A079138 Primes of the form k^2 + 7.

7, 11, 23, 43, 71, 107, 151, 263, 331, 491, 683, 907, 1031, 1163, 1303, 1451, 1607, 2311, 2711, 3371, 3607, 3851, 4363, 5483, 5783, 6091, 10007, 11243, 12107, 13003, 13463, 13931, 14407, 14891, 15383, 17431, 18503, 19051, 20743, 21323, 21911

Offset: 1

Author

Cino Hilliard, Dec 26 2002

Keywords

• easy
• nonn

Comments

The sum of the reciprocals converges to 0.350314... Are there infinitely many primes of this form?

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..6800

Programs

Magma

[a: n in [0..700] | IsPrime(a) where a is n^2+7]; // Vincenzo Librandi, Nov 30 2011

Mathematica

Intersection[Table[n^2+7,{n,0,10^2}],Prime[Range[9*10^3]]] ...or... For[i=7,i<=7,a={};Do[If[PrimeQ[n^2+i],AppendTo[a,n^2+i]],{n,0,100}];Print["n^2+",i,",",a];i++ ] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Select[Table[n^2+7,{n,0,70000}],PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

PARI

nsqpm(n) = {sr=0; forstep(x=0,n,2, y = x*x+7; if(isprime(y), print1(y" "); sr+=1.0/y; ); ); print(); print(sr); } \\ Primes of the form n^2 + 7 and the sum of the reciprocals.