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%I #16 Oct 27 2019 12:31:58
%S 60858179,186874511,291297353,1445838451,2943023729,4597225889,
%T 7024895393,8620560607,8656181357,19033631401,20711172773,25366690189,
%U 27187846201,32022299977,34351919351
%N First primes of arithmetic progressions of 11 primes each with the common difference 2310.
%C The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.
%C 16th term is greater than 40*10^9.
%H Zak Seidov, <a href="/A227285/b227285.txt">Table of n, a(n) for n = 1..21</a>
%e p = 186874511 then the AP-11 is {186874511, 186876821, 186879131, 186881441, 186883751, 186886061, 186888371, 186890681, 186892991, 186895301, 186897611} with the difference 11# = 2*3*5*7*11 = 2310.
%t Clear[p]; d = 2310; ap11p = {}; 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}] == {True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap11p, p]], {p, 3, 40*10^9, 2}]; ap11p
%t ap11Q[n_]:=AllTrue[Rest[NestList[2310+#&,n,10]],PrimeQ]; Select[Prime[ Range[ 148*10^7]],ap11Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* The program will take a long time to run *) (* _Harvey P. Dale_, Oct 27 2019 *)
%Y Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227286.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Jul 05 2013
%E a(16)-a(21) from _Zak Seidov_, Jul 07 2014
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