Prime Number Distribution Explorer

Distribution analysis up to 10,000,000

1. Max Upper Limit

Max: 10M

Set the maximum search boundary.

Selected Limit 100,000
100K 2.5M 5M 7.5M 10M
Limit Presets

2. Interval Window Size

Define the range grouping (bin width) for distribution bucketing.

Selected Window 1,000
10 10K 50K 100K
Window Presets

Prime Metrics & Insights (1 to 100,000)

Total Primes 9,592 Found inside search space
Overall Density 9.59% 9,592 / 100,000 numbers
Max Primes / Window - In currently selected group
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Prime Number Theorem

The Prime Number Theorem states that the density of primes near a number $x$ is approximately $1 / \ln(x)$. As you scale up the upper limit to $1,000,000$ or even $10,000,000$, observe how the total density continuously shrinks! This demonstrates how prime numbers become increasingly scarce.

Parameters match live visualization. Adjust limits or windows to activate change.

Distribution Over Number Groups

Currently displaying windows of size: 1,000 for limit: 100,000

Primes Count
Window Area

Prime Number Index

Quick search or scroll over the first 500 prime numbers found in our array.

Showing matches up to index 500.

Distribution Analysis Breakdown

Granular performance statistics across intervals based on current window.

Interval Group Window Span Primes Found Local Density