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,^[1] a Chen prime^[2] and a Proth prime as it is a prime number of the form 7 × 2⁴ + 1. 113 is also an Eisenstein prime with no imaginary part and real part of the form $3n-1$ . In base 10, 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]
355/113 approximates pi to six decimal places, with an error of less than 1/113³. This means that 113/355 approximates the reciprocal of pi.
113 is the smallest positive integer that cannot be represented in the Four fours problem using standard rules. ^{[clarification needed]}^{[dubious – discuss]}

113, the number of surah al-Falaq in the Qur'an
Psalms 113–118 constitute the Hallel, which is recited on the three great feasts: Passover, Weeks, and Tabernacles

113 is:

113 (band), a French hip hop group
113, the port number of the IDENT Internet protocol that helps identify the user of a particular TCP connection
113, in enduro, is regarded as an unlucky number to be given to a race entrant and is colloquially known as a "blind pew"

^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
^ "Sloane's A109611 : Chen primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
^ "Sloane's A072857 : Primeval numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.
^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-26.