We can attempt proof of **Goldbach’s Conjecture** via 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 β‘ 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! π

Dave,

Reference Link: **Proof of Goldbach Conjecture.**

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Greetings! This is my 1st comment here so I just wanted to give a quick shout out and tell you I truly enjoy reading through your posts. Can you recommend any other blogs/websites/forums that cover the same subjects? Thanks a ton!

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Thanks for your comment! π

I recommend the website, https://www.math10.com/forum/ Enjoy! π

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We accept the truth of the Riemann Hypothesis, and there is a modest (relatively small and predictable) error associated with Riemann’s Prime Counting Function…

Go Blue! πβ

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