Jamel Ghanouchi, The Concept of Prime Number and the Legendre Conjecture, IFSL Volume 3, International Frontier Science Letters (Volume 3) https://www.scipress.com/IFSL.3.16 Abstract: In this paper, we generalize the concept of prime number and define new primes. It allows to apply the new concept to the Legendre conjecture and to prove it. Keywords: Conjecture, Legendre, Primes, Proof