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 . Some even integers can be written as the sum of two odd prime numbers in more than one way. For example . 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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1 solution
The even numbers less than or equal to 30 that can be written as a sum of two odd primes in exactly three ways are 2 2 2 4 2 6 3 0 = 3 + 1 9 = 5 + 1 7 = 1 1 + 1 1 = 5 + 1 9 = 7 + 1 7 = 1 1 + 1 3 = 3 + 2 3 = 7 + 1 9 = 1 3 + 1 3 = 7 + 2 3 = 1 1 + 1 9 = 1 3 + 1 7 Adding these we get 102.