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Prove Goldbach's "Weak" Conjecture

On June 7, 1742, Prussian mathematician Christian Goldbach wrote a letter to Leonhard Euler proposing the following conjecture: "Every integer greater than 2 can be written as the sum of three primes." (The number 1 is no longer considered to be prime, so the modern version stipulates “even numbers greater than 5”.) In the 350 years since it was first conceived, no one’s been able to provide a proof for it.

An easer conjecture has been subsequently proposed stating that “every odd number greater than 7 can be expressed as the sum of three odd primes.” While significant progress has been made to prove Goldbach's “weak” conjecture, the solution is still elusive.