1.\" Copyright (c) 1989, 1993
2.\" The Regents of the University of California. All rights reserved.
3.\"
4.\" This code is derived from software contributed to Berkeley by
5.\" Landon Curt Noll.
6.\"
7.\" Redistribution and use in source and binary forms, with or without
8.\" modification, are permitted provided that the following conditions
9.\" are met:
10.\" 1. Redistributions of source code must retain the above copyright
11.\" notice, this list of conditions and the following disclaimer.
12.\" 2. Redistributions in binary form must reproduce the above copyright
13.\" notice, this list of conditions and the following disclaimer in the
14.\" documentation and/or other materials provided with the distribution.
15.\" 3. Neither the name of the University nor the names of its contributors
16.\" may be used to endorse or promote products derived from this software
17.\" without specific prior written permission.
18.\"
19.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
20.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29.\" SUCH DAMAGE.
30.\"
31.\" @(#)factor.6 8.1 (Berkeley) 5/31/93
32.\"
33.\" $FreeBSD: head/games/factor/factor.6 272166 2014-09-26 09:40:48Z cperciva $
34.\"
35.\" By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
36.\"
37.\" chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
38.\"
39.Dd October 10, 2002
40.Dt FACTOR 6
41.Os
42.Sh NAME
43.Nm factor , primes
44.Nd factor a number, generate primes
45.Sh SYNOPSIS
46.Nm
47.Op Fl h
48.Op Ar number ...
49.Nm primes
50.Op Fl h
51.Op Ar start Op Ar stop
52.Sh DESCRIPTION
53The
54.Nm
55utility will factor positive integers.
56When a number is factored, it is printed, followed by a
57.Ql \&: ,
58and the list of factors on a single line.
59Factors are listed in ascending order, and are preceded by a space.
60If a factor divides a value more than once, it will be printed more than once.
61.Pp
62When
63.Nm
64is invoked with one or more arguments, each argument will be factored.
65.Pp
66When
67.Nm
68is invoked with no arguments,
69.Nm
70reads numbers, one per line, from standard input, until end of file or error.
71Leading white-space and empty lines are ignored.
72Numbers may be preceded by a single
73.Ql + .
74Numbers are terminated by a non-digit character (such as a newline).
75After a number is read, it is factored.
76.Pp
77The
78.Nm primes
79utility prints primes in ascending order, one per line, starting at or above
80.Ar start
81and continuing until, but not including
82.Ar stop .
83The
84.Ar start
85value must be at least 0 and not greater than
86.Ar stop .
87The
88.Ar stop
89value must not be greater than the maximum.
90The default and maximum value of
91.Ar stop
92is 4294967295 on 32-bit architectures
93and 3825123056546413050 on 64-bit ones.
94.Pp
95When the
96.Nm primes
97utility is invoked with no arguments,
98.Ar start
99is read from standard input and
100.Ar stop
101is taken to be the maximum.
102The
103.Ar start
104value may be preceded by a single
105.Ql + .
106The
107.Ar start
108value is terminated by a non-digit character (such as a newline).
109.Sh DIAGNOSTICS
110.Bl -diag
111.It "negative numbers aren't permitted"
112.It "illegal numeric format"
113.It "start value must be less than stop value"
114.It "Result too large"
115.El
116.Sh BUGS
117.Nm
118cannot handle the
119.Dq "10 most wanted"
120factor list,
121.Nm primes
122will not get you a world record.
123.Pp
124.Nm primes
125is unable to list primes between 3825123056546413050 and 18446744073709551615
126since it relies on strong pseudoprime tests after sieving, and nobody has
127proven how many strong pseudoprime tests are required to prove primality for
128integers larger than 3825123056546413050.
2.\" The Regents of the University of California. All rights reserved.
3.\"
4.\" This code is derived from software contributed to Berkeley by
5.\" Landon Curt Noll.
6.\"
7.\" Redistribution and use in source and binary forms, with or without
8.\" modification, are permitted provided that the following conditions
9.\" are met:
10.\" 1. Redistributions of source code must retain the above copyright
11.\" notice, this list of conditions and the following disclaimer.
12.\" 2. Redistributions in binary form must reproduce the above copyright
13.\" notice, this list of conditions and the following disclaimer in the
14.\" documentation and/or other materials provided with the distribution.
15.\" 3. Neither the name of the University nor the names of its contributors
16.\" may be used to endorse or promote products derived from this software
17.\" without specific prior written permission.
18.\"
19.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
20.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29.\" SUCH DAMAGE.
30.\"
31.\" @(#)factor.6 8.1 (Berkeley) 5/31/93
32.\"
33.\" $FreeBSD: head/games/factor/factor.6 272166 2014-09-26 09:40:48Z cperciva $
34.\"
35.\" By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
36.\"
37.\" chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
38.\"
39.Dd October 10, 2002
40.Dt FACTOR 6
41.Os
42.Sh NAME
43.Nm factor , primes
44.Nd factor a number, generate primes
45.Sh SYNOPSIS
46.Nm
47.Op Fl h
48.Op Ar number ...
49.Nm primes
50.Op Fl h
51.Op Ar start Op Ar stop
52.Sh DESCRIPTION
53The
54.Nm
55utility will factor positive integers.
56When a number is factored, it is printed, followed by a
57.Ql \&: ,
58and the list of factors on a single line.
59Factors are listed in ascending order, and are preceded by a space.
60If a factor divides a value more than once, it will be printed more than once.
61.Pp
62When
63.Nm
64is invoked with one or more arguments, each argument will be factored.
65.Pp
66When
67.Nm
68is invoked with no arguments,
69.Nm
70reads numbers, one per line, from standard input, until end of file or error.
71Leading white-space and empty lines are ignored.
72Numbers may be preceded by a single
73.Ql + .
74Numbers are terminated by a non-digit character (such as a newline).
75After a number is read, it is factored.
76.Pp
77The
78.Nm primes
79utility prints primes in ascending order, one per line, starting at or above
80.Ar start
81and continuing until, but not including
82.Ar stop .
83The
84.Ar start
85value must be at least 0 and not greater than
86.Ar stop .
87The
88.Ar stop
89value must not be greater than the maximum.
90The default and maximum value of
91.Ar stop
92is 4294967295 on 32-bit architectures
93and 3825123056546413050 on 64-bit ones.
94.Pp
95When the
96.Nm primes
97utility is invoked with no arguments,
98.Ar start
99is read from standard input and
100.Ar stop
101is taken to be the maximum.
102The
103.Ar start
104value may be preceded by a single
105.Ql + .
106The
107.Ar start
108value is terminated by a non-digit character (such as a newline).
109.Sh DIAGNOSTICS
110.Bl -diag
111.It "negative numbers aren't permitted"
112.It "illegal numeric format"
113.It "start value must be less than stop value"
114.It "Result too large"
115.El
116.Sh BUGS
117.Nm
118cannot handle the
119.Dq "10 most wanted"
120factor list,
121.Nm primes
122will not get you a world record.
123.Pp
124.Nm primes
125is unable to list primes between 3825123056546413050 and 18446744073709551615
126since it relies on strong pseudoprime tests after sieving, and nobody has
127proven how many strong pseudoprime tests are required to prove primality for
128integers larger than 3825123056546413050.