Jamel Ghanouchi, The Real Primes and the Riemann Hypothesis, BMSA Volume 4, Bulletin of Mathematical Sciences and Applications (Volume 4) https://www.scipress.com/BMSA.4.9 Abstract: In this document, we deal with the concept of real prime number together with the Riemann hypothesis to the real numbers. Thus, we highlight the new hypothesis by a calculus of integral. Keywords: