A084670 Numbers k such that concatenation of prime(k) and k is prime.

3, 9, 19, 21, 37, 63, 77, 81, 87, 107, 121, 133, 177, 201, 211, 213, 217, 281, 293, 303, 321, 327, 329, 333, 351, 391, 393, 439, 481, 503, 507, 519, 543, 547, 551, 561, 579, 581, 599, 621, 639, 657, 663, 667, 711, 721, 727, 743, 793, 813, 819, 827, 829, 831, 837

Offset: 1

Author

Zak Seidov, Jun 29 2003

Keywords

• nonn
• base

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A075110, A084669.

Programs

Mathematica

Select[Range[1000],PrimeQ[Prime[#]10^IntegerLength[#]+#]&] (* Harvey P. Dale, Apr 09 2022 *)

PARI

is(k) = ispseudoprime(eval(Str(prime(k), k))); \\ Jinyuan Wang, Apr 10 2020

Python

from sympy import isprime, prime
def aupto(lim):
  return [k for k in range(1, lim+1) if isprime(int(str(prime(k))+str(k)))]
print(aupto(837)) # Michael S. Branicky, Mar 09 2021

Extensions

More terms from Jinyuan Wang, Apr 10 2020