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%I #14 Jul 01 2014 15:38:34
%S 14933623,2085471361,132420258931,185041386139,682539280751,
%T 834172298383,834172328413,856378247603,856378277633,888867525577,
%U 931115864233,1059709587163,1345030977911,1360910561113,1578280523803,1973348047529,1988253536611,2083502941613
%N First primes of arithmetic progressions of 13 primes each with the common difference 30030.
%C The minimal possible difference in an arithmetic progression of k primes is conjectured to be k# = A034386(k) for all k > 7. 13# = 30030.
%e p = 2085471361 then the AP-13 is {2085471361, 2085501391, 2085531421, 2085561451, 2085591481, 2085621511, 2085651541, 2085681571, 2085711601, 2085741631, 2085771661, 2085801691, 2085831721} with the difference 13# = 2*3*5*7*11*13 = 30030.
%t Clear[p]; d = 30030; ap13p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d, p + 11*d, p + 12*d}] == {True, True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap13p, p]], {p, 3, 41*10^9, 2}]; ap13p
%Y Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227285.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Jul 05 2013
%E More terms from _Jens Kruse Andersen_, Jun 27 2014