SOLUTIONS

PRIMALITY PROVING 程序包 符号
PrimeQCertificate
PrimeQCertificate[n]
gives a certificate that n is prime or that n is composite.
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 To use , you first need to load the Primality Proving Package using Needs["PrimalityProving`"].
 uses the Pratt certificate and the AtkinMorain certificate for primality.
 A certificate of compositeness is a list of three integers, either or , with .
 A prime always satisfies . The certificate can be used to show that n is composite by demonstrating that .
 Any number whose square is for prime must satisfy . The certificate can be used to show that n is composite by demonstrating that and .
 A certificate of primality consists of a recursive list of certificates which prove that is a prime if one or more smaller numbers are prime as well.
 has the same options as ProvablePrimeQ.
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基本范例 (2)基本范例 (2)
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A certificate that can be used to prove that is a prime:
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The same certificate can be obtained by using ProvablePrimeQ with the option "Certificate">True:
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A certificate that can be used to prove that is composite:
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The output is a list of three integers that indicate is composite, and that it violates Fermat's little theorem for primes, if is prime:
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