A227281 First primes of arithmetic progressions of 5 primes each with the common difference 30.

7, 11, 37, 107, 137, 151, 277, 359, 389, 401, 541, 557, 571, 877, 1033, 1493, 1663, 2221, 2251, 2879, 3271, 6269, 6673, 6703, 7457, 7487, 9431, 10103, 10133, 10567, 11981, 12457, 12973, 14723, 17047, 19387, 24061, 25643, 25673, 26861, 26891, 27337, 27367

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.

For k = 5, we have d = 3# = 6 and there is ONLY one AP-5 with this difference: {5, 11, 17, 23, 29}.

Examples

			p = 11 then {11, 11 + 1*30, 11 + 2*30, 11 + 3*30, 11 + 4*30} = {11, 41, 71, 101, 131}, which is 5 primes in arithmetic progression with the difference 5# = 30.
		

Links

• Sameen Ahmed Khan, Table of n, a(n) for n = 1..1184

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227282, A227283, A227284, A227285, A227286.

Programs

Mathematica

Clear[p]; d = 30; ap5p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d}] == {True, True, True, True, True}, AppendTo[ap5p, p]], {p, 3, 25000, 2}]; ap5p