Confirmation Of The Legendre And The Euler Conjectures
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].
Legendre conjecture, prime number, semi-prime number, Schoenfeld inequality, prime-counting function, Euler conjecture. 2010 Mathematics Subject Classification: 11 A xx (Elementary number theory
Legendre conjecture, prime number, semi-prime number, Schoenfeld inequality, prime-counting function, Euler conjecture. 2010 Mathematics Subject Classification: 11 A xx (Elementary number theory
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