Representing an integer as the sum of a prime and the product of two small factors

Roger Baker; Glyn Harman

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arXiv · 2011.10859

Representing an integer as the sum of a prime and the product of two small factors

Roger Baker·Glyn Harman

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Abstract

Let c > 0.55. Every large n can be written in the form p +ab, where p is prime, a and b are significantly smaller than x^1/2 and ab is less than n^c. This strengthens a result of Heath-Brown, which has the requirement c>3/4. We introduce the idea of 'intersecting two sieves' as a tool in the proof of this result.

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Roger Baker, Glyn Harman. 2020-11-21. Representing an integer as the sum of a prime and the product of two small factors. https://arxiv.org/abs/2011.10859

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