# A Sum of Odd Primes in Three Ways

Number Theory Level pending

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.

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