expensive than the verification of Pratt certificates, but does not require any computation to determine the certificate itself. References External links Mathworld: Primality Certificate Mathworld: Pratt Certificate Mathworld: Atkin-Goldwasser-Kilian-Morain Certificate The Prime Glossary: Certificate of Primality Vašek Chvátal. Lecture notes on Pratt's Primality Proofs. Department of Computer Science. Rutgers University. PDF version at Concordia University. Wim van Dam. Proof of Pratt's Theorem. (Lecture notes, PDF) Primality tests