Number Theory

    

Symmetries in Goldbach's Conjecture

Authors: Timothy Jones

We define a Goldbach table as a table consisting of two rows. The lower row counts from 0 to any n and and the top row counts down from 2n to n. All columns will have all numbers that add to 2n. Using a sieve, all composites are crossed out and only columns with primes are left. We then define a novel prime decimal system: it gives for every n remainders when n is divided by all primes less than the n. This suggests linear functions, the divisions used can give another perspective on all the column pairs. The inverses of these functions when put into tabular form give symmetries that suggest Goldbach's conjecture is correct.

Comments: 7 Pages.

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[v1] 2024-08-25 11:17:20

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