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Numbers k such that 8*k! + 1 is prime.
9

%I #13 Jul 03 2024 19:01:32

%S 2,4,9,10,11,12,15,25,31,46,53,78,318,615,955,1646,2669,2672,3515,7689

%N Numbers k such that 8*k! + 1 is prime.

%C a(20) > 3810. - _Jinyuan Wang_, Feb 05 2020

%C a(21) > 12000. - _Michael S. Branicky_, Jul 03 2024

%H <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes of the form k*n!+-1</a>

%t fQ[n_] := PrimeQ[8 n! + 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst

%o (PARI) for(k=1, 999, ispseudoprime(8*k!+1) & print1(k, ", "))

%o (PFGW) ABC2 8*$a!+1

%o a: from 1 to 1000 // _Jinyuan Wang_, Feb 05 2020

%Y Cf. A002981, A051915, A076679, A076680, A076681, A076682, A076683, A180626, A126896.

%K nonn,hard,more

%O 1,1

%A _Robert G. Wilson v_, Sep 13 2010 and _M. F. Hasler_, Sep 16 2010

%E a(16)-a(19) from _Jinyuan Wang_, Feb 05 2020

%E a(20) from _Michael S. Branicky_, Jul 02 2024