https://github.com/uutils/num-prime

Generic and optimized primality test, factorization and various number theoretic functions with arbitrary precision based on `num`.
https://github.com/uutils/num-prime

Last synced: 3 months ago
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Generic and optimized primality test, factorization and various number theoretic functions with arbitrary precision based on `num`.

• Host: GitHub
• URL: https://github.com/uutils/num-prime
• Owner: uutils
• License: apache-2.0
• Created: 2022-01-08T04:34:57.000Z (over 4 years ago)
• Default Branch: main
• Last Pushed: 2026-02-18T21:34:19.000Z (3 months ago)
• Last Synced: 2026-02-18T23:49:00.332Z (3 months ago)
• Language: Rust
• Homepage:
• Size: 521 KB
• Stars: 25
• Watchers: 3
• Forks: 14
• Open Issues: 20
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Roadmap: ROADMAP.md

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README

          
# num-prime

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This crate provides utilities for prime number related functionalities:

- Primality testing

  - Deterministic primality check of `u64` integers (using a very fast hashing algorithm)

  - Fermat probable prime test

  - Miller-rabin probable prime test

  - (strong/extra strong) Lucas probable prime test

  - Baillie-PSW test

  - Sophie Germain safe prime test

- Primes generation and indexing

  - A naive implementation of the sieve of Eratosthenes

  - Unified API to support other prime generation backends

  - Generate random (safe) primes

  - Find previous/next prime

- Integer factorization

  - Trial division

  - Pollard's rho algorithm

  - Shanks's square forms factorization (SQUFOF)

  - Fast factorization of `u64` and `u128` integers

- Number theoretic functions

  - Prime Pi function (number of primes under limit), its estimation and its bounds

  - Nth prime, its estimation and its bounds

  - Moebius function

  - Divisor Sigma function *([in examples](./examples/divisor_sigma.rs))*

  - Prime Omega function *([in examples](./examples/prime_omega.rs))*

It's based on the `num` creates and most functions are decently optimized with pre-computed tables (see **[benchmark results here](./PERFORMANCE.md)**).