gives a certificate that n is prime or that n is composite.
- To use PrimeQCertificate, you first need to load the Primality Proving Package using Needs["PrimalityProving`"].
- PrimeQCertificate uses the Pratt certificate and the Atkin–Morain certificate for primality.
- A certificate of compositeness is a list of three integers, either or , with .
- A prime always satisfies . The certificate can be used to show that n is composite by demonstrating that .
- Any number whose square is for prime must satisfy . The certificate can be used to show that n is composite by demonstrating that and .
- A certificate of primality consists of a recursive list of certificates which prove that is a prime if one or more smaller numbers are prime as well.
- PrimeQCertificate has the same options as ProvablePrimeQ.