A108403 Numbers n such that n^2-6 and n^2+6 are both prime.

5, 25, 65, 145, 355, 605, 985, 1075, 1295, 1465, 1565, 1675, 1915, 2345, 2425, 2585, 2755, 3005, 3155, 3785, 4595, 4625, 4975, 5225, 5465, 5665, 5905, 5915, 6115, 6295, 6305, 6415, 6485, 7235, 7775, 8185, 9065, 9275, 9415, 9755, 9835, 10145, 10195

Offset: 1

Author

John L. Drost, Jul 04 2005

Keywords

• nonn

Comments

All members of the sequence are divisible by 5 as if n is 1 or 4 mod 5 then n^2-6 is divisible by 5 and if n is 2 or 3 mod 5 then n^2+6 is divisible by 5.

Examples

			a(2)=25 since 25^2 - 6 = 619 and 25^2 + 6 = 631 are both prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A087681 (with n instead of n^2), A108701 (with 2 instead of 6).

Programs

Magma

[n: n in [2..100000] | IsPrime(n^2-6) and IsPrime(n^2+6)] // Vincenzo Librandi, Nov 13 2010

Mathematica

pQ[n_]:=Module[{n2=n^2},And@@PrimeQ[{n2-6,n2+6}]]; Select[5Range[2100], pQ]  (* Harvey P. Dale, Nov 06 2011 *)