# 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 $a$.

Title probable prime ProbablePrime 2013-03-22 15:53:46 2013-03-22 15:53:46 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 11A41