Express each of the following odd numbers as the sum of three odd prime numbers .
63

Options

A. 11 + 13 + 43
B. 10 + 13 + 40
C. 7 + 11 + 45
D. 7 + 13 + 43

Answer

To express the odd number 63 as the sum of three odd prime numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Odd Prime Numbers**:
First, we need to list some odd prime numbers. 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, etc.

2. **Choose Combinations**:
We want to find three odd prime numbers that add up to 63. We can start by testing combinations of these primes.

3. **Trial and Error**:
Let's try some combinations:
- Start with the smallest odd prime, 3, and see if we can find two other primes that sum with it to make 63.
- For example, if we start with 3, we need to find two primes that sum to 60 (since 63 - 3 = 60). However, this does not yield valid combinations.
- Next, try 5: 63 - 5 = 58. Again, no valid combinations.
- Continue this process with different combinations.

4. **Finding a Valid Combination**:
After testing various combinations, we find:
- 7 + 13 + 43 = 63
- Check: 7 is a prime, 13 is a prime, and 43 is a prime. All are odd.

5. **Conclusion**:
Therefore, we can express 63 as the sum of three odd prime numbers:
**63 = 7 + 13 + 43**.