TY - JOUR
T1 - A Proof of the Veracity of both Goldbach and De Polignac Conjectures
AU - Ghanouchi, Jamel
JF - Bulletin of Mathematical Sciences and Applications
VL - 6
SP - 10
EP - 20
SN - 2278-9634
PY - 2013
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/BMSA.6.10
UR - https://www.scipress.com/BMSA.6.10
KW - Algebraic Proof
KW - De Polignac
KW - Goldbach
KW - Twin Primes
AB - 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.
ER -