A385056 Prime numbers whose digit product is a positive cube.

11, 139, 181, 193, 241, 389, 421, 811, 839, 881, 983, 1181, 1193, 1319, 1777, 1811, 1913, 1931, 1999, 2141, 2221, 2269, 2411, 2663, 3119, 3191, 3313, 3331, 3463, 3643, 3833, 3889, 3911, 4211, 4363, 4441, 4691, 6229, 6263, 6343, 6491, 6661, 7177, 7717, 7877, 8111

Offset: 1

Author

Mohd Anwar Jamal Faiz, Jun 16 2025

Keywords

• nonn
• base

Crossrefs

Intersection of A000040 and A237767.

Subsequence of A038618.

Cf. A184328.

Programs

Maple

q:= n-> isprime(n) and (p-> p>0 and iroot(p, 3)^3=p)(mul(i, i=convert(n, base, 10))):
select(q, [$2..10000])[];  # Alois P. Heinz, Jun 16 2025

Mathematica

q[n_] := Module[{pd = Times @@ IntegerDigits[n]}, pd > 0 && IntegerQ[Surd[pd, 3]]]; Select[Prime[Range[1300]], q] (* Amiram Eldar, Jun 16 2025 *)

PARI

isok(k) = if (isprime(k), my(p=vecprod(digits(k))); p && ispower(p, 3)); \\ Michel Marcus, Jun 16 2025

Python

from sympy import primerange, integer_nthroot
from math import prod
is_cube = lambda n: n > 0 and integer_nthroot(n, 3)[1]
digit_product = lambda n: prod(map(int, str(n)))
cubigit_primes = [p for p in primerange(2, 100000) if is_cube(dp := digit_product(p))]
print(cubigit_primes)