113 is a 3-digit prime number. 113 is the 30th prime number, and the fifth prime number between 101 to 200.
Proofs[]
— 113 is divisible by 1.
— 113 is not divisible by 2-112.
- — 113 is divisible by 113.
Therefore, 113 is a prime number.
As an Exponent of Mersenne Number[]
2113 - 1 is divisible by prime factors such as 3,391, 23,279, and 65,993, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 107 is the second previous prime number.
- The difference between 113 and 107 is 6. Therefore, they are sexy primes.
- 109 is the prime number preceding 113.
- The difference between 113 and 109 is 4. Therefore, they are cousin primes.
- 111 is a composite number; its prime factorization is 3 × 37.
The numbers after[]
- 115 is the next odd number. It is a composite number; its prime factorization is 5 × 23.
- 117 is also a composite number; its prime factorization is 32 × 13.
- 119 is yet another composite number; its prime factorization is 7 × 17.
- 121 is a square number: 121 = 112
- 123 is unsurprisingly another composite number; its prime factorization is 3 × 41.
- 125 is a cube number: 125 = 53
- 127 is the prime number following 113.
In science[]
- 113 is the atomic number of nihonium.
Trivia[]
- The difference between 127 and 113 is 14. This is the largest gap between two consecutive prime numbers between 1 and 200.
- 113 is a Proth prime, since it is of the form In this case, x and y are equal to 7 and 4 respectively.
- 113 is the denominator of (also known as the Milü or 密率), an accurate approximation of π.
- 113 is a permutable prime with 131 and 311.
- This means 113 is also a circular prime.
- 113 is a centered square number, since it is the sum of two successive squares (72 + 82).
