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We dene the concept of q-pseudoprime to base b, which extends the idea of strong pseudoprime to base b. We stablish a new test of primality that renes the Pocklinton’s Theorem using some properties of the Midy numbers. Keywords:  Prime numbers, strong pseudoprimality, Midy’s numbers, Pocklington’s Theorem. To cite this article:  J.H. Castillo, G. Garcia-Pulgarin, J.M. Velasquez-Soto, De los numeros de Midy a la primalidad, Rev. Integr. Temas Mat. 33 (2015), no. 1, 1-10.

De los números de Midy a la primalidad