113

This number is a prime.

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113^2 + 131^2 = 173^2 + 1, where 113, 131, 173 are three consecutive Sophie Germain primes. Is this unique? [Gaydos]

The highest named prime-numbered chemical element is now Nihonium, atomic number 113. If you replace each letter in its name with its numeric position in the alphabet you get 1498151492113 (a prime number ending in 113). [Gaydos]

The sum of the first 113 Honaker numbers (32, 56, 88, 175, ...) is a perfect square. [Gaydos]

138 is both the 113th unhappy number and the 113th distinct digit number. [Gaydos]

The 113th Lucky number plus 113 equals the 113th Happy number. [Gaydos]

113 (exactly 1/13) of the first one thousand four hundred sixty-nine positive integers are palindromes. [Gaydos]

There are 113 distinct-digit numbers n for which n and n+9 have no digits in common. [Gaydos]

113 is the smallest prime number that has the same Collatz trajectory length as a smaller prime. [Gaydos]