A107692 Primes whose product of digits is 6.

23, 61, 1123, 1213, 1231, 1321, 2113, 2131, 2311, 3121, 11161, 11213, 11321, 12113, 13121, 16111, 31121, 111611, 611111, 1111213, 1112113, 1112131, 1131121, 1211311, 2111311, 3112111, 11111161, 11112113, 11211131, 11231111, 11312111

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, May 20 2005

Keywords

• base
• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10199 (all terms with <= 136 digits; terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A004022, A107612, A107689, A107690, A107691, A107693, A107694, A107695.

Cf. A107696, A107697, A107698.

Programs

Mathematica

Union[ Flatten[ Table[ Select[ Sort[ FromDigits /@ Join[ Permutations[ Flatten[{6, Table[1, {n}]}]], Permutations[ Flatten[{2, 3, Table[ 1, {n - 1}]}] ]]], PrimeQ[ # ] &], {n, 0, 7}]]]
Select[Prime[Range[750000]],Times@@IntegerDigits[#]==6&] (* Harvey P. Dale, May 29 2016 *)

Python

from sympy import prod, isprime
from sympy.utilities.iterables import multiset_permutations
def agen(maxdigits):
    for digs in range(1, maxdigits+1):
        for mp in multiset_permutations("1"*(digs-1) + "236", digs):
            if prod(map(int, mp)) == 6:
                t = int("".join(mp))
                if isprime(t): yield t
print(list(agen(8))) # Michael S. Branicky, Jun 16 2021