A129226 Residues of the Lucas - Lehmer primality test for M(31) = 2147483647.

4, 14, 194, 37634, 1416317954, 669670838, 1937259419, 425413602, 842014276, 12692426, 2044502122, 1119438707, 1190075270, 1450757861, 877666528, 630853853, 940321271, 512995887, 692931217, 1883625615, 1992425718

Offset: 0

Author

Sergio Pimentel, Apr 04 2007

Keywords

• fini
• nonn

Comments

Since a(29) = 0, M(31) = 2147483647 is prime. Mersenne numbers are only prime if a(p-2) = 0.

Examples

			a(29) = 65536^2 - 2 mod 2147483647 = 0.
		

Links

• Dennis Martin, Table of n, a(n) for n = 0..29
• Eric Weisstein's World of Mathematics, Lucas Lehmer Test.
• Wikipedia, Lucas Lehmer Primality Test.

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129224, A129225, A001348.

Programs

Python

p = 31; Mp = 2**p - 1
from itertools import accumulate
def f(anm1, _): return (anm1**2 - 2) % Mp
print(list(accumulate([4]*30, f))) # Michael S. Branicky, Apr 14 2021

Formula

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