113 (number)

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

Mathematics

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