probable prime
A sufficiently large odd integer 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 to be absolutely sure that 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 .
| Title | probable prime |
|---|---|
| Canonical name | ProbablePrime |
| Date of creation | 2013-03-22 15:53:46 |
| Last modified on | 2013-03-22 15:53:46 |
| Owner | PrimeFan (13766) |
| Last modified by | PrimeFan (13766) |
| Numerical id | 5 |
| Author | PrimeFan (13766) |
| Entry type | Definition |
| Classification | msc 11A41 |