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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{k = (10^n - 1)/9}, While[id = IntegerDigits@k; First@ Union@ id == 0 || !PrimeQ[Plus @@ Table[FromDigits@ Take[id, {1, k}]^FromDigits@ Take[id, {k + 1, n}], {k, n - 1}]], k++ ]; k]; Do[Print[f[n]] // Timing, {n, 2, 7}] - _(* _Robert G. Wilson v_, Apr 27 2006 *)
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(Python)
from sympy import isprime
from itertools import product
def a(n):
for p in product("123456789", repeat=n):
s = "".join(p)
if isprime(sum(int(s[:i])**int(s[i:]) for i in range(1, n))):
return int(s)
print([a(n) for n in range(2, 6)]) # Michael S. Branicky, Jun 27 2022
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a(n) is the smallest n-digit integer such that, if all numbers formed by inserting the exponentation exponentiation symbol between any two digits are added up, the sum is prime.
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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{k = (10^n - 1)/9}, While[id = IntegerDigits@k; First@ Union@ id == 0 || !PrimeQ[Plus @@ Table[FromDigits@ Take[id, {1, k}]^FromDigits@ Take[id, {k + 1, n}], {k, n - 1}]], k++ ]; k]; Do[Print[f[n]] // Timing, {n, 2, 7}] - _Robert G. Wilson v (rgwv(at)rgwv.com), _, Apr 27 2006
a(6) from _Robert G. Wilson v (rgwv(at)rgwv.com) _ and Farideh Firoozbakht, Apr 27 2006