

A206039


Values of the difference d for 5 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 4.


15



6, 12, 42, 48, 96, 126, 252, 426, 474, 594, 636, 804, 1218, 1314, 1428, 1566, 1728, 1896, 2106, 2574, 2694, 2898, 3162, 3366, 4332, 4368, 4716, 4914, 4926, 4962, 5472, 5586, 5796, 5838, 6048, 7446, 7572, 7818, 8034, 8958, 9168, 9204, 9714
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OFFSET

1,1


COMMENTS

The computations were done without any assumptions on the form of d.
All terms are multiples of 6.  Zak Seidov, Jan 07 2014
Equivalently, integers d such that the largest possible arithmetic progression (AP) of primes with common difference d has exactly 5 elements (see example). These 5 elements are not necessarily consecutive primes. In fact, for each term d, there exists only one such AP of primes, and this one always starts with A342309(d) = 5, so this unique AP is (5, 5+d, 5+2d, 5+3d, 5+4d).  Bernard Schott, Jan 25 2023


LINKS

Diophante, A1880. NP en PA (prime numbers in arithmetic progression) (in French).


FORMULA



EXAMPLE

d = 12 then {5, 5 + 1*12, 5 + 2*12, 5 + 3*12, 5 + 4*12} = {5, 17, 29, 41, 53}, which is 5 primes in arithmetic progression.


MAPLE

filter := d > isprime(5+d) and isprime(5+2*d) and isprime(5+3*d) and isprime(5+4*d) : select(filter, [$(1 .. 10000)]); # Bernard Schott, Jan 25 2023


MATHEMATICA

t={}; Do[If[PrimeQ[{5, 5 + d, 5 + 2*d, 5 + 3*d, 5 +4*d}] == {True, True, True, True, True}, AppendTo[t, d]], {d, 10000}]; t
Select[Range[10000], AllTrue[5+#*Range[0, 4], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 09 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



