|
%I #44 Jan 08 2023 08:18:56
%S 1210230,2523780,4788210,10527720,12943770,19815600,22935780,28348950,
%T 28688100,32671170,43443330,47330640,51767520,54130440,59806740,
%U 60625110,63721770,66761940,77811300,80892420,87931620,90601140,102994500,108310650,115209570,117639480
%N Values of the difference d for 8 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 7.
%C The computations were done without any assumptions on the form of d.
%H Sameen Ahmed Khan, <a href="/A206042/b206042.txt">Table of n, a(n) for n = 1..210</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 = 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.
%t 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},
%t AppendTo[t,d]], {d, 0, 200000000}]; t
%t Select[Range[117640000],AllTrue[11+#*Range[0,7],PrimeQ]&] (* _Harvey P. Dale_, Dec 31 2021 *)
%Y Cf. A040976, A206037, A206038, A206039, A206040, A206041, A206043, A206044, A206045.
%K nonn
%O 1,1
%A _Sameen Ahmed Khan_, Feb 03 2012
|
