A100423 Numbers n such that 30*n+{1,7,11,13,17,19,29} are all prime.

62, 188, 9491, 31982, 38226, 38520, 89459, 168237, 175125, 368248, 471078, 634892, 704416, 803102, 994748, 1436315, 1488857, 1605484, 1842553, 1945824, 2282958, 2465266, 2620715, 2627029, 2705037, 4282305, 5569899, 5914824

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

Values are 6 mod 7.

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

Crossrefs

Cf. A005776, A007775, A076205, A100418-A100422.

Programs

Magma

[ n: n in [0..6000000] | forall{ q: q in [1, 7, 11, 13, 17, 19, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011

Mathematica

Select[Range[6*10^6],AllTrue[30#+{1,7,11,13,17,19,29},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 21 2021 *)

Extensions

Edited by Don Reble, Nov 17 2005