A complete, proof-of-concept, C# implementation of the General Number Field Sieve algorithm for factoring very large semi-prime numbers. The focus was on readability and understandability of the code, not performance.

A Java math library focused on number theory and integer factorization in particular.

R Package for Factoring Big Integers using the C Library GMP (GNU Multiple Precision Arithmetic)

High-performance integer factorization suite implementing GNFS, MPQS, and QS algorithms with optimized lattice reduction, vectorization, GPU acceleration, and tensor-based linear algebra. Features automatic algorithm selection, NUMA-aware scheduling, and checkpoint/restore for computational number theory research and cryptanalytic analysis.

EPR: A Factoring and Primality checking library for C++

A collection of Integer factorization algorithms

A collection of notes on mathematical Cryptography, ranging from classical methods through contemporary.

Very large integer factorization implemented in Python

Taxicab numbers, upper bounds up to BTa(23), their decomposition x³ + y³ (and prime factor decomposition)

Implementation of batch smoothness checking and factorization for Coppersmith's factorization factory.

A Python implementation of the General number field sieve algorithm for factoring large integers

Educational Python toolkit for integer factorization with CLI, API, benchmarks, and documented algorithms.

A Practical Study and Comparison of Integer Factorization Methods

This project implements the Rabin Cryptosystem in SageMath, a public-key encryption algorithm based on the integer factorization problem. The system uses blum primes for p and q to simplify the decryption process.

Fast and efficient Fermat factorization CLI

Empirical suite for the Z/6Z Topological Prior. This quantum state preparation protocol uses bounded MPS to confine amplitudes to prime channels, inducing a resilient Non-Ergodic Extended (NEE) phase under Lindblad noise. By passively purging 66.6% of the search space, it massively reduces T-count for FTQC and enables NISQ cryptanalysis.

格子を用いた素因数分解法

Prime decomposition of Kaprekar numbers (up to 29 digits)

素数判定法と素因数分解アルゴリズムに関する教科書(pythonコード付き)

CADO-NFS (modern): an enhanced modernization + performance fork of CADO-NFS (Number Field Sieve — integer factorization & discrete log) on current toolchains. Adds GPU linear algebra + full vector residency, a GPU ECM pre-factoring front-end, SDE-validated AVX-512 VPCLMULQDQ/IFMA kernels, and Rust orchestration. LGPL-2.1.