A227286 First primes of arithmetic progressions of 13 primes each with the common difference 30030.

14933623, 2085471361, 132420258931, 185041386139, 682539280751, 834172298383, 834172328413, 856378247603, 856378277633, 888867525577, 931115864233, 1059709587163, 1345030977911, 1360910561113, 1578280523803, 1973348047529, 1988253536611, 2083502941613

Offset: 1

Author

Sameen Ahmed Khan, Jul 05 2013

Keywords

• nonn

Comments

The minimal possible difference in an arithmetic progression of k primes is conjectured to be k# = A034386(k) for all k > 7. 13# = 30030.

Examples

			p = 2085471361 then the AP-13 is {2085471361, 2085501391, 2085531421, 2085561451, 2085591481, 2085621511, 2085651541, 2085681571, 2085711601, 2085741631, 2085771661, 2085801691, 2085831721} with the difference 13# = 2*3*5*7*11*13 = 30030.
		

Crossrefs

Cf. A001359, A023241, A023271, A094220, A156204, A227281, A227282, A227283, A227284, A227285.

Programs

Mathematica

Clear[p]; d = 30030; ap13p = {}; 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, p + 11*d, p + 12*d}] == {True, True, True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap13p, p]], {p, 3, 41*10^9, 2}]; ap13p

Extensions

More terms from Jens Kruse Andersen, Jun 27 2014