A084671 Primes such that the decimal concatenation of prime(n) and n is prime.

5, 23, 67, 73, 157, 307, 389, 419, 449, 587, 661, 751, 1051, 1229, 1297, 1303, 1327, 1823, 1913, 1999, 2131, 2179, 2207, 2239, 2371, 2689, 2699, 3067, 3433, 3593, 3623, 3719, 3919, 3943, 4001, 4073, 4229, 4241, 4397, 4591, 4733, 4919, 4957, 4987, 5393, 5449, 5503

Offset: 1

Author

Zak Seidov, Jun 29 2003

Keywords

• nonn
• base

Examples

			23 is a term because 23=prime(9) and concatenation of 23 and 9 is prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Programs

Mathematica

a=ParallelTable[Prime[k],{k,1,10^6}];k=2;Monitor[Parallelize[While[True,If[ToExpression[StringJoin[ToString/@{k,FromDigits[Position[a,k]//Flatten]}]]//PrimeQ,Print[k]];k++];k],k] (* J.W.L. (Jan) Eerland, Dec 22 2022 *)

Python

from itertools import islice
from sympy import isprime, sieve
def agen(): yield from (pn for n, pn in enumerate(sieve, 1) if isprime(int(str(pn)+str(n))))
print(list(islice(agen(), 52))) # Michael S. Branicky, Dec 22 2022

Extensions

Edited by Charles R Greathouse IV, Apr 27 2010

a(45)-a(52) from J.W.L. (Jan) Eerland, Dec 22 2022