What is the smallest odd numberyou can find that is the sum of three different prime numbers?

3+5+11 = 19

I have not checked carefully for a smaller one.

3+5 + 7 = 15

Keep looking, there may be more.

To find the smallest odd number that is the sum of three different prime numbers, we can follow these steps:

1. List out the prime numbers: Start by listing out the prime numbers in ascending order. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on.

2. Find the sum of three different primes: Start by selecting the first three prime numbers from the list and find their sum. If it is an odd number, then we have found the answer. If not, continue to the next step.

3. Repeat the process: If the sum in step 2 is not odd, now select the next three prime numbers from the list and find their sum. Repeat this process until you find an odd sum.

Following these steps, we can find the smallest odd number that is the sum of three different prime numbers:

1. The first three prime numbers are 2, 3, and 5. Their sum is 2 + 3 + 5 = 10, which is even.
2. The next three prime numbers are 7, 11, and 13. Their sum is 7 + 11 + 13 = 31, which is odd.

Therefore, the smallest odd number that can be obtained as the sum of three different prime numbers is 31.