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arXiv · 2411.01296

A Density Theorem for Higher Order Sums of Prime Numbers

Michael T. Lacey·Hamed Mousavi·Yaghoub Rahimi·Manasa N. Vempati
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Abstract

Let $P$ be a subset of the primes of lower density strictly larger than $\frac12$. Then, every sufficiently large even integer is a sum of four primes from the set $P$. We establish similar results for $k$-summands, with $k\geq 4$, and for $k \geq 4$ distinct subsets of primes. This extends the work of H.~Li, H.~Pan, as well as X.~Shao on sums of three primes, and A.~Alsteri and X.~Shao on sums of two primes. The primary new contributions come from elementary combinatorial lemmas.

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Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi, Manasa N. Vempati. 2024-11-02. A Density Theorem for Higher Order Sums of Prime Numbers. https://arxiv.org/abs/2411.01296

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