113 (number)

Template:Infobox number 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 $7\times 2^4+1.$ 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 the denominator of 355/113, an accurate approximation to Template:Pi.

$F_7(113)=\frac{113^{128}+1}{2}$ is the smallest generalized Fermat prime with odd base and $k\ge 7$.

References

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