A165218 Primes q of the form q=p^2+4 (p=prime) such that r=q^2+4 is also prime.

13, 293, 10613, 18773, 76733, 97973, 458333, 552053, 1247693, 2647133, 4012013, 4592453, 11607653, 13520333, 20097293, 25877573, 34845413, 51509333, 53772893, 65399573, 65496653, 66373613, 72880373, 73496333, 86359853, 89737733

Offset: 1

Author

Zak Seidov, Sep 08 2009

Keywords

• nonn

Comments

Intersection of A062324 and A045637. Except of the first term, 13, all terms == 5 (mod 6) == 5 (mod 12) == 5 (mod 24) == 23 (mod 30)== 53 (mod 120). Values of primes p in A116886.

Examples

			Prime q=13=p^2+4 (p=3) and r=q^2+4=13^2+4=173 (prime).
Prime q=293=p^2+4 (p=17) and r=q^2+4=293^2+4=85853 (prime).
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045637, A062324, A116886.

Programs

Mathematica

Reap[For[p = 2, p < 10^4, p = NextPrime[p], If[PrimeQ[q = p^2+4] && PrimeQ[q^2+4], Print[q]; Sow[q]]]][[2, 1]] (* Jean-François Alcover, Nov 07 2013 *)
Select[Prime[Range[2000]]^2+4,AllTrue[{#,#^2+4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2018 *)

Formula

a(n) = (A116886(n))^2 + 4.