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Groups > comp.programming > #5722
| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Newsgroups | comp.programming |
| Subject | Re: really? (lame question about primes) |
| Date | 2015-09-02 16:37 +0200 |
| Organization | A noiseless patient Spider |
| Message-ID | <ms71gl$hho$1@dont-email.me> (permalink) |
| References | (9 earlier) <ms6ov4$evq$1@dont-email.me> <yPBFx.319631$IK6.308401@fx46.am4> <ms6rm0$td4$1@speranza.aioe.org> <ms6uia$57r$1@dont-email.me> <ms710a$beb$1@speranza.aioe.org> |
On 02/09/15 16:27, bartekltg wrote: > On 02.09.2015 15:47, David Brown wrote: >> On 02/09/15 14:56, bartekltg wrote: >>> On 02.09.2015 14:19, Richard Heathfield wrote: >>>> On 02/09/2015 13:12, David Brown wrote: >>>>> >>>> <snip> >>>>> >>>>> There are a number of ways of doing this check faster than the >>>>> bit-for-bit long division you suggested elsewhere, >>>> >>>> The advantage of that way is that it's easy to explain, and relatively >>>> easy to implement. Having said that, I *haven't* implemented it (in >>>> software). My bignum library uses Algorithm D, from TAOCP II. >>> >>> I think explain something by using wrong algorithm can hurt >>> someone who think, so propably everyone who is listening to >>> 'how to factorize an integer;-)' >>> >>> But we can resurect this idea. >>> >>> Table of all n-digits prime can be too big for the universe, >>> so we have to generate it. One ot the simplest method is >>> to implement 'nextprime' - function that get the next odd*) >>> number and run fast primality test (Miller-Rabin), >>> repeat it until the number is pseudoprime. >>> >> >> The principle here is that to find the factors of C, we run through all >> primes A up to sqrt(C), and test if C % A == 0. (It may be that there >> are other faster algorithms, but I don't know of any.) If you know for >> sure the number of digits in A, then you could start 10^(noOfDigits-1), >> but that would only save 10% of the test time. >> >> Testing for the primality of each A is going to take a great deal more >> time than simply trying C % A == 0, even with a probable prime test. It >> is simply not worth doing. >> >> What would be worth doing, I think, is to keep a track of A % p for p in >> the first n primes. As you run through the A's, adding 2 to A each >> step, you add 2 to each of these remainders in your tracking array. If >> these hit 0 (modulo their prime), then A is clearly non-prime and you >> can skip it. This will let you skip a number of your test divisions >> with relatively little work - as you make that array of n primes bigger, >> you cut out yet more divisions. However, there is going to be a point >> where doing this tracking for the modulo A % p will cost more (in memory >> or speed) than 1/p times the cost of calculating C % A - and when you >> reach that, you don't want to track any more modulos. >> >> I suspect there is scope for some interesting data structures to hold >> this list of modulos, rather than a simple array - perhaps a priority >> queue in a Fibonacci heap? > > > Yes, this is the "standard" algorithm I was talking about, in the last > post I even mentioned the heuristic you described it the third > paragraph. > Are you sure you wanted to post it as the answer to my post? > That's not how I understood your post. Though I agree the basic algorithm is the same, the details are very different. In particular, your third paragraph suggested Miller-Rabin testing before division, which I think would be terribly inefficient.
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really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-08-31 12:07 -0700
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-08-31 23:23 +0100
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 01:18 -0700
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-01 11:01 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 12:20 +0100
Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-01 15:48 +0100
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:26 -0700
Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-09-02 02:12 -0500
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 08:38 +0100
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:03 +0200
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:24 -0700
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 22:27 +0100
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 15:02 -0700
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 23:20 +0100
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:22 +0200
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 17:18 -0700
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:19 +0100
Re: really? (lame question about primes) James Dow Allen <gmail@jamesdowallen.nospam> - 2015-09-02 12:42 +0000
Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 14:21 +0100
Re: really? (lame question about primes) Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-09-02 17:45 +0200
Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 18:06 +0100
Re: really? (lame question about primes) James Dow Allen <jdallen2000@yahoo.com> - 2015-09-03 17:05 -0700
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-04 02:18 +0200
Re: really? (lame question about primes) Chad <cdalten@gmail.com> - 2015-09-03 22:37 -0700
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-03 23:49 -0700
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-04 00:18 -0700
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-04 08:25 +0100
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 14:36 +0100
Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 16:49 +0100
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 17:32 +0100
Re: really? (lame question about primes) Kaz Kylheku <kaz@kylheku.com> - 2015-09-01 22:55 +0000
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:15 +0200
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 03:19 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:37 +0100
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 11:24 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 10:42 +0100
Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-02 03:01 -0700
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 12:28 +0200
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:12 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:19 +0100
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 14:56 +0200
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 15:47 +0200
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 16:27 +0200
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 16:37 +0200
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 17:01 +0200
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 10:55 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:05 +0100
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 11:49 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:54 +0100
Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 13:22 +0200
Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-03 13:58 +0200
Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:34 +0100
Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-08-31 23:10 -0500
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