The Primitive(a) mod p command returns true if the univariate polynomial a over the integers mod p is "primitive", and false otherwise.

If $a$ is an irreducible polynomial in ${\mathbb{Z}}_p\left[x\right]$ of degree $k$, then it is primitive if $x$ is a primitive element in the finite field${\mathbb{Z}}_p\left[x\right]\/\left(a\right)$ Thus, $x^i$, for $i=1..p^k-1$ is the set of all non-zero elements in the field.

$\mathrm{Primitive}\left(x^4+x+1\right)\mathbf{mod}2$

$\mathrm{true}$

$\mathrm{Primitive}\left(x^4+x^3+x^2+x+1\right)\mathbf{mod}2$

$\mathrm{false}$