New Mathematical Rules and Methods for the Strong Conjecture of Goldbach to be Verified

Abstract

Bouchaib Bahbouhi

This article emphasizes the most fundamental rules to verify Goldbach's strong conjecture that an even number is the sum of two primes. One rule states that for an even number E to split into two primes there must be two equidistant prime numbers p and p' such that E/2 - p = p' - E/2. The strong conjecture also applies to biprime numbers that are x2 – y2 . Two prime numbers equidistant with respect to an integer n have a specific property of Modulo when divided by the gap that separates them from n. The paper further proposes methods to convert even and odd numbers into sums of two and three prime numbers by the equation M ± 1 such that M is prime or multiple of primes except 2 and 3 knowing that there are two types of prime numbers 6x - 1 and 6x + 1. The data also show a strong correlation coefficient between close equidisant primes indicating they are likely to happen in a regular fashion. Finally, the paper describes new rules that explain how a prime numbers gives another one and this is where the truth of Goldbach's conjecture lies and show congruence rules between the two additive primes. These rules allow to demonstrate how an even ends up to be a sum of two primes and proves Goldbach's strong conjecture. This article can have new applications in computing and sheds new lights on the Goldbach's strong and weak conjectures.

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