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

%I

%S 13,293,10613,18773,76733,97973,458333,552053,1247693,2647133,4012013,

%T 4592453,11607653,13520333,20097293,25877573,34845413,51509333,

%U 53772893,65399573,65496653,66373613,72880373,73496333,86359853,89737733

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

%C 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.

%H Zak Seidov, <a href="/A165218/b165218.txt">Table of n, a(n) for n = 1..10000</a>

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

%e Prime q=13=p^2+4 (p=3) and r=q^2+4=13^2+4=173 (prime).

%e Prime q=293=p^2+4 (p=17) and r=q^2+4=293^2+4=85853 (prime).

%t 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-Fran├žois Alcover_, Nov 07 2013 *)

%t 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 *)

%Y Cf. A045637, A062324, A116886.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 08 2009

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Last modified November 19 11:09 EST 2019. Contains 329319 sequences. (Running on oeis4.)