Quadratic Polynomials Which Have a High Density of Prime Values
نویسندگان
چکیده
The University of Manitoba Sieve Unit is used to find several values of A (> 0) such that the quadratic polynomial x + x + A will have a large asymptotic density of prime values. The Hardy-Littlewood constants which characterize this density are also evaluated.
منابع مشابه
New quadratic polynomials with high densities of prime values
Hardy and Littlewood’s Conjecture F implies that the asymptotic density of prime values of the polynomials fA(x) = x 2 + x + A, A ∈ Z, is related to the discriminant ∆ = 1 − 4A of fA(x) via a quantity C(∆). The larger C(∆) is, the higher the asymptotic density of prime values for any quadratic polynomial of discriminant ∆. A technique of Bach allows one to estimate C(∆) accurately for any ∆ < 0...
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