A103144 Decimal primes whose decimal representation in hex is also prime.

2, 3, 5, 7, 11, 13, 17, 29, 43, 47, 53, 59, 61, 67, 71, 83, 89, 97, 101, 107, 137, 139, 151, 167, 191, 199, 223, 233, 239, 241, 251, 257, 269, 277, 281, 283, 293, 313, 337, 347, 359, 373, 397, 409, 419, 443, 449, 463, 503, 509, 557, 577, 593, 599, 607, 617, 641

Offset: 1

Author

Lei Zhou, Jan 26 2005

Keywords

• easy
• nonn
• base

Examples

			11 is prime, Hex(11) = 17 is prime, hence 11 is in the sequence.
		

Links

• Andreas Boe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A089971.

Programs

MATLAB

a = primes(300000); j = 0; for i = 1:19000 b = dec2hex(a(i)); c = num2str(b); d = str2num(c); if d < 2^32 if isprime(d) j = j + 1; e(j) = d; end; end; end;

Mathematica

Select[Prime@ Range@ 120, PrimeQ@ FromDigits[IntegerDigits@ #, 16] &] (* Michael De Vlieger, Nov 05 2018 *)

PARI

isok(p) = isprime(p) && isprime(fromdigits(digits(p), 16)); \\ Michel Marcus, Nov 05 2018

Python

from sympy import isprime
def ok(n): return isprime(n) and isprime(int(str(n), 16))
print([k for k in range(642) if ok(k)]) # Michael S. Branicky, Dec 04 2022