Imported and adapted from FreeBSD svn r272166 and r272207; this fixes

false positives for products of primes larger than 2^16. For example,
before this commit:

  $ /usr/games/primes 4295360521 4295360522
  4295360521
but
  $ /usr/games/factor 4295360521
  4295360521: 65539 65539

or
  $ /usr/games/primes 3825123056546413049 3825123056546413050
  3825123056546413049
yet
  $ /usr/games/factor 3825123056546413049
  3825123056546413049: 165479 23115459100831

or
  $ /usr/games/primes 18446744073709551577
  18446744073709551577
although
  $ /usr/games/factor 18446744073709551577
  18446744073709551577: 139646831 132095686967

Incidentally, the above examples show the smallest and largest cases that
were erroneously stated as prime in the range 2^32 .. 3825123056546413049
.. 2^64; the primes(6) program now stops at 3825123056546413050 as
primality tests on larger integers would be by brute force factorization.

In addition, special to the NetBSD version:
. for -d option, skip first difference when start is >65537 as it is incorrect
. corrected usage to mention both the existing -d as well as the new -h option

For original FreeBSD commit message by Colin Percival, see:
http://svnweb.freebsd.org/base?view=revision&revision=272166

1 files changed, 30 insertions, 12 deletions

diff --git a/primes/primes.6 b/primes/primes.6
index 9499398f..6928fe66 100644
--- a/primes/primes.6
+++ b/primes/primes.6
@@ -1,4 +1,4 @@
-.\"	$NetBSD: primes.6,v 1.3 2008/02/03 03:29:17 wiz Exp $
+.\"	$NetBSD: primes.6,v 1.4 2014/10/02 21:36:37 ast Exp $
 .\"
 .\" Copyright (c) 1989, 1993
 .\"	The Regents of the University of California.  All rights reserved.
@@ -33,9 +33,7 @@
 .\"	@(#)factor.6	8.1 (Berkeley) 5/31/93
 .\"
 .\"
-.\" By: Landon Curt Noll   chongo@toad.com,   ...!{sun,tolsoft}!hoptoad!chongo
-.\"
-.\"   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+.\" By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
 .\"
 .Dd February 3, 2008
 .Dt PRIMES 6
@@ -46,6 +44,7 @@
 .Sh SYNOPSIS
 .Nm primes
 .Op Fl d
+.Op Fl h
 .Op Ar start Op Ar stop
 .Sh DESCRIPTION
 The
@@ -61,18 +60,18 @@ value must be at least 0 and not greater than
 .Ar stop .
 The
 .Ar stop
-value must not be greater than 4294967295.
+value must not be greater than 3825123056546413050.
 The default value of
 .Ar stop
-is 4294967295.
+is 3825123056546413050.
 .Pp
 When the
 .Nm
 utility is invoked with no arguments,
 .Ar start
-is read from standard input.
+is read from standard input and
 .Ar stop
-is taken to be 4294967295.
+is taken to be 3825123056546413050.
 The
 .Ar start
 value may be preceded by a single
@@ -81,15 +80,34 @@ The
 .Ar start
 value is terminated by a non-digit character (such as a newline).
 The input line must not be longer than 255 characters.
+.Pp
 When given the
 .Fl d
 argument,
 .Nm
 prints the difference between the current and the previous prime.
+.Pp
+When given the
+.Fl h
+argument,
+.Nm
+prints the prime numbers in hexadecimal.
 .Sh DIAGNOSTICS
 Out of range or invalid input results in
-an appropriate error message
-being written to standard error.
-.Sh BUGS
+an appropriate error message to standard error.
+.Sh AUTHORS
+Originally by
+.An Landon Curt Noll ,
+extended to some 64-bit primes by
+.An Colin Percival .
+.Sh CAVEATS
+This
 .Nm
-won't get you a world record.
+program won't get you a world record.
+.Pp
+The program is not able to list primes between
+3825123056546413050 and 18446744073709551615 (2^64
+- 1) as it relies on strong pseudoprime tests after
+sieving, and it is yet unknown how many of those
+tests are needed to prove primality for integers
+larger than 3825123056546413050.