probable prime

A sufficiently large odd integer $q$ believed to be a prime number because it has passed some preliminary primality test relative to a given base, or a pattern suggests it might be prime, but it has not yet been subjected to a conclusive primality test.

For primes with no specific form, it is required to test every potential prime factor $p<\\sqrt{q}$ to be absolutely sure that $q$ is in fact a prime. For Mersenne probable primes, the Lucas-Lehmer test is accepted as a conclusive primality test.

Once a probable prime is conclusively shown to be a prime, it of course loses the label ”probable.” It also loses it if conclusively shown to be composite, but in that case it might then be called a pseudoprime (http://planetmath.org/PseudoprimeP) relative to base $a$ .

单词	ProbablePrime
释义	probable prime A sufficiently large odd integer $q$ believed to be a prime number because it has passed some preliminary primality test relative to a given base, or a pattern suggests it might be prime, but it has not yet been subjected to a conclusive primality test. For primes with no specific form, it is required to test every potential prime factor $p<\\sqrt{q}$ to be absolutely sure that $q$ is in fact a prime. For Mersenne probable primes, the Lucas-Lehmer test is accepted as a conclusive primality test. Once a probable prime is conclusively shown to be a prime, it of course loses the label ”probable.” It also loses it if conclusively shown to be composite, but in that case it might then be called a pseudoprime (http://planetmath.org/PseudoprimeP) relative to base $a$ .
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