A227283 First primes of arithmetic progressions of 8 primes each with the common difference 210.

199, 409, 619, 881, 3499, 3709, 10627, 10859, 11069, 30097, 31583, 120661, 120737, 153319, 182537, 471089, 487391, 564973, 565183, 825991, 1010747, 1280623, 1288607, 1288817, 1302281, 1302491, 1395209, 1982599, 2358841, 2359051, 2439571, 3161017, 3600521

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.

Links

• Sameen Ahmed Khan, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227284, A227285, A227286.

Programs

Mathematica

Clear[p]; d = 210; ap8p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d}] == {True, True, True, True, True, True, True, True}, AppendTo[ap8p, p]], {p, 3, 3000000, 2}]; ap8p
Select[Prime[Range[260000]],AllTrue[NestList[#+210&,#,7],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 03 2018 *)