A059925 Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime.

1006301, 2594951, 3919211, 9600551, 10531061, 108816311, 131445701, 152370731, 157131641, 179028761, 211950251, 255352211, 267587861, 557458631, 685124351, 724491371, 821357651, 871411361, 1030262081, 1103104361, 1282160021, 1381201271, 1427698631, 1432379951, 1443994001

Offset: 1

Author

Martin Raab, Mar 03 2001

Keywords

• nonn

Comments

Each term is the initial member of two prime quadruples (A007530) with the smallest possible difference of 30.

Links

• Jud McCranie and Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 (first 1238 terms from Jud McCranie)
• J. Brüggemann, The twins of prime quadruples up to 10^17 [71 MB].
• D. La Pierre Ballard, Prime Number Quadruplets 30 Apart

Crossrefs

Cf. A007530, A256842.

Programs

Mathematica

Select[Prime[Range[5582*10^4]],AllTrue[#+{2,6,8,30,32,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2019 *)

PARI

is(n)=my(v=[0,2,6,8,30,32,36,38]);for(i=1,8, if(!isprime(n+v[i]), return(0)));1 \\ Charles R Greathouse IV, Jun 18 2013

Formula

a(n) = 2 (mod 21). - Hugo Pfoertner, Dec 29 2024

Extensions

For clarity, replaced definition by a comment from Charles R Greathouse IV. - N. J. A. Sloane, Nov 26 2020