The prime number nearest to 80 is–

Step-by-Step Solution
To find the prime number nearest to 80, we look for prime numbers in the immediate vicinity of 80 by checking the integers directly above and below it.

Check integers below 80:

79: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Since 79 is not divisible by any prime numbers up to its square root (which is less than 9, so we test 2, 3, 5, 7), 79 is a prime number.

The distance from 80 to 79 is: |80 - 79| = 1.

Check integers above 80:

81: Divisible by 3 and 9 (not prime).

82: Even number (not prime).

83: Checking for divisibility, 83 is not divisible by 2, 3, 5, or 7, so it is a prime number.

The distance from 80 to 83 is: |80 - 83| = 3.

Compare distances:

The distance to 79 is 1.

The distance to 83 is 3.

Since 1 is smaller than 3, 79 is the prime number nearest to 80.