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arXiv · 2506.12063

On the Density of Prime Imbalances in the Unit Interval

Paul Alexander Bilokon
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Abstract

We prove that the set of normalized differences between primes, defined as $S = \{(p-q)/(p+q) : p > q \text{ are primes}\}$, is dense in the open unit interval $(0,1)$. Our proof provides an explicit construction algorithm with quantitative bounds, relying on elementary results from prime number theory including Bertrand's postulate and explicit bounds on prime gaps in long intervals.

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Paul Alexander Bilokon. 2025-06-01. On the Density of Prime Imbalances in the Unit Interval. https://arxiv.org/abs/2506.12063

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