Distribution of Irreducible Polynomials over F2
Using a polynomial analogue of the wheel sieve, we discuss the distribution of irreducible polynomials over F 2. In particular, we provide considerable numerical evidence that in analogue to integer arithmetic progressions, irreducible polynomials over F 2 are binomially distributed in the progressions of the wheel sieve. We also present, numerical evidence that the irreducibles of fixed degree are binomially distributed by weight. Also briefly discussed is the distribution of self-reciprocal irreducible polynomials. A number of conjectures are raised.
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