
TL;DR
This paper establishes an improved upper bound on the number of pairs from two subsets of integers whose sum is prime, advancing understanding of prime distributions in sumsets.
Contribution
It provides a tighter upper bound for prime-sum pairs in large subsets, improving previous results by Balog, Rivat, and Sárközy.
Findings
Derived a new upper bound for prime-sum pairs
Enhanced previous bounds by Balog, Rivat, and Sárközy
Applicable for large subsets with product size significantly exceeding N^2/(log N)^2
Abstract
We obtain an upper bound for the number of pairs such that is a prime number, where with , an integer. This improves on a bound given by Balog, Rivat and S\'ark\"ozy.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Advanced Mathematical Identities
