A206040 Values of the difference d for 6 primes in arithmetic progression with the minimal start sequence {7 + j*d}, j = 0 to 5.

30, 150, 930, 2760, 3450, 4980, 9150, 14190, 19380, 20040, 21240, 28080, 33930, 57660, 59070, 63600, 69120, 76710, 80340, 81450, 97380, 100920, 105960, 114750, 117420, 122340, 134250, 138540, 143670, 150090, 164580, 184470, 184620, 189690, 231360, 237060

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 = 150 then {7, 7 + 1*150, 7 + 2*150, 7 + 3*150, 7 + 4*150, 7 + 5*150} = {7, 157, 307, 457, 607, 757} which is 6 primes in arithmetic progression.
		

Links

• Sameen Ahmed Khan, Table of n, a(n) for n = 1..10000
• 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, A206041, A206042, A206043, A206044, A206045.

Programs

Mathematica

a = 7; t = {}; Do[If[PrimeQ[{a, a + d, a + 2*d, a + 3*d, a + 4*d, a + 5*d}] == {True, True, True, True, True, True}, AppendTo[t,d]], {d, 300000}]; t
Select[Range[250000],AllTrue[7+#*Range[0,5],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 26 2017 *)