1. **Problem:** How many ways can the number 27 be expressed as the sum of two prime numbers? 2. **Formula and Rules:** This is related to the Goldbach conjecture for odd numbers, but since 27 is odd, it can only be expressed as the sum of 2 and an odd prime (because 2 is the only even prime). 3. **Step-by-step:** - Check pairs (2, 25), (3, 24), (5, 22), (7, 20), (11, 16), (13, 14), etc. - 2 + 25: 25 is not prime. - 3 + 24: 24 is not prime. - 5 + 22: 22 is not prime. - 7 + 20: 20 is not prime. - 11 + 16: 16 is not prime. - 13 + 14: 14 is not prime. No pairs of primes sum to 27. 4. **Conclusion:** There are 0 ways to express 27 as the sum of two prime numbers. **Final answer:** 0