29, 5 and 3
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3, 7 and 37
3, 3, 37 or 3, 11, 29 or 3, 17, 23
The only way for three prime numbers to have a sum of 42 is if one of the prime numbers is 2, as 2 is the only even prime number. The other two prime numbers must add up to 40, which can only be achieved by 3 and 37. Therefore, the three prime numbers that have a sum of 42 are 2, 3, and 37.
3 + 37 = 4011 + 29 = 4017 + 23 = 40
There are not three prime numbers that have the sum of 3. The smallest prime number is 2. If all three prime numbers were 2, the sum would 2 + 2 + 2 = 6, so that is the smallest number that is the sum of three prime numbers.