A180362 Primes of the form k * m^m + 1 with k < m^m.

5, 13, 109, 163, 257, 271, 379, 433, 487, 541, 769, 3329, 7681, 7937, 9473, 10753, 11777, 12289, 13313, 14081, 14593, 15361, 17921, 18433, 19457, 22273, 23041, 23297, 25601, 26113, 26881, 30977, 31489, 32257, 36097, 36353, 37501, 37633, 37889, 39937, 40193

Offset: 1

Author

Kevin Batista (kevin762401(AT)yahoo.com), Aug 30 2010, Sep 01 2010

Keywords

• nonn

Comments

A result of Heath-Brown shows, on the GRH, that this sequence is infinite; can this be proved unconditionally? The averaged result of Bombieri-Friedlander-Iwaniec does not seem to be strong enough.

Examples

			a(4) = 109, because 4 * 3^3 + 1 = 109, which is prime, and 4 < 27.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proceedings of the London Mathematical Society 64:3 (1992), pp. 265-338.

Programs

Mathematica

Take[Select[Union[Flatten[Table[k m^m+1,{m,5},{k,m^m-1}]]],PrimeQ],50] (* Harvey P. Dale, Jul 28 2025 *)

PARI

isA180362(n)=my(b=2);while(b^b
				

Formula

k * m^m + 1, where k < m^m.

Extensions

Edited by Charles R Greathouse IV, Sep 01 2010