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
Programs
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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
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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
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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)