A102328 Primes p such that the largest prime divisor of p^6 + 1 is less than p.

30977, 69127, 104681, 109807, 114671, 141637, 146057, 160319, 160639, 170371, 171169, 176087, 211723, 216119, 217081, 319321, 381673, 389083, 390151, 416219, 437401, 484609, 492257, 525571, 564713, 565241, 574127, 591601, 612173, 621259

Offset: 1

Author

Labos Elemer, Jan 05 2005

Keywords

• nonn

Examples

			p = 30977, p^6 + 1 = 883560179055825771003237890 = 2*5*13*37*61*113*181*13921*18517*22189*25741, so the largest prime factor is 25741 < p = 30977.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A006530, A065091, A073501, A102327.

Programs

Mathematica

Select[Prime[Range[60000]], Max[PrimeFactorList[1 + #^6]] < # &] (* Ray Chandler, Jan 08 2005 *)

PARI

is(k) = isprime(k) && vecmax(factor(k^6+1)[, 1]) < k; \\ Amiram Eldar, Jun 21 2024

Formula

Solutions to {A006530(p^6+1) < p} where p is a prime number.

Extensions

Extended by Ray Chandler, Jan 08 2005