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On the Asymptotic Density of Prime k-tuples and a Conjecture of Hardy and Littlewood

Tóth L.

Computational Methods in Science and Technology

2019

Vol. 25, No. 3

143--148

In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. In 2011, Wolf computed the “Skewes number” for twin primes, i.e., the first prime at which a reversal of the HardyLittlewood inequality occurs. In this paper, we find “Skewes numbers” for 8 more prime k-tuples and provide numerical data in support of the Hardy-Littlewood conjecture. Moreover, we present several algorithms to compute such numbers.