.TH FACTOR 1 
.SH NAME
factor, lfactor, qfactor, primes \- factor a number, generate large primes
.SH SYNOPSIS
.B factor
[ number ]
.PP
.B lfactor
.PP
.B qfactor
.PP
.B primes
[ start [ finish ] ]
.SH DESCRIPTION
.I factor
prints
.I number
and its prime factors,
each repated the proper number of times.
The number must be positive and less than
.if n 2**56
.if t 2\u\s756\s0\d
(about
.if n 7.2e16)
.if t 7.2\(mu10\u\s716\s0\d\|).
.PP
If no
.I number 
is given,
.I factor
reads a stream of numbers from the standard input and factors them.
It exits on any input not a positive integer.
.PP
Maximum time to factor is proportional to
.if n sqrt(n)
.if t \(sr\o'\fIn\fR\(rn'
and occurs when
.I n
is prime
or the square of a prime.
.PP
.I lfactor
reads one number from the standard input and factors it.
Worst-case running time is proportional to
.if n .IR n **(1/5);
.if t .IR n \u\s-21/5\s0\d;
it beats
.I factor
for hard 12-digit problems and is workable to around
.if n .IR n =10**30.
.if t .IR n =10\u\s-230\s0\d.
.I qfactor
reads one number from the standard input and factors it.
It is almost always better than
.I lfactor ,
and will factor numbers
up to about 40 digits.
.PP
.I primes
prints the prime numbers ranging from
.I start
to
.I finish,
where
.I start
and
.I finish
are positive numbers less than 
.if n 2**56.
.if t 2\u\s756\s0\d.
If 
.I finish
is missing,
.I primes
prints without end;
if
.I start
is missing, it reads the starting number from the
standard input.
.SH DIAGNOSTICS
`Ouch.' for input out of range or for garbage input.
.SH BUGS
.I lfactor
makes mysterious progress reports on its arcane inner workings.
.I qfactor
does too.