A348699 Primes with a prime number of prime digits.

23, 37, 53, 73, 127, 137, 157, 173, 223, 227, 229, 233, 239, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 433, 457, 503, 521, 523, 547, 557, 563, 571, 577, 587, 593, 653, 673, 677, 727, 733, 739, 743, 751, 757, 773, 787, 797

Offset: 1

Author

Jens Ahlström, Oct 30 2021

Keywords

• base
• easy
• nonn

Links

• Jens Ahlström, Table of n, a(n) for n = 1..5853 (all terms < 10^5)
• Hackerearth, Optimus prime

Crossrefs

Intersection of A000040 and A092619.

Cf. A217090.

Programs

Mathematica

Select[Range[800], And @@ PrimeQ[{#, Count[IntegerDigits[#], ?PrimeQ]}] &] (* _Amiram Eldar, Nov 04 2021 *)

Python

from sympy import isprime as i
from sympy import primerange as p
print([x for x in p(1, 800) if i(len([d for d in str(x) if i(int(d))]))])

Python

from sympy import isprime
def ok(n): return isprime(n) and isprime(sum(1 for d in str(n) if d in "2357"))
print([k for k in range(800) if ok(k)]) # Michael S. Branicky, Jun 26 2025