113 (one hundred [and] thirteen) is the natural number following 112 and preceding 114.

• 113 is the 30th prime number (following 109 and preceding 127), so it can only be divided by one and itself. 113 is the smallest prime number before a prime gap of length 14. 113 is a Sophie Germain prime,^[1] an emirp, an isolated prime, a Chen prime^[2] and a Proth prime as it is a prime number of the form ${\displaystyle 7\times 2^{4}+1.}$ 113 is also an Eisenstein prime with no imaginary part and real part of the form ${\displaystyle 3n-1}$. In decimal, this prime is a primeval number^[3] and a permutable prime with 131 and 311.
• 113 is a highly cototient number^[4] and a centered square number.^[5]
• 113 is the denominator of 355/113, an accurate approximation to π.

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134

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