prime
Factor the given integer with the default factorization method.
Factor the given integer using trial division.
Factor the given integer using trial division.
This is the slowest method, but is still reasonable for numbers up to about 14 decimal digits or so.
Factor the given integer using trial division with a wheel.
Factor the given integer using trial division with a wheel.
This is slightly faster than basic trial divison (about 30% or so). It's still mostly appropriate for small-ish numbers.
Determine if the given integer is prime.
Determine if the given integer is prime.
Currently this using a strong pseudo-primality test (so there is a 1-in-1,000,000,000,000 chance of being wrong).
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, use BigInteger.isProbablePrime(30) 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.