A129224 Residues of the Lucas - Lehmer primality test for M(23) = 8388607.

4, 14, 194, 37634, 7031978, 7033660, 1176429, 7643358, 3179743, 2694768, 763525, 4182158, 7004001, 1531454, 5888805, 1140622, 4321431, 7041324, 2756392, 1280050, 6563009, 6107895

Offset: 0

Author

Sergio Pimentel, Apr 04 2007

Keywords

• fini
• full
• nonn

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Lucas Lehmer Test.
• Wikipedia, Lucas Lehmer Primality Test.

Crossrefs

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

Formula

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