• 113 is the smallest natural number that cannot be obtained using four 4's, the common arithmetic operations, factorial, roots, and the notations and .

113 has 2 divisors, whose sum is σ = 114. Its totient is φ = 112.

The previous prime is 109. The next prime is 127. The reversal of 113 is 311.

113 is nontrivially palindromic in base 8.

113 is an esthetic number in base 13 and base 15, because in such bases its adjacent digits differ by 1.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 64 + 49 = 8^2 + 7^2 .

113 is a truncatable prime.

It is an emirp because it is prime and its reverse (311) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 113 - 2^{2} = 109 is a prime.

It is a Sophie Germain prime.

It is a Chen prime.

113 is an undulating number in base 8.

It is a Curzon number.

It is the 6-th primeval number, because it sets a new record (7) in the number of distinct primes that is it possible to write using its digits.

It is a plaindrome in base 9, base 10, base 13 and base 15.

It is a nialpdrome in base 7, base 11, base 12, base 14 and base 16.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 97 and 106.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 56 + 57.

It is an arithmetic number, because the mean of its divisors is an integer number (57).

It is a Proth number, since it is equal to 7 ⋅ 2^{4} + 1 and 7 < 2^{4}.

113 is the 8-th centered square number.

It is an amenable number.

113 is a deficient number, since it is larger than the sum of its proper divisors (1).

113 is an equidigital number, since it uses as much as digits as its factorization.

113 is an evil number, because the sum of its binary digits is even.

The product of its digits is 3, while the sum is 5.

The square root of 113 is about 10.6301458127. The cubic root of 113 is about 4.8345881271.

Adding to 113 its reverse (311), we get a palindrome (424).

It can be divided in two parts, 11 and 3, that multiplied together give a palindrome (33).

The spelling of 113 in words is "one hundred thirteen", and thus it is an aban number.

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