High Quality Content by WIKIPEDIA articles! In mathematics, Pepin's test is a primality test, which can be used to determine whether a Fermat number is prime. It is a variant of Proth's test. The test is named for a French mathematician, Theophile Pepin. Let F_n=2^{2^n}+1 be the nth Fermat number. Pepin's test states that for n > 0, Fn is prime if and only if 3^{(F_n-1)/2}equiv-1pmod{F_n}. The expression, 3^{(F_n-1)/2} can be evaluated modulo Fn by repeated squaring. This makes the test a fast polynomial-time algorithm. However, Fermat numbers grow so rapidly that only a handful of Fermat numbers can be tested in a reasonable amount of time and space. Other bases may be used in place of 3, for example 5, 6, 7, or 10 (sequence A129802 in OEIS).

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