What could be an indirect proof of Goldbach’s Conjecture?

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

Suppose there exists a positive even integer, e > 4 * 10^{18}, that is not a sum of two odd primes.

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

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

e = 3 + n_{1}q_{1};

e = 5 + n_{2}q_{2};

e = 7 + n_{3}q_{3};

e = p_{k} + n_{k}q_{k}

where odd integer, n_{i} > 1 for i \in {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! πŸ™‚


Reference Link: Proof of Goldbach Conjecture.

Published by Dave

"May all beings be happy and peaceful. Thank you, Lord GOD! Praise you, Lord GOD! Love you, Lord GOD! Trust you, Lord GOD! Bless you, Lord GOD! Amen!" πŸ˜‚ P.S. Go Blue! πŸ‘ ✌

3 thoughts on “What could be an indirect proof of Goldbach’s Conjecture?

  1. 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!

    Liked by 1 person

  2. 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! πŸ‘βœŒ

    Liked by 1 person

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