A074478 Largest prime factor of 5^n + 1.

2, 3, 13, 7, 313, 521, 601, 449, 11489, 5167, 9161, 5281, 390001, 38923, 234750601, 7621, 29423041, 41540861, 6597973, 213029, 632133361, 7603, 1030330938209, 42272797713043, 152587500001, 50150933101, 83181652304609, 16018507

Offset: 0

Author

Rick L. Shepherd, Aug 23 2002

Keywords

• nonn

Examples

			5^11 + 1 = 48828126 = 2*3*23*67*5281, so a(11) = 5281.
		

Links

• Table of n, a(n) for n = 0..471
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A002587 (largest prime factor of 2^n + 1), A074479 (largest prime factor of 5^n - 1), A074476 (largest prime factor of 3^n + 1), A227575 (largest prime factor of 7^n + 1).

Cf. A006530, A034474.

Programs

Magma

[Maximum(PrimeDivisors(5^n+1)): n in [0..30]]; // Vincenzo Librandi, Jul 09 2016

Mathematica

Table[FactorInteger[5^n + 1][[-1, 1]], {n, 0, 30}] (* Bruno Berselli, Aug 23 2013 *)

PARI

for(n=0,30, v=factor(5^n+1); print1(v[matsize(v)[1],1],","))

Formula

a(n) = A006530(A034474(n)). - Michel Marcus, Jul 09 2016

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 09 2016

a(101)-a(451) in b-file from Amiram Eldar, Feb 01 2020

a(452)-a(471) in b-file from Max Alekseyev, Apr 25 2022, Jan 04 2024