Identify Integers in Range

First, list all integers between 109 and 121, inclusive:

• 109
• 110
• 111
• 112
• 113
• 114
• 115
• 116
• 117
• 118
• 119
• 120
• 121

Check Primality of Each Integer

Determine if each number is prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

• 109: Check divisibility by primes up to $\sqrt{109} \approx 10.4$ (2, 3, 5, 7). 109 is not divisible by any of these. 109 is prime.
• 110: Divisible by 2, 5, 10. Not prime.
• 111: Sum of digits $1+1+1 = 3$. Divisible by 3 ($111 = 3 \times 37$). Not prime.
• 112: Divisible by 2. Not prime.
• 113: Check divisibility by primes up to $\sqrt{113} \approx 10.6$ (2, 3, 5, 7). 113 is not divisible by any of these. 113 is prime.
• 114: Divisible by 2. Not prime.
• 115: Divisible by 5. Not prime.
• 116: Divisible by 2. Not prime.
• 117: Sum of digits $1+1+7 = 9$. Divisible by 3 and 9 ($117 = 9 \times 13$). Not prime.
• 118: Divisible by 2. Not prime.
• 119: Check divisibility by primes up to $\sqrt{119} \approx 10.9$ (2, 3, 5, 7). $119 = 7 \times 17$. Not prime.
• 120: Divisible by 2, 3, 5, 10. Not prime.
• 121: $121 = 11 \times 11$. Not prime.

Count the Prime Numbers

The prime numbers identified in the range are 109 and 113.

There are 2 prime numbers between 109 and 121, inclusive.