

A227285


First primes of arithmetic progressions of 11 primes each with the common difference 2310.


6



60858179, 186874511, 291297353, 1445838451, 2943023729, 4597225889, 7024895393, 8620560607, 8656181357, 19033631401, 20711172773, 25366690189, 27187846201, 32022299977, 34351919351
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OFFSET

1,1


COMMENTS

The minimal possible difference in an APk is conjectured to be k# for all k > 7.
16th term is greater than 40*10^9.


LINKS



EXAMPLE

p = 186874511 then the AP11 is {186874511, 186876821, 186879131, 186881441, 186883751, 186886061, 186888371, 186890681, 186892991, 186895301, 186897611} with the difference 11# = 2*3*5*7*11 = 2310.


MATHEMATICA

Clear[p]; d = 2310; ap11p = {}; Do[If[PrimeQ[{p, p + d, p + 2*d, p + 3*d, p + 4*d, p + 5*d, p + 6*d, p + 7*d, p + 8*d, p + 9*d, p + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, AppendTo[ap11p, p]], {p, 3, 40*10^9, 2}]; ap11p
ap11Q[n_]:=AllTrue[Rest[NestList[2310+#&, n, 10]], PrimeQ]; Select[Prime[ Range[ 148*10^7]], ap11Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* The program will take a long time to run *) (* Harvey P. Dale, Oct 27 2019 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



