113 (one hundred [and] thirteen) is the natural number following 112 and preceding 114.
Mathematics 113 is a prime number, a Sophie Germain prime, an emirp, an isolated prime, a Chen prime, a highly cototient number, a centered square number, and a Proth prime as it is a prime number of the form 113 is also an Eisenstein prime with no imaginary part and real part of the form . In decimal, this prime is a primeval number and a permutable prime with 131 and 311.
113 is the denominator of 355/113, an accurate approximation to .
is the smallest generalized Fermat prime with odd base and .
The ratio , where is the prime-counting function, attains its maximum value of at .
References
Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134