FACTOR(1)                                               FACTOR(1)

     NAME
          factor, lfactor, qfactor, primes - factor a number, generate
          large primes

     SYNOPSIS
          factor [ number ]

          lfactor

          qfactor

          primes [ start [ finish ] ]

     DESCRIPTION
          Factor prints number and its prime factors, each repated the
          proper number of times.  The number must be positive and
          less than 2**56 (about 7.2e16)

          If no number is given, factor reads a stream of numbers from
          the standard input and factors them.  It exits on any input
          not a positive integer.

          Maximum time to factor is proportional to sqrt(n) and occurs
          when n is prime or the square of a prime.

          Lfactor reads one number from the standard input and factors
          it.  Worst-case running time is proportional to n**(1/5); it
          beats factor for hard 12-digit problems and is workable to
          around n=10**30. Qfactor reads one number from the standard
          input and factors it.  It is almost always better than
          lfactor , and will factor numbers up to about 40 digits.

          Primes prints the prime numbers ranging from start to
          finish, where start and finish are positive numbers less
          than 2**56.  If finish is missing, primes prints without
          end; if start is missing, it reads the starting number from
          the standard input.

     DIAGNOSTICS
          `Ouch.' for input out of range or for garbage input.

     BUGS
          Lfactor makes mysterious progress reports on its arcane
          inner workings.  Qfactor does too.