A036937 Smallest n-digit prime containing only digits 2 and 3.

2, 23, 223, 2333, 23333, 222323, 2222333, 22222223, 222323333, 2222232323, 22222222223, 222222333323, 2222222222323, 22222222223323, 222222222332233, 2222222222323223, 22222222222233323, 222222222222233323, 2222222222222233333, 22222222222222232233

Offset: 1

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base

Comments

It is conjectured that such a prime exists for every value of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..400
• Robert G. Wilson v, Comments and first 121 terms

Crossrefs

Cf. A036229, A020458, A036310, A069841.

Programs

Mathematica

Do[p = 2(10^n - 1)/9; k = 0; While[ ! PrimeQ[p], k++; p = FromDigits[ PadLeft[ IntegerDigits[k, 2], n] + 2]]; Print[p], {n, 1, 30}] (* Robert G. Wilson v, Apr 20 2002 *)
Table[SelectFirst[FromDigits/@Tuples[{2,3},n],PrimeQ],{n,20}] (* Harvey P. Dale, Nov 07 2021 *)

Python

from sympy import isprime
from itertools import product
def a(n):
  for b in product("01", repeat=n):
    m = int("".join(b).replace("0", "2").replace("1", "3"))
    if isprime(m): return m
  return None
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Feb 23 2021 after Robert G. Wilson v

Extensions

Edited by Jon E. Schoenfield, Mar 27 2014