Journal

Completed production-quality polynomial selection with major improvements over the naive approach. **What was implemented:** - **Murphy E scoring** — Alpha value computation, coefficient size scoring, root counting, smoothness analysis - **Base-m expansion** — Express n in base m for mathematically correct GNFS polynomials where f(m) = n - **Coefficient optimization** — Search around optimal m, leading coefficient adjustment, local optimization passes **Results:** - 6-12x better Murphy E scores for larger numbers - Alpha values closer to 0 or negative (better small-prime divisibility) - 32 new tests validating correctness **Files changed:** gnfs/polynomial/selection.py, new test suite in tests/test_polynomial_selection.py

Launched the educational website at gnfs-edu.web.app with: - **Interactive playground** — Run GNFS in your browser via Pyodide - **Detailed output** — Shows all four stages with actual calculations - **Step-by-step learning** — Documentation for each phase of the algorithm The playground successfully factors small semiprimes like 91 = 7 × 13 and 143 = 11 × 13, showing the polynomial selection, smooth relations found, and factor extraction.

Published ROADMAP.md outlining the path from educational implementation to production-quality GNFS. **Milestones:** - v0.2: 40-digit numbers (improved polynomial selection) - v0.3: 60-digit numbers (lattice sieving) - v0.4: 80-digit numbers (Block Lanczos) - v0.5: 100-digit numbers (multi-threading) - v1.0: 120+ digit numbers (production ready) **Key technical decisions:** - Pure Python with optional gmpy2 for performance - Target ~10x slower than CADO-NFS (acceptable for Python)