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单词 FermatCompositenessTest
释义

Fermat compositeness test


The Fermat compositeness testMathworldPlanetmath is a primality test based on the observation that by Fermat’s little theorem if bn-11(modn) and b0(modn), then n is composite. The Fermat compositeness test consists of checking whether bn-11(modn) for a handful of values of b. If a b with bn-11(modn) is found, then n is composite.

A value of b for which bn-11(modn) is called a witness to n’s compositeness. If bn-11(modn), then n is said to be pseudoprime base b.

It can be proven that most composite numbers can be shown to be composite by testing only a few values of b. However, there are infinitely many composite numbers that are pseudoprime in every base. These are Carmichael numbers (see OEIS sequence http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002997A002997 for a list of first few Carmichael numbers).

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更新时间:2025/5/4 14:07:07