num-prime

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)
  • Prime Omega function (in examples)

It's based on the num creates and most functions are decently optimized with pre-computed tables (see benchmark results here).