113 is a prime number from 101-200. 113 is prime because it only has 2 factors, 1 and 113. It is the 30th prime number, and the fifth prime number between 101 to 200.
Proofs[]
As an Exponent of Mersenne Number[]
2113 - 1 is divisible by numbers such as 3,391, 23,279, and 65,993, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- The previous odd number, 111, is not a prime number. It can be factorized into 3 x 37.
- The odd number previous to 111 is 109. 109 is a prime number.
- 109 and 113 are four numbers apart; therefore, they are cousin primes.
- The odd number previous to 109 is 107. 107 is a prime number.
- 107 and 113 are six numbers apart; therefore, they are sexy primes.
The numbers after[]
- The next prime number is 127. It features a huge gap, as 113 and 127 are fourteen numbers apart.
- Among the composite numbers between them:
- 115 is divisible by 5.
- 117 is divisible by 3.
- 119 is divisible by 7.
- 121 is divisible by 11. In addition, it is a square number.
- 123 is divisible by 3.
- 125 is divisible by 5. In addition, it is a cube number.
Trivia[]
- The next prime number is 127, a number 14 numbers apart, this is the longest gap between primes in the range 1-200.