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The present algebraic development begins by an exposition of the data of the problem. The definition of the primal radius r &gt; 0 is : For all positive integer x ³ 3 exists a finite number of integers called the primal radius r &gt; 0 , for which x + r and x - r are prime numbers. The corollary is that 2x = (x + r) +(x -r) is always the sum of a finite number of primes. Also, for all positive integer x ³ 0 , exists an infinity of integers r &gt; 0 , for which x + r and r - x are prime numbers. The conclusion is that 2x = (x + r) -(r - x) is always an infinity of differences of primes.

A Proof of the Veracity of both Goldbach and De Polignac Conjectures