A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number 
. Witnesses are most commonly used in connection with Fermat's
little theorem converse. A Pratt certificate
uses witnesses to prove primality, and Miller's
primality test uses witnesses to prove compositeness.
Witness
See also
Adleman-Pomerance-Rumely Primality Test, Fermat's Little Theorem Converse, Miller's Primality Test, Pratt Certificate, Primality CertificateExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Witness." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Witness.html