A129225 Residues of the Lucas - Lehmer primality test for M(29) = 536870911.

4, 14, 194, 37634, 342576132, 250734296, 433300702, 16341479, 49808751, 57936161, 211467447, 71320725, 91230447, 153832672, 217471443, 239636427, 223645010, 90243197, 27374393, 490737401, 35441039, 303927542, 202574536

Offset: 0

Author

Sergio Pimentel, Apr 04 2007

Keywords

• fini
• nonn
• full

Comments

Since a(27) > 0, M(29) = 536870911 is composite. Mersenne numbers are only prime if a(p-2) = 0.

Examples

			a(27) = 365171774^2 - 2 mod 536870911 = 458738443.
		

Links

• Dennis Martin, Table of n, a(n) for n = 0..27
• Eric Weisstein's World of Mathematics, Lucas Lehmer Test.
• Wikipedia, Lucas Lehmer Primality Test.

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129224, A129226, A001348.

Programs

Mathematica

NestList[Mod[#^2-2, 2^29-1] &, 4, 27] (* Ben Whitmore, Dec 28 2024 *)

Formula

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