A206042 Values of the difference d for 8 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 7.

1210230, 2523780, 4788210, 10527720, 12943770, 19815600, 22935780, 28348950, 28688100, 32671170, 43443330, 47330640, 51767520, 54130440, 59806740, 60625110, 63721770, 66761940, 77811300, 80892420, 87931620, 90601140, 102994500, 108310650, 115209570, 117639480

Offset: 1

Author

Sameen Ahmed Khan, Feb 03 2012

Keywords

• nonn

Comments

The computations were done without any assumptions on the form of d.

Examples

			d = 2523780 then {11 + j*d}, j = 0 to 7, is {11, 2523791, 5047571, 7571351, 10095131, 12618911, 15142691, 17666471} which is 8 primes in arithmetic progression.
		

Links

• Sameen Ahmed Khan, Table of n, a(n) for n = 1..210
• Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083 [math.NT], 2012. - From _N. J. A. Sloane_, Sep 15 2012

Crossrefs

Cf. A040976, A206037, A206038, A206039, A206040, A206041, A206043, A206044, A206045.

Programs

Mathematica

a = 11; t = {}; Do[If[PrimeQ[{a, a + d, a + 2*d, a + 3*d, a + 4*d, a + 5*d, a + 6*d, a + 7*d}] == {True, True, True, True, True, True, True, True},
   AppendTo[t,d]], {d, 0, 200000000}]; t
Select[Range[117640000],AllTrue[11+#*Range[0,7],PrimeQ]&] (* Harvey P. Dale, Dec 31 2021 *)