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We take an approach toward counting the number of n for which the curves E_n:y^2=x^3-n^2x have 2-Selmer groups of a given size. This question was alsodiscussed in a pair of Invent. Math. papers by Roger Heath-Brown. We discussthe connection between computing the size of these Selmer groups and verifyingcases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for theasymptotic formulae is the ``independence'' of the Legendre symbol evaluated atthe prime divisors of an integer with exactly k prime factors.

2-Selmer Groups and the Birch-Swinnerton-Dyer Conjecture for the Congruent Number Curve