@article{ghanouchi2013,
author = {Ghanouchi, Jamel},
title = {A Proof of the Veracity of both Goldbach and De Polignac Conjectures},
year = {2013},
month = {11},
volume = {6},
pages = {10--20},
journal = {Bulletin of Mathematical Sciences and Applications},
doi = {10.18052/www.scipress.com/BMSA.6.10},
keywords = {Goldbach, De Polignac, Twin Primes, Algebraic Proof},
abstract = {The present algebraic development begins by an exposition of the data of the problem. The definition of the primal radius r > 0 is : For all positive integer x ³ 3 exists a finite number of integers called the primal radius r > 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 > 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.}
}