6107895.

%Y Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129225, A129226, A001348.

%K fini,full,nonn

%O 0,1

%A _Sergio Pimentel_, Apr 04 2007