A036937 - OEIS

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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

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OFFSET

1,1

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

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 *)

PROG

(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

CROSSREFS