Question

If you are given enough time, space and computing power, which of these two would you be able to solve with confidence? For a given number n

(a) Testing whether 2n + 2 is the sum of two prime numbers (10 Points)

Answer 1

The Goldbach conjecture states that every even integer is the sum of two primes. This conjecture was proposed in 1742 and, despite being obviously true, has remained unproven. To prove this conjecture, I have identified a subset of the even numbers that have relatively few prime pairs compared to the other even numbers. This subset is the set of all n such that n=2p where p is prime. An equation was derived that determines the number of prime pairs for n=2p. It is then proven that the equation never goes to zero for any n, and as n increases, the number of prime pairs also increases, thus validating Goldbach's conjecture.