A381126 Primes that are the concatenation of prime(p) and p where p is a prime.

53, 6719, 15737, 587107, 1297211, 1823281, 1913293, 3067439, 3593503, 3943547, 4397599, 5503727, 5651743, 6353827, 6361829, 6823877, 7109911, 7283929, 7523953, 85131061, 85271063, 87611093, 88071097, 104331277, 125031493, 128411531, 130031549, 133311583, 141071663

Offset: 1

Author

Maja Gwozdz, Feb 14 2025

Keywords

• nonn
• base

Examples

			1297211 is a term since it is prime and is the concatenation of prime(p) = 1297 and p = 211.
		

Links

• Wikipedia, Super-prime

Crossrefs

Subsequence of A084669.

Cf. A006450, A084667, A229814.

Programs

Maple

f:= p-> (h-> `if`(andmap(isprime, [p, h]), h, [][]))(parse(cat(ithprime(p), p))):
map(f, [$1..2000])[];  # Alois P. Heinz, Feb 15 2025

PARI

a381126(limit) = {forprime (p=2, limit, my(pd=digits(p), ppd=digits(prime(p)), pc=fromdigits(concat(ppd,pd))); if(isprime(pc), print1(pc,", ")))};
a381126(2000) \\ Hugo Pfoertner, Feb 14 2025

Python

from sympy import isprime, primerange, prime
def a(limit: int) -> list[int]:
    result: list[int] = []
    for p in primerange(2, limit):
        pth_prime = prime(p)
        rc_val = int(f"{pth_prime}{p}")
        if isprime(rc_val):
            result.append(rc_val)
    return result
print(a(1700))