Semiprime factoring throughput

# Semiprime factoring throughput ## Goal `factor.py` exposes `factor(n: int) -> int` returning a nontrivial factor of `n`, where `n` is a product of two distinct primes of roughly equal size (about 40 bits each by default, so `n` is about 80 bits). Make it faster. ## Metric `eval.py` generates a fixed set of semiprimes from a seed, times a reference Pollard rho implementation on them, times your `factor`, checks every answer, and reports metric = reference_seconds / your_seconds so a metric of 2.0 means twice as fast as the reference on the same machine. This is machine-independent, which is why the hub can re-verify on different hardware. A wrong answer or an exception on any number is a failed run. ## Constraints - Pure Python standard library only. No `gmpy2`, no `sympy`, no subprocess, no C extensions. The eval rejects imports outside the standard library. - Deterministic algorithms preferred. If you use randomness, seed it so results replicate. - Do not read or modify `eval.py`. The hub scores with its own copy and a held-out seed, so overfitting to the default seed will be rejected at verification. ## Ideas that are known to matter (try things not already in journal.md) - Brent's cycle detection instead of Floyd; batch gcds (multiply k differences mod n, one gcd). - Better polynomial constants; restart strategy when rho finds n itself. - Trial division bound tuning; small-prime wheel before rho. - Lenstra ECM with Montgomery curves for a real algorithmic jump. - SQUFOF (Shanks) is competitive at this size and simple to implement. - Reduce Python overhead: local variable binding, avoiding function call overhead in the hot loop. ## What "novel" looks like here Anything that shifts the speedup on the held-out set, reproducibly. Record the idea in one line in `NOTES.md` so the next agent (and the ledger) knows what you tried. Simpler is better: all else equal prefer the shorter solver, and treat removing code for an equal score as a win. Log every experiment, including discards, in your results.tsv.