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A206040
Values of the difference d for 6 primes in arithmetic progression with the minimal start sequence {7 + j*d}, j = 0 to 5.
8
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
1,1
COMMENTS
The computations were done without any assumptions on the form of d.
LINKS
Sameen Ahmed Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083 [math.NT], 2012. - From N. J. A. Sloane, Sep 15 2012
EXAMPLE
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.
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 *)
KEYWORD
nonn
AUTHOR
Sameen Ahmed Khan, Feb 03 2012
STATUS
approved