Understanding the Problem
To express 88 as the sum of two odd prime numbers, we first need to understand the characteristics of odd prime numbers and their combinations.
What Are Odd Prime Numbers?
- Odd prime numbers are prime numbers greater than 2.
- The first few odd prime numbers are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Finding Pairs That Add Up to 88
To find pairs of odd prime numbers that sum to 88, we can use a systematic approach:
1. Start with the smallest odd prime (3) and find its complement:
- 88 - 3 = 85 (not prime)
2. Move to the next odd prime (5):
- 88 - 5 = 83 (prime)
3. Continue this process:
- 88 - 7 = 81 (not prime)
- 88 - 11 = 77 (not prime)
- 88 - 13 = 75 (not prime)
- 88 - 17 = 71 (prime)
By continuing this process, we find that:
Valid Combinations
- 5 + 83 = 88
- 17 + 71 = 88
Conclusion
Thus, we can express 88 as the sum of two odd prime numbers in two valid ways:
- 5 and 83
- 17 and 71
These combinations highlight the interesting nature of prime numbers and their sums.