Number Theory

    

A Simple Proof that Goldbach's Conjecture is True

Authors: Timothy W. Jones

A induction proof shows Goldbach's conjecture is correct. It is as simple as can be imagined. A table consisting of two rows is used. 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. For the base case of k=5 suppose that primes on the lower row always map to composites on the top and that this results in too many composites on the top. This is true for this base case. Suppose it is true for k=n, then the shifts and additions necessary for the k=n+1 case maintain this property of too many composites on top. The contrapositive is that there exists a prime on the bottom that maps to a prime on top and Goldbach is established: the sum of these two primes is 2(n+1).

Comments: 3 Pages.

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[v1] 2022-08-02 12:58:55

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