Express the following as the sum of two odd primes.
36

Answer

To express the number 36 as the sum of two odd prime numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Prime Numbers**:
- A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The only even prime number is 2; all other prime numbers are odd.

2. **List the Odd Prime Numbers**:
- The odd prime numbers less than 36 are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.

3. **Find Combinations of Two Odd Primes**:
- We need to find two odd primes that add up to 36. We can do this by trying different combinations of the listed odd primes.

4. **Testing Combinations**:
- Start with the largest odd prime less than 36 and check if the difference with 36 is also an odd prime:
- 31 + 5 = 36
- 29 + 7 = 36
- 23 + 13 = 36
- 19 + 17 = 36

5. **Select Valid Combinations**:
- From the combinations tested, we find:
- 31 and 5
- 29 and 7
- 23 and 13
- 19 and 17
- All these pairs are valid as they consist of odd primes.

6. **Conclusion**:
- Therefore, 36 can be expressed as the sum of two odd primes in multiple ways, such as:
- 31 + 5
- 29 + 7
- 23 + 13
- 19 + 17

### Final Answer:
36 = 31 + 5 or 36 = 29 + 7 or 36 = 23 + 13 or 36 = 19 + 17