109

This number is a prime.

109 is the smallest multidigit prime that is the digit sum of both p^p − (p−1)^(p−1) and p^(p−1) + (p−1)^(p−1) for a prime p. This occurs when p = 19, as both 19¹⁹ − 18¹⁸ and 19¹⁸ + 18¹⁸ have digit sum 109. Curiously, the same digit sum is also obtained from 37¹⁸ − 18¹⁸ and 37¹⁹ + 18¹⁸ where 37=19+18. [Ahmed]