A309871 Numbers n for which 18n+1, 18n+5, 18n+7, 18n+11, 18n+13 and 18n+17 are primes.

892, 2432, 156817, 806697, 822937, 1377022, 1389412, 1418007, 1619642, 1753552, 2017732, 2058647, 2329302, 2554142, 2703347, 3058772, 3135107, 3326522, 3391797, 3723457, 4126867, 4132782, 4171422, 4411837, 4610252, 6378487, 6440087, 6878987, 6897782, 6991547

Offset: 1

Author

Ely Golden, Aug 21 2019

Keywords

• nonn

Links

• Ely Golden, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A123986, A056956, A007811, A123985.

Programs

Mathematica

tot[n_] := Select[Range[n], CoprimeQ[#, n] &]; m = 18; t = tot[m]; aQ[n_] := AllTrue[m * n + t, PrimeQ]; Select[Range[10^6], aQ] (* Amiram Eldar, Aug 22 2019 *)

SageMath

x = 1
for i in range(5000000):
    if (18*i+1 in Primes()
    and 18*i+5 in Primes()
    and 18*i+7 in Primes()
    and 18*i+11 in Primes()
    and 18*i+13 in Primes()
    and 18*i+17 in Primes()):
        print(str(x)+" "+str(i))
        x += 1