How many of primitive point on the elliptic curve?
In a group of size $n$ (e.g. an elliptic curve), the order of a subgroup generated by a group element necessarily divides $n$. We usually choose curves so that their order $n$ is prime; in that case, the order of a point must be either $1$ (the point is the "point at infinity") or $n$ (all other points). Thus, if $n$ is prime, then every non-zero point is necessarily a generator for the whole curve.

In general, if $n$ is not prime but you know its factorization, then you can test whether a point $P$ generates the whole curve in the following way: for every prime $k$ that divides $n$, compute $(n/k)P$. If none of these points is zero, then $P$ generates the whole curve.

(All of this applies to every finite group, not just elliptic curves.)