smallest prime divisor

Lets try a list of primes

2: 5^23 is odd 2^23 is even No

3: 5^23 is -1mod3 2^23 is -1mod3 No

5.: 5^23 is divisible by 5 2^23 is not No

7: 5 and 2 are additive inverses mod 7. Exponent is odd. Yessssss

:D