coreutils: factor invocation

1 
1 26.1 ‘factor’: Print prime factors
1 ==================================
1 
1 ‘factor’ prints prime factors.  Synopses:
1 
1      factor [NUMBER]...
1      factor OPTION
1 
1    If no NUMBER is specified on the command line, ‘factor’ reads numbers
1 from standard input, delimited by newlines, tabs, or spaces.
1 
1    The ‘factor’ command supports only a small number of options:
1 
1 ‘--help’
1      Print a short help on standard output, then exit without further
1      processing.
1 
1 ‘--version’
1      Print the program version on standard output, then exit without
1      further processing.
1 
1    Factoring the product of the eighth and ninth Mersenne primes takes
1 about 30 milliseconds of CPU time on a 2.2 GHz Athlon.
1 
1      M8=$(echo 2^31-1|bc)
1      M9=$(echo 2^61-1|bc)
1      n=$(echo "$M8 * $M9" | bc)
1      /usr/bin/time -f %U factor $n
1      4951760154835678088235319297: 2147483647 2305843009213693951
1      0.03
1 
1    Similarly, factoring the eighth Fermat number 2^{256}+1 takes about
1 20 seconds on the same machine.
1 
1    Factoring large numbers is, in general, hard.  The Pollard-Brent rho
1 algorithm used by ‘factor’ is particularly effective for numbers with
1 relatively small factors.  If you wish to factor large numbers which do
1 not have small factors (for example, numbers which are the product of
1 two large primes), other methods are far better.
1 
1    If ‘factor’ is built without using GNU MP, only single-precision
1 arithmetic is available, and so large numbers (typically 2^{128} and
1 above) will not be supported.  The single-precision code uses an
1 algorithm which is designed for factoring smaller numbers.
1 
1    An exit status of zero indicates success, and a nonzero value
1 indicates failure.
1