Ubuntu Manpages

math::numtheory

Number Theory






package require Tcl ?8.5?


package require math::numtheory ?1.0?


math::numtheory::isprime N ?option
    value ...?










This package is for collecting various number-theoretic
    operations, though at the moment it only provides that of testing whether an
    integer is a prime.



  

  
The isprime command tests whether the integer N is a prime,
      returning a boolean true value for prime N and a boolean false
      value for non-prime N. The formal definition of ´prime' used
      is the conventional, that the number being tested is greater than 1 and
      only has trivial divisors.
    
To be precise, the return value is one of 0 (if
        N is definitely not a prime), 1 (if N is definitely
        a prime), and on (if N is probably prime); the latter two
        are both boolean true values. The case that an integer may be classified
        as "probably prime" arises because the Miller-Rabin algorithm
        used in the test implementation is basically probabilistic, and may if
        we are unlucky fail to detect that a number is in fact composite.
        Options may be used to select the risk of such "false
        positives" in the test. 1 is returned for "small"
        N (which currently means N < 118670087467), where it is
        known that no false positives are possible.

    
The only option currently defined is:

  







  

  
which controls how many times the Miller-Rabin test should be repeated
      with randomly chosen bases. Each repetition reduces the probability of a
      false positive by a factor at least 4. The default for repetitions
      is 4.







  

  
Unknown options are silently ignored.








number theory, prime






Mathematics





Copyright (c) 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>