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A short set of data that proves the primality of a number. A certificate can, in general, be checked much more quickly than the time required to generate the certificate. Varieties of primality certificates include the Pratt Certificate and Atkin-Goldwasser-Kilian-Morain Certificate.
See also Atkin-Goldwasser-Kilian-Morain Certificate, Compositeness Certificate, Pratt Certificate
References
Wagon, S. ``Prime Certificates.'' §8.7 in Mathematica in Action. New York: W. H. Freeman,
pp. 277-285, 1991.