We can attempt a proof of **Goldbach’s Conjecture** via a proof by contradiction.

Suppose there exists a positive even integer, , that is not a sum of two odd primes.

We let e = p + nq (or equivalently, e â‰¡ p mod q) where odd primes, p and q, are less than e with odd integer, n > 1.

But there are k odd primes, , less than e. Therefore, we generate a system of k Diophantine equations:

;

;

;

…

where odd integer, for {1, 2, 3,…, k}.

**Remark**: We must show that least one of those equations is false (contradicting our assumption that *e is not a sum of two odd primes*) to prove Goldbach’s Conjecture is true.

**Claim**: We strongly believe Goldbach’s Conjecture is provable with some more analysis and with the help of some tools/methods from prime number theory.

**A Crucial Idea**: The distribution of all odd primes less than e helps us to prove Goldbach’s Conjecture.

Good Luck! ðŸ™‚

Dave.

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