Prime Neighborhood Navigator

A neighborhood around pₙ with walls at pₙ₋₁ and pₙ₊₁. The ball bounces with acceleration driven by Δ² = (pₙ₊₁−pₙ) − (pₙ−pₙ₋₁). The "second ratio" is r = Δ² / (pₙ₊₁−pₙ₋₁), shown as a compass needle: 0 down, −1 up, +1 right.

Data Visualizations OEIS Explorer

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primes: —

Prime limit (sieve up to) Start index (n) Playback speed (steps/sec) Δ² force scale Friction

Tip: raise limit if you run out of primes near the chosen start index.

pₙ₋₁

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pₙ

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pₙ₊₁

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span (pₙ₊₁−pₙ₋₁)

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gₙ₋₁ = (pₙ−pₙ₋₁)

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gₙ = (pₙ₊₁−pₙ)

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Δ² = gₙ − gₙ₋₁

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r = Δ² / (pₙ₊₁−pₙ₋₁)

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This is intentionally “geography-like”: the same coordinate (index n) always lands on the same neighborhood. The animation is only a rendering of invariant measurements: gap, second difference, and normalized second ratio.