A038537 Primes base 10 that remain primes in eight bases b, 2<=b<=10, when the expansions are interpreted as decimal numbers.

2, 3, 379081, 59771671, 146752831, 764479423, 1479830551, 3406187401, 5631714889, 7740024337, 8256310441, 8772257161, 9522879913, 10350894331, 12852250993, 14261996563, 16082349433, 16199980009, 17727606151, 18172964503, 18294784903, 19393314433, 19472325391, 20582035993

Offset: 1

Author

Carlos Rivera

Keywords

• nonn
• base
• hard
• nice

Links

• Sebastian Petzelberger, Table of n, a(n) for n = 1..54 (terms up to 10^12).
• Carlos Rivera, Puzzle 24: Primes in several bases, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A052026, A038537, A052027-A052033, A084482, A236356

Programs

Mathematica

Select[Prime[Range@ 50000], Count[PrimeQ /@ Table[FromDigits[IntegerDigits[#, i]], {i, 2, 10}], True] == 8 &] (* Michael De Vlieger, Mar 20 2015, after Harvey P. Dale at A052032 *)

Extensions

a(4)-a(7) found by Jack Brennen (see link) added by Patrick De Geest, Dec 15 1999

Terms beyond a(7) from Sebastian Petzelberger, Mar 21 2015