.TH FACTOR 1 
.SH NAME
factor, primes \- factor a number, generate large primes
.SH SYNOPSIS
.B factor
[ number ]
.PP
.B primes
.SH DESCRIPTION
When
.I factor
is invoked without an argument, it waits for a number to be typed in.
If you type in a positive
number less than 2\u\s756\s0\d (about
.if n 7.2e16)
.if t 7.2\(mu10\u\s716\s0\d\|)
it will factor the number and print its prime factors; each one is printed
the proper number of times.
Then it waits for another number.
It exits if it encounters a zero or any non-numeric character.
.PP
If
.I factor
is invoked with an argument, it factors the number
as above and then exits.
.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.
It takes 1 minute to factor a prime
near
10\u\s714\s0\d
on a PDP11.
.PP
When
.I primes
is invoked, it waits for a number to be typed in.
If you type in a positive
number less than 2\u\s756\s0\d
it will print all primes greater than or
equal to this number.
.SH DIAGNOSTICS
`Ouch.' for input out of range or for garbage input.