On the upper and lower bound orders of almost prime triples

Runbo Li

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arXiv · 2401.01348

On the upper and lower bound orders of almost prime triples

Runbo Li

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Abstract

A Hardy-Littlewood triple is a 3-tuple of integers with the form $(n, n+2, n+6)$. In this paper, we study Hardy-Littlewood triples of the form $(p, P_{a}, P_{b})$ and improve the upper and lower bound orders of it, where $p$ is a prime and $P_{r}$ has at most $r$ prime factors. Our new results generalize and improve the previous results.

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Runbo Li. 2023-11-27. On the upper and lower bound orders of almost prime triples. https://arxiv.org/abs/2401.01348

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