A052029 Primes base 10 that remain primes in five bases b, 2<=b<=10, expansions interpreted as decimal numbers.

7, 43, 71, 163, 199, 283, 307, 367, 463, 571, 757, 1033, 1163, 1627, 1873, 2683, 3041, 3691, 3967, 4483, 4651, 4729, 4951, 4973, 5407, 6073, 6961, 7351, 7537, 8053, 8599, 9103, 9817, 10321, 10831, 11251, 11383, 11743, 12433, 12853, 13219, 14419, 14479

Offset: 1

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

Links

• Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
• C. Rivera, PP&P Puzzle 24: Primes in several bases

Crossrefs

Cf. A038537, A052026-A052033.

Programs

Mathematica

Select[Prime[Range@ 1800], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 5 &] (* Michael De Vlieger, Mar 20 2015, after Harvey P. Dale at A052032 *)

PARI

lista(nn, nb=5) = {forprime(p=2, nn, if (sum(b=2, 10, isprime(subst(Pol(digits(p, b)), x, 10))) == nb, print1(p, ", ")););} \\ Michel Marcus, Mar 21 2015