A161863 Numbers k such that k^2+k+3 and k^2+k-3 are both prime.

4, 7, 10, 22, 25, 34, 70, 79, 112, 130, 139, 172, 187, 217, 229, 262, 274, 295, 304, 322, 337, 364, 397, 400, 472, 499, 574, 580, 592, 622, 634, 655, 664, 697, 829, 844, 925, 1057, 1144, 1165, 1255, 1300, 1309, 1357, 1414, 1420, 1489, 1537, 1642, 1669, 1744

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

Keywords

• nonn
• easy

Examples

			4 is in the list because 16+4+-3 = 23 and 17 are primes.
7 is in the list because 49+7+-3 = 53 and 59 are primes.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088485, A027752

Programs

Magma

[k:k in [1..1750]| IsPrime(k^2+k+3) and IsPrime(k^2+k-3)]; // Marius A. Burtea, Feb 17 2020

Mathematica

q=3;lst3={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst3,n]],{n,0,7!}];lst3
Select[Range[2000],AllTrue[#^2+#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 01 2019 *)

Extensions

Definition rephrased by R. J. Mathar, Jun 27 2009