%I #24 Jan 22 2020 12:26:22
%S 3,7,47,2207,4870847,23725150497407,562882766124611619513723647,
%T 9932388036497706472820043948129789713,
%U 102423269049837077051675109560558766898,7949236499829405891753012242872011683,119093374737774941856311333667076322210
%N Residues of the Lucas-Lehmer primality test for M(127) = 2^127 - 1.
%C Since a(125) = 0, 2^127 - 1 = 170141183460469231731687303715884105727 is prime. This calculation was carried out by hand by Edouard Lucas. It took him 19 years from 1857 to 1876. The method works with a(0) = 3 since M(127) == 3 (mod 4). It also works with a(0) = 4 or a(0) = 10.
%H Sergio Pimentel, <a href="/A331038/b331038.txt">Table of n,a(n) for n = 0..125</a>
%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(n) = (a(n-1)^2 - 2) mod (2^127-1) with a(0) = 3; a(125) is the final term.
%Y Cf. A000043, A000668, A001566, A095847.
%Y Cf. also A129219, A129220, A129221, A129222, A129223, A129224, A129225.
%K nonn,full,fini
%O 0,1
%A _Sergio Pimentel_, Jan 08 2020