A187060 Primes p such that the polynomial x^2 + x + p generates only primes for x = 1..7.

11, 17, 41, 21557, 26681, 128981, 844427, 2073347, 3992201, 4889237, 6184637, 11900501, 21456047, 24598361, 33771581, 34864211, 50943791, 51448361, 51867197, 55793951, 56421347, 61218251, 67787537, 69726647, 76345121

Offset

1,1

Comments

From Weber, p. 15. However, erroneous.

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

Links

Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (Zak Seidov found the first 400 terms)

H. J. Weber, Regularities of Twin, Triplet and Multiplet Prime Numbers, arXiv:1103.0447 [math.NT], 2011-2012.

Example

a(4) <> 21577 because 0^2 + 0 + 21577 = 21577; 1^2 + 1 + 21577 = 21579 = 3 * 7193 thus exposing an error in Weber's paper; 2^2 + 2 + 21577 = 21583 = 113 * 191; 3^2 + 3 + 21577 = 21589 is prime; 4^2 + 4 + 21577 = 21597 = 3 * 23 * 313; 5^2 + 5 + 21577 = 21607 = 17 * 31 * 41 (a "3-brilliant number" rather than a prime); 6^2 + 6 + 21577 = 21619 = 13 * 1663; 7^2 + 7 + 21577 = 21633 = 3 * 7211.

Mathematica

okQ[n_] := And @@ PrimeQ[Table[i^2 + i + n, {i, 0, 7}]]; Select[Range[10000], okQ] (* T. D. Noe, Mar 03 2011 *)

Prog

(PARI) for(k=1, 50000, p=prime(k); if(isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+20) && isprime(p+30) && isprime(p+42) && isprime(p+56), print(p), )) \\ Nathaniel Johnston, Apr 26 2011
(PARI) p=2; q=3; forprime(r=5, 1e6, if(r-p==6 && q-p==2 && isprime(p+12) && isprime(p+20) && isprime(p+30) && isprime(p+42) && isprime(p+56), print(p)); p=q; q=r) \\ Charles R Greathouse IV, Mar 04 2012

Crossrefs

Cf. A187057, A187058, A144051.

Sequence in context: A187058 A144051 A331940 * A190800 A191456 A146036

Adjacent sequences: A187057 A187058 A187059 * A187061 A187062 A187063

Keyword

nonn

Author

Jonathan Vos Post, Mar 03 2011

Extensions

a(12)-a(25) from Nathaniel Johnston, Apr 26 2011

Status

approved