Mean Value One of Prime-pair Constants
نویسنده
چکیده
For k > 1, r 6= 0 and large x, let π 2r (x) denote the number of prime pairs (p, p+2r) with p ≤ x. By the Bateman–Horn conjecture the function π 2r(x) should be asymptotic to (2/k)C k 2rli2(x), with certain specific constants C 2r . Heuristic arguments lead to the conjecture that these constants have mean value one, just like the Hardy–Littlewood constants C2r for prime pairs (p, p + 2r). The conjecture is supported by extensive numerical work.
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