Why it matters

Pollard's rho finds small factors. Understanding shapes factoring.

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The architecture

Sequence x_{i+1} = x_i^2 + c mod n.

Cycle detection via Floyd or Brent.

gcd(x_i - x_j, n) may factor.

Pollard's rho flowSequencex^2 + c mod nCycle detectionFloyd / Brentgcdfactor foundBrent's variant faster; combined with trial division + Miller-Rabin for full factoring
Pollard's rho.
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How it works end to end

Floyd's tortoise + hare cycle detection.

Brent's improved cycle detection.

May need retry with different c.