Pseudoprimes stronger than strong pseudoprimes
  We introduce a new class of pseudoprimes. In this work we characterize Midy pseudoprimes, give some of their properties and established interesting connections with other known pseudoprimes, in particular we show that every divisor of a Midy pseudoprime is either a prime or a Midy pseudoprime and in the last case it is a strong pseudoprime. 
John H. Castillo and Gilberto Garc\'ia-Pulgar\'in and Juan Miguel   Vel\'asquez-Soto
math.NT