A Sum of Odd Primes in Three Ways
The Goldbach conjecture states that every even integer greater than 2 can be written as a sum of two odd prime numbers. For example \(12 = 7+5\). Some even integers can be written as the sum of two odd prime numbers in more than one way. For example \(22 = 3 + 19 = 5 + 17\). Find the sum of all even integers less than or equal to 30 that can be written as a sum of two odd primes in exactly three ways.