A227285 First primes of arithmetic progressions of 11 primes each with the common difference 2310.

60858179, 186874511, 291297353, 1445838451, 2943023729, 4597225889, 7024895393, 8620560607, 8656181357, 19033631401, 20711172773, 25366690189, 27187846201, 32022299977, 34351919351

Offset: 1

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

• nonn

Comments

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7.

16th term is greater than 40*10^9.

Examples

			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.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..21

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227286.

Programs

Mathematica

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
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 *)

Extensions

a(16)-a(21) from Zak Seidov, Jul 07 2014