CONFIRMATION OF THE LEGENDRE AND THE EULER CONJECTURES

I show the veracity of the Legendre conjecture, which says that  a prime integer such that : ,  remained open since 1833 (date of the Legendre extinction). I show also the veracity of the Euler conjecture, which says that there is an infinite number of prime numbers of the form  remained open since 1760. I do this by using the Schoenfeld inequality that I have showed in my work [4], and by using the same approach of my papers [5], [6].