A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number n. 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.

See also

Adleman-Pomerance-Rumely Primality Test, Fermat's Little Theorem Converse, Miller's Primality Test, Pratt Certificate, Primality Certificate

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Cite this as:

Weisstein, Eric W. "Witness." From MathWorld--A Wolfram Web Resource.

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