A100422 Numbers n such that 30*n+{1,7,11,13,17,23,29} are all prime.

1, 53887, 114731, 123306, 139742, 210554, 471745, 480859, 619039, 630862, 858929, 1075873, 1306614, 1714945, 1913514, 2767458, 3014285, 3454137, 3518243, 3699151, 3864512, 3874291, 4274376, 4862362, 4878329, 4937822

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

Values are 1 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-A100423.

Programs

Magma

[ n: n in [0..5000000] | forall{ q: q in [1, 7, 11, 13, 17, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 23 2011

Maple

a:= proc(n) option remember;
      local m;
      if n=1 then 1
      else for m from 30*(a(n-1)+7) by 210
           while not (isprime (m+1) and isprime (m+7) and
                 isprime (m+11) and isprime (m+13) and
                 isprime (m+17) and isprime (m+23) and
                 isprime (m+29))
           do od; m/30
        fi
    end:
seq (a(n), n=1..10);

Mathematica

Select[Range[5000000],And@@PrimeQ/@(30(#)+{1,7,11,13,17,23,29})&]  (* Harvey P. Dale, Feb 23 2011 *)

Extensions

Edited by Don Reble, Nov 17 2005