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%I #23 Jan 08 2023 08:19:05
%S 30,150,930,2760,3450,4980,9150,14190,19380,20040,21240,28080,33930,
%T 57660,59070,63600,69120,76710,80340,81450,97380,100920,105960,114750,
%U 117420,122340,134250,138540,143670,150090,164580,184470,184620,189690,231360,237060
%N Values of the difference d for 6 primes in arithmetic progression with the minimal start sequence {7 + j*d}, j = 0 to 5.
%C The computations were done without any assumptions on the form of d.
%H Sameen Ahmed Khan, <a href="/A206040/b206040.txt">Table of n, a(n) for n = 1..10000</a>
%H Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1203.2083">Primes in Geometric-Arithmetic Progression</a>, arXiv preprint arXiv:1203.2083 [math.NT], 2012. - From _N. J. A. Sloane_, Sep 15 2012
%e 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.
%t 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
%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 *)
%Y Cf. A040976, A206037, A206038, A206039, A206041, A206042, A206043, A206044, A206045.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Feb 03 2012
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