What question did this study set out to answer?

The aim is to explore a new number system with significantly high prime density and its implications.

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June 5, 2026Open Access

High Prime Density and Regularity in the "9091" Number System

Key Points

The aim is to explore a new number system with significantly high prime density and its implications.
Analyzed the prime density within a new number system up to 100,000 digits in length.
Investigated the relationship between numerical value and prime density in this system.
Found an increasing trend in prime density as numerical value increases.
Noted that the rate of increase in prime density gradually slows, contrary to predictions of the prime number theorem.

Abstract

This paper presents a new type of number system with very high prime density. Within a range of up to 100,000 digits in length, it has been verified that as the numerical value increases, the density of prime numbers actually shows an increasing trend, although the rate of increase gradually slows down, which is inconsistent with the prime number theorem in the natural number system.

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