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A036937
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Smallest n-digit prime containing only digits 2 and 3.
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5
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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
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1,1
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COMMENTS
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It is conjectured that such a prime exists for every value of n.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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