f(θ) = 2 + sin(1θ) · sin(3θ / 32)
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f(θ) — Cartesian
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⟵ Wave Scrub ⟶
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Gap Families — ζ(s)
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64π
Harmonics · Farey Intervals
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Sphere Color Mode
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Farey Intervals
1:1
q≤4
q≤16
q≤64
q>64
— Hz
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Audio
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220 Hz
35%
Arnold Tongue · Warp
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Gap Decomposition · ζ(s)
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Statistics
Gap Ratio Analysis: Twin Prime Conjecture Evidence
Tracks Count(gap=2)/Count(gap=4) and other gap ratios. Hardy-Littlewood predicts twin primes (gap 2) and
cousin primes (gap 4) have identical singular series constants, so their ratio should approach
1.0 as N→∞. Gap 6 (sexy primes) has a 2× larger constant
due to the p=3 factor — so it is asymptotically twice as frequent as gap 2 or gap 4, not equal.
Gap Ratio Data
| Metric | Value | Target | Status | Interpretation |
|---|---|---|---|---|
| Run Gap Decomposition to populate… | ||||
ζ Riemann Zeta · ζ(½+it) Critical Line
▼
T = 50
N = 3000
Set Tmax and click Compute to draw ζ(½+it).