A102327 Primes p such that the largest prime factor of p^5 + 1 is less than p.

1753, 2357, 7103, 9749, 13441, 16453, 21467, 22739, 25153, 28409, 29059, 33247, 33347, 36781, 42853, 51427, 57751, 58453, 62347, 65777, 66593, 69119, 72923, 78643, 80407, 83591, 85619, 89909, 91411, 99409, 101209, 101363, 113171, 124337

Offset: 1

Author

Labos Elemer, Jan 05 2005

Keywords

• nonn

Examples

			p = 1753, 1 + p^5 = 16554252702583994 = 2*41*151*691*877*1361*1621, so the largest prime factor is 1621 < p = 1753.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A006530, A065091, A073501.

Programs

Mathematica

Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^5]] < # &] (* Ray Chandler, Jan 08 2005 *)
Select[Prime[Range[12000]],FactorInteger[#^5+1][[-1,1]]<#&]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

isok(p)= isprime(p) && (vecmax(factor(p^5+1)[,1]) < p); \\ Michel Marcus, Jul 11 2018

Formula

Solutions to {A006530(1 + p^5) < p} where p is a prime.

Extensions

Extended by Ray Chandler, Jan 08 2005