Irreducible polynomials mod 2

Let F2[x] {\mathbb F}_2[x] be the ring of polynomials with coefficients in F2=Z/2Z {\mathbb F}_2 = {\mathbb Z}/2{\mathbb Z} . Recall that a polynomial is irreducible if it has no nonconstant factors of smaller degree.

For example, there are three irreducible polynomials of degree 4 4 in F2[x] {\mathbb F}_2[x] , namely x4+x+1,x4+x3+1,x4+x3+x2+x+1. x^4+x+1, x^4+x^3+1, x^4+x^3+x^2+x+1.

How many irreducible polynomials of degree 17 are there in F2[x]? {\mathbb F}_2[x]?


Hint: read the finite fields wiki!
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