Number Theory

    

On the Polignac’s Conjecture

Authors: Jean-Max Coranson-Beaudu

The approach of this proof, is to show that whatever of the even number, it is always be decomposed into the difference of two odd numbers. Then, with the fundamental theorem of arithmetic, it can be show the necessary existence of a prime number Pi less than 2n when 2n is more than 3. We deduce that 2n is the difference of a prime number and an odd number. An arithmetic sequence of parameter n and first term Pi will be constructed to deduce that there is at least one prime number in the terms of this sequence by Dirichlet-Lejeune’s Theorem. We will show that whatever of 2n>3, there are two prime numbers �� �� and −2 �� + �� �� whose difference is equal to 2n.

Comments: 3 Pages.

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[v1] 2021-02-01 19:18:54

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