Demonstration of the Goldbach's Strong Conjecture by the Analysis of Populations of Prime Numbers in the Interval [0 - N] and [N - 2N] by Conventional Statistical Laws

Abstract

Bahbouhi Bouchaib

In this article I apply classical statistical laws to analyze prime numbers assimilated to populations. The statistical analysis focuses on prime numbers in the intervals [0–S/2] and [S/2–S] with S an even > 4. The results show that the even number S > 4 is enclosed by two populations of prime numbers P in the interval [0 - S/2] and Q in [S/2 - S] which have approximately the same standard deviation relative to their means. Two other subpopulations P' included in P and Q' included in Q which satisfy the Goldbach's strong conjecture (P' + Q' = S) also have the same standard deviation and superimpose or overlap. This result shows that an even number is enclosed by two populations P' and Q' of prime numbers which are symmetric with respect to S/2 and therefore S = P' + Q'. This result also shows that any natural number N > 4 is enclosed by at least two equidistant and symmetric prime numbers. Therefore, for every N > 4 there exists a number t < N such that N – t = P' and N + t = Q' are primes and so 2N = P' + Q'.

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