A242244 Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.

11, 17, 53, 73, 79, 83, 97, 251, 269, 281, 379, 389, 433, 461, 601, 631, 691, 739, 827, 929, 947, 983, 1033, 1087, 1187, 1303, 1423, 1483, 1531, 1637, 1709, 1847, 1879, 2447, 2473, 2683, 2833, 2843, 3301, 3463, 3557, 3719, 3727, 3779, 3833, 3907, 3931, 4157

Offset: 1

Author

K. D. Bajpai, May 09 2014

Keywords

• nonn

Comments

Primes p such that p^2 + 2 = 3q, where q is prime, and p^2 - 2 is semiprime.

Examples

			a(1) = 11 is prime: 11^2 + 2 = 123 = 3 * 41 which is semiprime: 11^2 - 2 = 119 = 7 * 17 which is also semiprime.
a(2) = 17 is prime: 17^2 + 2 = 291 = 3 * 97 which is semiprime: 17^2 - 2 = 287 = 7 * 41 which is also semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3670

Crossrefs

Cf. A000040, A005383, A063643, A115395.

Programs

Maple

with(numtheory):A242244:= proc()if isprime(x) and bigomega(x^2+2)=2 and bigomega(x^2-2)=2 then RETURN (x); fi; end: seq(A242244 (),x=1..5000);

Mathematica

A242244 = {}; Do[p = Prime[n]; If[PrimeOmega[p^2 + 2] == 2 && PrimeOmega[p^2 - 2] == 2, AppendTo[A242244, p]], {n, 2000}]; A242244
Select[Prime[Range[600]],PrimeOmega[#^2+{2,-2}]=={2,2}&] (* Harvey P. Dale, Apr 07 2018 *)

PARI

is(n)=isprime(n) && isprime((n^2+2)\3) && bigomega(n^2-2)==2 \\ Charles R Greathouse IV, May 15 2014