For some reason I need some primitive polynomial $f$ on $\mathbb{F}_2[x]$ where $\deg f \in [1,10^4]$. (Especially for $\deg f = 10\pm \epsilon, 10^2\pm \epsilon, 10^3\pm \epsilon, 10^4 \pm \epsilon$.) Could someone give information about this? For example, a table or some references are helpful. Thx.
Edit: If $2^{\deg f} - 1 \in \mathbb{P}$ we have that an irreducible polynomial $f$ is primitive immediately. However assuredly primitive polynomial exists for all $\deg f \in \mathbb{Z}^+ $.