A331038 Residues of the Lucas-Lehmer primality test for M(127) = 2^127 - 1.

3, 7, 47, 2207, 4870847, 23725150497407, 562882766124611619513723647, 9932388036497706472820043948129789713, 102423269049837077051675109560558766898, 7949236499829405891753012242872011683, 119093374737774941856311333667076322210

Offset: 0

Author

Sergio Pimentel, Jan 08 2020

Keywords

• nonn
• full
• fini

Comments

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.

Links

• Sergio Pimentel, Table of n,a(n) for n = 0..125
• Eric Weisstein's World of Mathematics, Lucas Lehmer Test.
• Wikipedia, Lucas Lehmer Primality Test.

Crossrefs

Cf. A000043, A000668, A001566, A095847.

Cf. also A129219, A129220, A129221, A129222, A129223, A129224, A129225.

Programs

Mathematica

NestList[Mod[#^2-2,2^127-1]&, 3,10] (* Stefano Spezia, Mar 28 2025 *)

Formula

a(n) = (a(n-1)^2 - 2) mod (2^127-1) with a(0) = 3; a(125) is the final term.