Prior to this commit, primes(6) relied solely on sieving with primes up
to 65537, with the effect that composite numbers which are the product
of two non-16-bit primes would be incorrectly identified as prime. For
example,
# primes 1099511627800 1099511627820
would output
1099511627803
1099511627807
1099511627813
when in fact only the first of those values is prime.
This commit adds strong pseudoprime tests to validate the candidates
which pass the initial sieving stage, using bases of 2, 3, 5, 7, 11,
13, 17, 19, and 23. Thanks to papers from C. Pomerance, J.L. Selfridge,
and S.S. Wagstaff, Jr.; G. Jaeschke; and Y. Jiang and Y. Deng, we know
that the smallest value which passes these tests is 3825123056546413051.
At present we do not know how many strong pseudoprime tests are required
to prove primality for values larger than 3825123056546413050, so we
force primes(6) to stop at that point.
Reviewed by: jmg
Relnotes: primes(6) now correctly enumerates primes up to
3825123056546413050
MFC after: 7 days
Sponsored by: EuroBSDCon devsummit
and finish the job. ncurses is now the only Makefile in the tree that
uses it since it wasn't a simple mechanical change, and will be
addressed in a future commit.
Use '0' for base rather than 10 to allow for more flexible input bases.
Inspired by changes in PR 7402, but mostly redone by me to get past
bde filter.
Submitted by: Timo J. Rinne
PR: 7402
PR7402 was even less suitable for committing almost verbatim than at
first appearance. Rev.1.9 of primes.c has at least the following defects.
- no update for man page.
- no update for usage string.
- blowing away of a previous commit to change EOF to -1 in getopt() test.
- blowing away of a previous commit to fix printf format errors.
- new printf format errors.
- one gratuitous ANSIism.
- two style bugs.
- ... and a partition in a pear tree.
PR: 7402
EOF? The getopt(3) manpage clearly states that the return value is *-1*,
not EOF! Besides, getopt(3) isn't reading from a file. :)
Noticed-while: merging to 2.2 (where this is correct).
of the x11 based games. I'm not going to tag the originals with bsd_44_lite
and do this in two stages since it's just not worth it for this collection,
and I've got directory renames to deal with that way. Bleah.
Submitted by: jkh
