They add up to 17
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The prime numbers 3 an 7 are both odd and sum to 10.
There are not three odd primes with the sum of 14. The sum of three odd primes will be an odd number.
Sure. All composite numbers can be written as a product of primes. It shouldn't be tough to find a composite number that's the sum of three other composite numbers. Let's try 30. 2 x 3 x 5 = 30 Product of primes, check. 6 (2 x 3) + 10 (2 x 5) + 14 (2 x 7) = 30 Sum of three products of primes, check.
This question cannot be answered because three odd primes always have an odd number for their sum.
Goldbach's conjecture: Every even integer n greater than two is the sum of two primes see below for the reference