109

This number is a prime.

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109 is the sum of the first four prime-indexed Fibonacci primes (2 + 5 + 13 + 89), and is itself prime. In Zeckendorf representation: 109 = F₃ + F₅ + F₇ + F₁₁. [Ahmed]

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]