To find the sum of prime numbers between 80 and 90, we can follow these steps:
1. Identify all the prime numbers in the specified range (80 to 90).
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. It is only divisible by 1 and itself.
2. Check each number within the range to see if it is a prime number:
- 80: Not a prime number (divisible by 2, 4, 5, 8, 10, 16, 20, 40).
- 81: Not a prime number (divisible by 3, 9, 27).
- 82: Not a prime number (divisible by 2, 41).
- 83: Prime number (only divisible by 1 and 83).
- 84: Not a prime number (divisible by 2, 3, 4, 6, 7, 12, 14, 21, 28, 42).
- 85: Not a prime number (divisible by 5, 17).
- 86: Not a prime number (divisible by 2, 43).
- 87: Not a prime number (divisible by 3, 29).
- 88: Not a prime number (divisible by 2, 4, 8, 11, 22, 44).
- 89: Prime number (only divisible by 1 and 89).
- 90: Not a prime number (divisible by 2, 3, 5, 6, 9, 10, 15, 18, 30, 45).
From this, we identify that the prime numbers in the range 80 to 90 are 83 and 89.
3. Sum the prime numbers found:
[tex]\[
83 + 89 = 172
\][/tex]
Thus, the sum of the prime numbers between 80 and 90 is 172.
