2687

This number is a prime.

Some primes have only one odd digit - the units digit. There are also twin prime pairs for which this is true. The only two-digit instance is 41 and 43. The record digit sum for such primes thus begins 3, 5, 7 and is unaffected until 227 and 229 when it increases to 11 and then 13. Next stop is 827 and 829 when it rises to 17 and then 19. 2687 and 2689 are the next record holders. 2687 has a digit sum of 23 which is a record for a member of a twin prime pair composed solely of even digits with one odd digit. [Edwards]

Alice must calculate A = g^a (mod 2687) in Secret History: The Story of Cryptology by Craig P. Bauer.