core

Basic tools for prime factorization.

This package is intended to provide tools for factoring numbers, checking primality, generating prime numbers, etc. For now, its main contributions are a method for factoring integers (spire.math.prime.factor) and a type for representing prime factors and their exponents (spire.math.prime.Factors).

The factorization currently happens via an implementation of Pollard-Rho with Brent's optimization. This technique works very well for composites with small prime factors (up to 10 decimal digits or so) and can support semiprimes (products of two similarly-sized primes) of 20-40 digits.

The implementation does cheat, using BigInteger.isProbablePrime(40) to test basic primality. This has a roughly 1-in-1,000,000,000,000 chance of being wrong.

Since Pollard-Rho uses random primes, its performance is somewhat non-deterministic. On this machine, factoring 20-digit semiprimes seem to average about 1.5s and factoring 30-digit semiprimes seem to average about 20s. Much larger numbers can be factored provided they are either prime or composites with smallish factors.