A381878 Prime numbers p such that the sum of the d_i-th prime numbers, where (d_i) are the nonzero digits of p, is also a prime.

2, 3, 5, 7, 13, 17, 31, 71, 103, 107, 181, 211, 223, 227, 229, 233, 239, 257, 277, 293, 347, 383, 389, 433, 443, 449, 467, 479, 487, 499, 523, 563, 569, 587, 647, 653, 659, 677, 683, 701, 727, 743, 769, 787, 811, 839, 857, 859, 863, 877, 883, 947, 967, 983

Offset: 1

Author

Jean-Marc Rebert, Mar 09 2025

Keywords

• nonn
• base
• less

Examples

			13 is a term, because prime(1) + prime(3) = 2 + 5 = 7 is prime.
		

Crossrefs

Cf. A046704, A052034.

Programs

Mathematica

Select[Prime[Range[170]], PrimeQ[Total[Prime[DeleteCases[IntegerDigits[#],0]]]] &] (* Stefano Spezia, Mar 09 2025 *)

Python

from sympy import isprime, prime
def ok(p): return isprime(p) and isprime(sum(prime(di) for di in map(int, str(p)) if di))
print([k for k in range(1, 999) if ok(k)]) # Michael S. Branicky, Mar 09 2025