A100419 Numbers k such that 30*k+{1,7,13,17,19,23,29} are all prime.

89, 6627, 18674, 223949, 229269, 240007, 267356, 606681, 638454, 771496, 951060, 1068030, 1150693, 1254839, 1688923, 1920084, 2413577, 2433289, 2649414, 3053398, 3080572, 3337444, 3586658, 3604256, 3830335, 4137166

Offset: 1

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004

Keywords

• nonn

Comments

Values are 5 mod 7.

In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - Peter Munn, Sep 06 2023

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2020 from Robert Israel)

Crossrefs

Cf. A005776, A007775, A076205, A100418, A100420-A100423.

Programs

Magma

[ n: n in [5..70000000 by 7] | forall{ q: q in [1, 7, 13, 17, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011

Maple

filter:= proc(n) local j; andmap(isprime, [seq(30*n+j,j=[1,7,13,17,19,23,29])]) end proc:
select(filter, [seq(i,i=5..5*10^6,7)]); # Robert Israel, Nov 04 2024

Mathematica

Select[Range[42*10^5],AllTrue[30#+{1,7,13,17,19,23,29},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2018 *)

Extensions

Edited by Don Reble, Nov 17 2005