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A100421
Numbers n such that 30*n+{1,7,11,13,19,23,29} are all prime.
1
2, 79, 391701, 505017, 740413, 787187, 933025, 1169863, 1333719, 1406792, 2212261, 2719950, 2962738, 3125992, 3284955, 3384586, 3727271, 3821295, 3861881, 4320864, 4439878, 4764356, 5014865, 5480190, 5879274, 6124442
OFFSET
1,1
COMMENTS
Values are 2 mod 7.
In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - Peter Munn, Sep 06 2023
MATHEMATICA
Select[Range[7*10^6], AllTrue[30#+{1, 7, 11, 13, 19, 23, 29}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 16 2016 *)
PROG
(Magma) [ n: n in [2..70000000 by 7] | forall{ q: q in [1, 7, 11, 13, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011
KEYWORD
easy,nonn
AUTHOR
Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004
EXTENSIONS
Edited by Don Reble, Nov 17 2005
STATUS
approved