Write all prime numbers between: 80 and 100

To find all the prime numbers between 80 and 100, we first need to understand what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In simpler terms, a prime number has exactly two distinct positive divisors: 1 and itself.

Identifying Prime Numbers

Let's look at the numbers between 80 and 100: 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, and 100. We will check each of these numbers to see if they are prime.

Step-by-Step Analysis

• 81: Divisible by 3 (3 x 27), not prime.
• 82: Divisible by 2 (2 x 41), not prime.
• 83: Not divisible by 2, 3, 5, or 7 (the primes less than √83). Thus, 83 is prime.
• 84: Divisible by 2 (2 x 42), not prime.
• 85: Divisible by 5 (5 x 17), not prime.
• 86: Divisible by 2 (2 x 43), not prime.
• 87: Divisible by 3 (3 x 29), not prime.
• 88: Divisible by 2 (2 x 44), not prime.
• 89: Not divisible by 2, 3, 5, or 7. Therefore, 89 is prime.
• 90: Divisible by 2 (2 x 45), not prime.
• 91: Divisible by 7 (7 x 13), not prime.
• 92: Divisible by 2 (2 x 46), not prime.
• 93: Divisible by 3 (3 x 31), not prime.
• 94: Divisible by 2 (2 x 47), not prime.
• 95: Divisible by 5 (5 x 19), not prime.
• 96: Divisible by 2 (2 x 48), not prime.
• 97: Not divisible by 2, 3, 5, or 7. Hence, 97 is prime.
• 98: Divisible by 2 (2 x 49), not prime.
• 99: Divisible by 3 (3 x 33), not prime.
• 100: Divisible by 2 (2 x 50), not prime.

Final List of Prime Numbers

After evaluating each number, we find that the prime numbers between 80 and 100 are:

• 83
• 89
• 97

So, the complete list of prime numbers in that range is 83, 89, and 97. Understanding how to identify prime numbers can be a valuable skill in various areas of mathematics, including number theory and cryptography.