113

This number is a prime.

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The smallest emirp that has an emirp number of composites between it and the next prime. [Honaker]

113 is the sum of all "hints" in a Sudoku created by Finnish mathematician Arto Inkala which he claims is the hardest ever. This can be shown by the fact that 113 appears 14 seconds into the video "Alone Again" by hard rock band Dokken. Corollary: Three hundred fifty-five divided by 113. Q.E.D. [Honaker]