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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A017350 A017470 A017602 * A172584 A210354 A309062

Adjacent sequences: A227282 A227283 A227284 * A227286 A227287 A227288

Keyword

nonn

Author

Sameen Ahmed Khan, Jul 05 2013

Extensions

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

Status

approved