Confirmed Factors of Mersenne Numbers

✅ Version 2 Announcement: Complete Coverage up to 36 Bits This new version marks a major milestone in the project: ✅ All verified factors of Mersenne numbers up to 36 bits have now been found and published. The dataset now contains a complete set of factors of the form: n = 2 k p + 1 where: p is a prime exponent of a Mersenne number (Mₚ = 2ᵖ − 1) k is a positive integer n is a prime factor of Mₚ with bit length ≤ 36 🧩 The full range of odd primes less than 2³⁶ = 68,719,476,736 has been searched.Every matching factor has been mathematically verified — no probabilistic tests were used. 📈 Dataset Growth Previous total (v1): 42,187,622 confirmed factors New in this release: 21,921,439 additional factors (all 36-bit) Total as of version 2: 64,109,061 verified Mersenne factors The new data is split across 6 additional .csv files (parte_010 through parte_015), following the same structure and format as the previous ones. 🔬 Methodology All factors have been verified to divide their corresponding Mersenne number using deterministic checks.The internal algorithm used is proprietary and not published at this time, but: ✅ The scan included all odd primes less than 2³⁶.✅ Every valid Mersenne relation n = 2 · k · p + 1 was tested.✅ No factors were skipped or filtered. Anyone is welcome to independently verify the results. 🚀 What's Next? Work has already started on the 37-bit range (n < 2³⁷).Future versions will continue incrementally — adding only new files, never altering previous results.