Fastest single-file factorization and primality testing for 32-bit and 64-bit integers on x86.

Primality testing:

bool IsPrime(U32 x);
bool IsPrime(U64 x);

Factorization:

FactorizeResult32 Factorize(U32 x);
FactorizeResult64 Factorize(U64 x);

Up to about 2³⁸, it is possible to test for primality even faster if you're okay with consuming a bunch of memory, using a fast prime sieve. See https://github.com/komrad36/PrimeSieve

For BigInts - integers larger than a machine word (32 or 64 bits), see https://github.com/komrad36/EllipticCurveFactorization.