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In this note we studied the primitive varieties of general type with $q(X) =dim(X)$ and non-birational bicanonical maps. Let $X$ be such a variety. Webounded the degree of its bicanonical map. If moreover the Albanese variety$Alb(X)$ is simple, we proved that the Euler number $\chi(\omega_X) = 1$, and$|2K_X|$ separates the points mapped to the same general point via the Albanesemap.

On the bicanonical maps of primitive varieties with $q(X) = dim(X)$: the degree and the Euler number