Number Theory

    

A Direct Proof that Goldbach's Conjecture is True

Authors: Timothy Jones

We introduce a Goldbach table. It consists of two rows. A bottom row counts from zero to a given n and the top counts from the right from n to 2n. The columns generated give all the whole numbers that add to 2n. We confirm that using a sieve, we do always seem to get top and bottom primes that show Goldbach's conjecture is true for the particular 2n depicted by this table. Next we cumulatively depict these tables and we see some interesting patterns. We can infer that all prime pairs will occur in one of these tables. We also see diagonal prime lines that seem to start and stop in symmetrical ways. These patterns suggest that for any even number we can choose a column and then find a prime pair.

Comments: 4 Pages.

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Submission history

[v1] 2024-08-01 12:08:51

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