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%I #11 Jul 06 2013 02:29:55
%S 81647160420,170655787050,211212209880,227961624450
%N Values of the difference d for 12 primes in geometric-arithmetic progression with the minimal sequence {13*13^j + j*d}, j = 0 to 11.
%C Primality requires d to be multiple of 7# = 2*3*5*7 = 210.
%C Fifth term is > (1600*10^6)*(210) = 336000000000.
%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1203.2083/">Primes in Geometric-Arithmetic Progression</a>, arXiv:1203.2083v1 [math.NT], (Mar 09 2012).
%e d = 170655787050 then {13*13^j + j*d}, j = 0 to 11, is {13, 170655787219, 341311576297, 511967389711, 682623519493, 853283762059, 1023997470817, 1195406240071, 1375850795773, 1673760575299, 3498718264537, 25175298780031}, which is 12 primes in geometric-arithmetic progression.
%t Clear[p]; p = 13; gapset12d = {}; Do[If[PrimeQ[{p, p*p + d, p*p^2 + 2*d, p*p^3 + 3*d, p*p^4 + 4*d, p*p^5 + 5*d, p*p^6 + 6*d, p*p^7 + 7*d, p*p^8 + 8*d, p*p^9 + 9*d, p*p^10 + 10*d, p*p^11 + 11*d}] == {True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[gapset12d, d]], {d, 2, 10^11, 2}]; gapset12d
%Y Cf. A172367, A209202, A209203, A209204, A209205, A209206, A209207, A209208, A209209, A209210.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Jul 05 2013
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