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.
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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