A114335 Numbers k such that k^2 + 1 and k^2 - 3 are both prime.

4, 10, 14, 20, 26, 40, 110, 124, 146, 206, 250, 326, 340, 350, 436, 440, 470, 634, 686, 704, 920, 1004, 1054, 1060, 1124, 1156, 1246, 1276, 1294, 1316, 1376, 1420, 1550, 1570, 1654, 1664, 1784, 1966, 1970, 2026, 2116, 2210, 2380, 2516, 2594, 2654, 2780

Offset: 1

Author

John L. Drost, Feb 07 2006

Keywords

• nonn

Comments

This is the intersection of A028873 and A005574; this sequence is also a subset of A090120 (n such that closest primes above and below n^2 differ by 4).

Examples

			a(2) = 10 since 10^2 + 1 = 101 and 10^2 - 3 = 97 are both prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005574, A028873, A090120.

Programs

Magma

[n: n in [2..100000] |IsPrime(n^2+1) and IsPrime(n^2-3)]; // Vincenzo Librandi, Nov 13 2010

Mathematica

Select[Range[3,3000],AllTrue[#^2+{1,-3},PrimeQ]&] (* Harvey P. Dale, Jul 25 2024 *)

PARI

isok(k) = isprime(k^2 + 1) && isprime(k^2 - 3); \\ Amiram Eldar, Mar 01 2025