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%I #16 Aug 11 2019 10:26:15
%S 11,17,41,347,641,1277,1427,1607,2687,3527,4001,4637,4931,13901,19421,
%T 21011,21557,22271,23741,26681,26711,27941,28277,31247,32057,33617,
%U 43781,45821,55331,55661,55817,68207,68897,71327,91571,97367,113147,128657,128981
%N Primes p such that the polynomial x^2 + x + p generates only primes for x = 0, ..., 4.
%C From Weber, p. 15.
%H Charles R Greathouse IV, <a href="/A187057/b187057.txt">Table of n, a(n) for n = 1..10000</a>
%H H. J. Weber, <a href="http://arxiv.org/abs/1103.0447">Regularities of Twin, Triplet and Multiplet Prime Numbers</a>, Mar 2, 2011.
%e a(1) = 11 because x^2 + x + 11 generates 0^2 + 0 + 11; 1^2 + 1 + 11 = 13; 2^2 + 2 + 11 = 17; 3^2 + 3 + 11 = 23; 4^2 + 4 + 11 = 31, all primes.
%t okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 4}]]; Select[Range[10000], okQ] (* _T. D. Noe_, Mar 03 2011 *)
%t Select[Prime[Range[12500]],AllTrue[#+{2,6,12,20},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 11 2019 *)
%o (PARI) forprime(p=2, 1e4, if(isprime(p+2)&&isprime(p+6)&&isprime(p+12) &&isprime(p+20), print1(p", "))) \\ _Charles R Greathouse IV_, Mar 04 2012
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 03 2011