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  From now on, we are stuck; indeed the mysterious bit will always be equal to $0$ and so, after the shift to the right, we will always obtain $(0,0,0)$  \end{Example}  We recall the notion of irreducible polynomial (Definition 1). An irreducible polynomial cannot be written as product of two non-trivial factors. It turns out that there is a close links between primitive polynomials and irreducible polynomials, as shown in the following theorem.  \begin{Theorem}  If $p\in \Fb[x]$ is primitive then is irreducible.  \end{Theorem}  The vice versa does not hold. previous theorem cannot be inverted.  For example, the polynomial $x^4 + x^3 + x^2 + x + 1$ is irreducible but it is not primitive. \begin{Exercise}  Verify that $x^4 + x^3 + x^2 + x + 1$ is not primitive via a LFSR.