On primitive elements in finite fields and on elliptic curves

An asymptotic formula for the number of primitive polynomials of the form $f(x)+a$, $a=1,\dots,h$, where $f(x)\in F_p[x]$, is obtained, “on the average” over all polynomials $f$ of fixed degree, and an estimate for the number of “sparse” factorable polynomials is also obtained.