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%I #32 Jul 23 2023 01:52:56
%S 1917214927,1917281213,2540118761,2560601663,2977271357,3059526377,
%T 3868900621,4211712397,4237592851,4823026847,4899889741,5120099581,
%U 5719551907,5822257871,5880593053,6362295487
%N Primes p > 3 such that p+6*k is composite for all k from 1 to 100.
%C In some sense this is the opposite to the problem of (consecutive) primes in the arithmetic progression PAP or CPAP.
%C Note that in many cases p + 6*k are composite for k = 1..m with m > 100.
%C Maximal found value of m = 148 for a(615) = 50100585793 = prime(2123734960).
%C Is it possible to find primes p giving, say, thousand composites p+6*k, k = 1..1000 or even more?
%C Of course we exclude the cases p = 2 and 3 as they give an infinite number of composites of the form p + 6*k.
%H Zak Seidov, <a href="/A233002/b233002.txt">Table of n, a(n) for n = 1..2035</a> (all terms up to 10^11)
%e 1917214927 + {6, 12, 18, 24, ..., 600} are all composite.
%t Select[Prime[Range[3*10^8]],AllTrue[#+6*Range[100],CompositeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 25 2018 *)
%K nonn,more
%O 1,1
%A _Zak Seidov_, Dec 03 2013
%E First two terms prepended by _Harvey P. Dale_, Mar 25 2018
%E 2, 3 removed again by _Georg Fischer_, Jan 20 2019