(coreutils.info.gz) factor invocation

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 26.1 'factor': Print prime factors
 ==================================
 
 'factor' prints prime factors.  Synopses:
 
      factor [NUMBER]...
      factor OPTION
 
    If no NUMBER is specified on the command line, 'factor' reads numbers
 from standard input, delimited by newlines, tabs, or spaces.
 
    The 'factor' command supports only a small number of options:
 
 '--help'
      Print a short help on standard output, then exit without further
      processing.
 
 '--version'
      Print the program version on standard output, then exit without
      further processing.
 
    Factoring the product of the eighth and ninth Mersenne primes takes
 about 30 milliseconds of CPU time on a 2.2 GHz Athlon.
 
      M8=$(echo 2^31-1|bc)
      M9=$(echo 2^61-1|bc)
      n=$(echo "$M8 * $M9" | bc)
      /usr/bin/time -f %U factor $n
      4951760154835678088235319297: 2147483647 2305843009213693951
      0.03
 
    Similarly, factoring the eighth Fermat number 2^{256}+1 takes about
 20 seconds on the same machine.
 
    Factoring large numbers is, in general, hard.  The Pollard Rho
 algorithm used by 'factor' is particularly effective for numbers with
 relatively small factors.  If you wish to factor large numbers which do
 not have small factors (for example, numbers which are the product of
 two large primes), other methods are far better.
 
    If 'factor' is built without using GNU MP, only single-precision
 arithmetic is available, and so large numbers (typically 2^{64} and
 above) will not be supported.  The single-precision code uses an
 algorithm which is designed for factoring smaller numbers.
 
    An exit status of zero indicates success, and a nonzero value
 indicates failure.
 

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