A144051 Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..6.

11, 17, 41, 1277, 21557, 26681, 28277, 113147, 128981, 421697, 665111, 844427, 1164587, 1615631, 2073347, 2798921, 2846771, 3053747, 3992201, 4889237, 5071667, 5093507, 5344247, 5706641, 6184637, 6383051, 8396777

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 08 2008

Keywords

• nonn

Comments

All terms = {11,17} mod 30. - Zak Seidov, May 08 2011

Examples

			a(3) = 41 because 0^2 + 0 + 41 = 41; 1^2 + 1 + 41 = 43; 2^2 + 2 + 41 = 47; 3^2 + 3 + 41 = 53; 4^2 + 4 + 41 = 61; 5^2 + 5 + 41 = 71; 6^2 + 6 + 41 = 83, all primes.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, arXiv:1103.0447 [math.NT], 2011-2012.

Crossrefs

Cf. A187057, A187058.

Programs

Mathematica

lst={}; Do[p1=Prime[n]; If[PrimeQ[p2=p1+2] && PrimeQ[p3=p1+6] && PrimeQ[p4=p1+12] && PrimeQ[p5=p1+20] && PrimeQ[p6=p1+30] && PrimeQ[p7=p1+42], AppendTo[lst,p1]], {n,10^5}]; lst
okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 6}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)