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researchv10 Dan Cross

.TH FACTOR 1 
.CT 1 numbers
.SH NAME
factor, qfactor, primes \(mi factor a number, generate large primes
.SH SYNOPSIS
.B factor
[
.I number
]
.PP
.B qfactor
.PP
.B primes
[
.I start
[
.I finish
]
]
.SH DESCRIPTION
.I Factor
prints
.I number
and its prime factors,
each repeated 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.
Maximum running time is proportional to
.if n sqrt(n).
.if t .I \(sr\o'n\(rn'.
.PP
.ig
.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 will factor numbers
up to about 40 digits.
For large numbers it is much faster than
.I factor.
.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.

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