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For an integral convex polytope $\Pc \subset \RR^N$ of dimension $d$, we call$\delta(\Pc)=(\delta_0, \delta_1,..., \delta_d)$ the $\delta$-vector of $\Pc$and $\vol(\Pc)=\sum_{i=0}^d\delta_i$ its normalized volume. In this paper, wewill establish the new equalities and inequalities on $\delta$-vectors forintegral simplices whose normalized volumes are prime. Moreover, by usingthose, we will classify all the possible $\delta$-vectors of integral simpliceswith normalized volume 5 and 7.

Ehrhart polynomials of integral simplices with prime volumes