A206043 Values of the difference d for 9 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 8.

32671170, 54130440, 59806740, 145727400, 224494620, 246632190, 280723800, 301125300, 356845020, 440379870, 486229380, 601904940, 676987920, 777534660, 785544480, 789052530, 799786890, 943698210, 1535452800, 1536160080, 1760583300, 1808008020

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 = 54130440 then {11, 54130451, 108260891, 162391331, 216521771, 270652211, 324782651, 378913091, 433043531} which is 9 primes in arithmetic progression.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1419
• 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, A206042, 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, a + 8*d}] == {True, True, True, True, True, True, True, True, True}, AppendTo[t,d]], {d, 10^9}]; t

PARI

forstep(k=210,1e10,210,forstep(p=k+11,8*k+11,k,if(!isprime(p), next(2)));print1(k", ")) \\ Charles R Greathouse IV, Feb 09 2012

Extensions

a(20) corrected by Charles R Greathouse IV, Feb 09 2012