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Pollard-Rho Ladder

Who This Is For

Use this lane when basic number theory feels fine, but 64-bit factorization still feels like a black box and trial division is no longer viable.

Warm-Up

  • trial division and SPF sieve
  • fast modular multiplication / exponentiation
  • why primality testing must come before recursive splitting

Core

  • deterministic Miller-Rabin for 64-bit primality
  • Pollard-Rho to split one composite into two smaller factors
  • recurse until all leaves are prime
  • flagship verifier-style rep: Factorize

Stretch

  • explain why this lane is "split then recurse", not "search divisors directly"
  • compare 64-bit factorization with Primitive Root as a consumer of the factorization layer
  • say when ordinary trial division is still the better route

Retrieval Layer

Repo Anchors

Exit Criteria

You are ready to move on when you can:

  • explain why Miller-Rabin is the gate before Pollard-Rho
  • say what counts as a successful Pollard-Rho split
  • recurse to a sorted prime multiset without losing multiplicities
  • tell when trial division is still simpler and more appropriate

External Practice