00:00:00 --- log: started forth/02.11.16 00:36:23 lament: how do you get dvorak??? 00:36:57 I even e-mailed the guy who wrote the drivers for the targus folding keyboard and he said that it didn't support dvorak, and it probably never would 00:37:01 but this was probably 2 years ago 00:44:42 hmm 00:44:47 I think my keyboard is a Targus 00:45:02 all the folding ones are I think 00:45:02 So I guess they changed their mind 00:45:10 awesome 00:45:23 I just got my visor to synch with my computer so I can use it again 00:45:44 the keyboard drivers let you choose dvorak then? 00:48:30 yes. 00:49:13 Actually, for layout, you have a choice of English(US), English(US-Dvorak), German and Japanese. 00:49:41 coool 00:49:44 aha it has a button "Layout Info" 00:50:06 which says that the Dvorak layout was created by Think Outside, Inc on Jun 6, 2002 00:50:30 that's recent! 00:50:32 So I was really lucky to buy the keyboard almost immediately after that. 00:51:02 I'll have to grab the new driver :) (I don't have any driver at the moment...) 00:51:20 and now, to bed 00:51:23 goodnight all 00:52:46 --- quit: Herkamire ("zzzzzzzz") 00:59:29 --- join: Serg_Penguin (~Z@nat-ch1.nat.comex.ru) joined #forth 01:00:47 hi, who's alive ? 01:20:25 Several billion people around the world. 01:24:32 Also, a very big number of people in other times. 01:24:50 Heh. Yup. 01:34:30 had u ever tryed to write a proggie in one-line words ? 01:35:44 What? 01:36:32 all functions ( or forth words ) take one line, <80 chars 01:37:14 Yes, it's generally not very effective. 01:37:43 But if you buy into all of Chuck's rethoric... 01:37:51 Rhetoric. 01:38:06 then i tryed, i xperienced great code clarity and rapid writing 01:38:25 i rewrote my old sokoban game just to test the method 01:38:27 Yes, well try it with a non-trivial program. 01:39:07 for example, old level-decode was one word , 11 lines of write-only mess 01:39:22 now - 3 short, grok-at-glance words 01:39:38 ( i have bit-packed levels ) 01:40:00 non-trivial ? so what u suggest to write ? 01:40:00 Let's see your code. OK? 01:40:24 it's at home, will bring at monday and put on web 01:40:32 I see. 01:40:54 old is at http://cryptomancer.chat.ru, if not erased for being unvisited too long 01:41:43 its still alive 01:42:36 new will be at same place, if i didn't forgot passwd 01:43:32 so what 'non-trivial' proggie u suggest to write ? 01:45:11 i now plan a game, mix of logic puzzle and RPG 01:45:19 I'm not suggesting any program in particular. I'm just saying that applying some irrational "1-line" function rule is not particularly effective in practice, even if it looks good in theory. 01:46:45 it's not irrational - human keeps 7+-2 in attention buffer, so short words are easier to grasp 01:47:35 * Serg_Penguin sometimes optimizes not for speed and size but for concept clarity 01:47:51 Well, in any case, you (hopefully) keep track of several concepts at once. 01:48:04 It's kind of like trying to read a poster with a microscope. 01:49:50 anyway, stuff found at UT makes sense 01:51:30 Yes, it's quite well written. Unfortunatley, there are almost no decent concrete code examples illustrating the concepts. 01:55:15 i wrote one :) 01:58:29 i think ColorForth is good example, but my CRT dunno hold such hirez 01:58:43 so i can't dig it in depth 02:00:32 Yes, well forth implementation's are a dime a dozen. :) 02:03:11 now i dig isForth - it became much better w/ new version i440r gave me, some nasty bugz gone 02:03:27 but it has too much fat 02:10:00 Yes, and it's x86/linux specific. 02:10:43 Morning all. 02:22:47 hey Robert 02:36:21 Hi. 02:46:44 sorry, i was trying to find an rtfm on aerodynamics 03:06:40 --- quit: Robert (Remote closed the connection) 03:06:50 --- join: Robert (~Robert@robost86.tsps1.freenet6.net) joined #forth 03:17:48 --- quit: Serg_Penguin () 04:36:17 --- quit: lament ("Client Exiting") 05:05:39 --- quit: ChanServ (ACK! SIGSEGV!) 05:25:07 --- join: Sorcer (~s0rcer@62.139.18.11) joined #forth 05:25:56 --- part: Sorcer left #forth 06:54:48 --- join: ChanServ (ChanServ@services.) joined #forth 06:54:48 --- mode: benford.freenode.net set +o ChanServ 06:54:48 --- mode: ChanServ set +l 83 07:05:52 --- join: divgrad (~wer@81.25.34.10) joined #forth 08:08:24 --- quit: divgrad () 08:18:39 --- join: XeF4 (xef4@lowfidelity.org) joined #forth 08:20:52 !seen joonas 08:22:53 --- join: Herkamire (~jason@ip68-9-59-184.ri.ri.cox.net) joined #forth 08:23:08 Herkamire: have you seen joonas? 08:23:19 XeF4: no 08:24:32 Robert: I had entirely too much fun last night with that primes thing you were talking about 08:24:54 :) 08:24:57 So did I, heh. 08:25:04 I even got a guy to implement it in SML. 08:25:13 lol 08:25:49 I did some shortcuts, and my pragram prints all of them that are less that 1 billion in 0.7 secconds 08:26:19 Whoa. 08:26:26 That's quite good. 08:26:34 What shortcuts? :) 08:27:27 after the first six, all the digits must add up to 23 08:27:44 so I just printed out the first six, and check for the digits totalling 23 08:27:54 that's it really 08:27:58 Yeah.. I do that, too. 08:28:06 heh :) 08:28:17 It returns true if the number gets 23. 08:28:22 your sqrt function is very silly and complex, and I don't even get it. 08:28:29 Hehe. 08:28:35 I know :) How did you code it? 08:29:14 Takes 30 seconds here for 100,000,000 numbers. 08:29:35 I can't get how you do ten times more in 1/50 of the time. 08:29:43 variable lsqrt : sqrt ( x -- n ) lsqrt @ dup * swap lt if lsqrt @ 1 + dup lsqrt ! exit then lsqrt @ ; 08:30:05 What's "lt"? 08:30:12 lessthat :) sorry 08:30:23 Ah, OK. 08:31:14 Well, I just use new guess = ((x/old guess) + old guess) / 2 08:31:42 However, I don't think that makes this much difference. My assembly program uses a lot more time than your Forth program. 08:31:55 The SML program does, too. 08:33:27 What is the definition of the numbers it prints? 08:33:34 --- join: tathi (~josh@ip68-9-58-207.ri.ri.cox.net) joined #forth 08:33:50 Hi tathi. 08:34:02 hey Robert 08:34:15 Robert: your sqrt function can just check if the last sqrt is too small, and if it is, then up it by one 08:34:36 in this pragram sqrt never needs to go up by more than one 08:34:45 --- join: nDuff (~cduffy@cs666889-197.austin.rr.com) joined #forth 08:35:00 Here's what I use: (a) the number should be a prime, (b) each of the decimal digits should be a prime (2,3,5 or 7), (c) the sum of its decimal digits should be a dunder prime. (unless it's below 10, then (c) shouldn't be used, since it will recurse forever). 08:35:06 I think the big speedup is that he's just generating the numbers that have digits 2,3,5,7, and only checking those 08:35:15 then checking if the digits add up to 23 08:35:20 _then_ checking if it's a prime 08:35:46 I only check them for primality. 08:35:54 (Those who contain 2,3,5,7) 08:36:36 It returns immediatley from the recursion if the number is 23... 08:36:44 But I guess I could optimize that part a bit more. 08:36:47 I'm looking for a scripting language with an interpreter tiny enough to be cache-locked (ie. fit inside just a page or two)... might any of 'yall suggest a forth interpreter that might be particularly interesting from this perspective? 08:37:04 Rpbert_ amd tje öpw bot sjpiöd be + inless it is 2 08:37:05 er 08:37:12 Rober: and the low bit should be 0 unless it is 2 08:37:28 nDuff: you could write one :) :) 08:37:33 * XeF4 will look at the monitor while typing from now on 08:37:48 * Herkamire tinks everyone should write a forth 08:38:24 Herkamire, indeed, but if one already exists I'd hate to reinvent the wheel. 08:38:32 XeF4: :) 08:38:58 s/it/the number/ 08:39:40 My Forth program sucks. 08:39:40 nDuff: pygmy will fit in a page or 2, but it's for 8086 08:39:50 I've made a better version in assembly now. 08:39:50 nDuff: 386 eforth might well do that 08:41:38 Hm. 08:41:52 How do you generate the numbers that only contain 2,3,5 and 7? 08:42:25 as decimal digits? 08:42:28 I do up to 100,000,000 now on just below 30 seconds. 08:42:29 Yes. 08:42:51 I guess the number of numbers I check is the critical point. 08:42:59 could you get away with using packed BCD for everything? 08:43:02 digit ( place n -- ) 08:43:11 place is a power of 10, n is the number you're generating 08:43:18 then it recurses 08:43:34 Hm, yes... 08:43:44 doooh 08:43:51 over / 10 mod 08:43:52 right 08:43:54 oh, my sqrt function isn't quite right when I skip all those numbers. one sec 08:44:14 heh 08:44:52 Mine checks each digit in the number, breaking when it finds a non-prime digit. 08:45:23 : digit swap 10 / swap over = if check drop ; then 08:45:27 --- join: thin (thin@h68-146-166-145.cg.shawcable.net) joined #forth 08:45:32 2dup over 2 * + digit 08:45:34 Hi thin. 08:45:51 2dup over 3 * + digit 08:45:52 etc 08:45:52 hi rob 08:45:56 hey thin 08:45:59 Hmm. 08:46:05 howdy tath 08:46:23 --- mode: ChanServ set +o thin 08:46:38 Now I see something I could do. 08:47:24 Robert: this way you're only checking 4^digits numbers, instead of 10^digits 08:47:41 but you have to call it for each length :) 08:48:37 I'll check another idea.. wait. 08:48:48 ok, fixing that added 50ms, so I'm at about 0.75 secconds for < 1,000,000,000 08:50:44 --- mode: thin set -o thin 08:54:00 Ah. 08:54:07 15 seconds now. 08:54:13 cool :) 08:54:34 Still wondering what makes your faster. 08:54:44 the Huge time savings was using correct digits and checking the sum before the prime 08:54:49 15 seconds for < 100,000,000... 08:55:08 oh, and I check that it is odd before check the sum 08:55:36 Yes... that's what I'm fixing now. 08:55:46 <1s for 1 billion is a lot faster, still. 08:57:23 --- nick: thin -> futhin 08:57:31 --- mode: ChanServ set +o futhin 08:57:45 Robert: I'm running a 450Mhz G4 which helps... 08:58:15 --- nick: futhin -> thin 08:58:28 yay 08:58:41 --- mode: thin set -o thin 08:58:44 er 08:58:51 heh 08:58:53 --- nick: thin -> bugslayer 08:58:55 --- nick: bugslayer -> thin 08:59:02 --- mode: ChanServ set +o thin 08:59:05 ewww!!!!!! 08:59:12 Herkamire: Hehe, nice. P200 here. 08:59:19 p100 here, ph33r 08:59:48 --- mode: thin set -o thin 08:59:51 --- nick: thin -> futhin 08:59:58 --- mode: ChanServ set +o futhin 09:00:01 :/ 09:00:17 --- mode: futhin set -o futhin 09:02:26 so how come nobody is using the forth webserver, ftpserver, emailserver? :P 09:02:37 the russian eserv proggie 09:02:55 because svn only works with apache2 09:03:01 didn't know about it 09:03:10 that too :) 09:04:11 lies, it's been mentioned before on this chan multiple times :P 09:04:36 * futhin has a theory that everybody stopped paying attention right about the time eserv was mentioned, and that happened multiple times! scary! 09:04:37 maybe I wasn't here :P 09:04:57 sounds vaguely familiar now that you mention it 09:05:02 http://www.eserv.ru/ 09:10:18 apache works fine for me. I don't feel like running two webservers 09:10:30 ok, scratch that, my sqrt was fine before 09:15:02 when I check up to 1 billion, it only has to check 1076 numbers to see if they are prime... seems pretty low 09:15:15 where does it say that eserv has anyhing to do with Forth? 09:18:04 humph, ok, my sqrt was not cool before :) :) 09:22:35 tathi: it doesn't say it, just like many other sites that don't say the product was coded in C :P 09:23:07 i think it used to say it but they've changed the site 09:23:51 what dialect is it coded in? 09:24:17 no idea 09:24:31 eserv seems to be a windows program 09:24:36 so i guess you guys couldn't use it heh 09:24:43 hmm, well, their website doesn't seem to work well in any of my browsers, _and_ I don't have the hardware to run it on anyway 09:25:13 I wish I remembered which company made that z80 Forth webserver I played with a couple years ago 09:25:29 eserve is for Windoze, of course we don't use it 09:26:44 totally off-topic, does anyone know how to make carob powder from carob fruits? 09:27:12 * XeF4 has a few here but isn't quite sure how one processes them into that cocoa-like stuff 09:28:26 I didn't think carob was a fruit... 09:28:54 carob is a tree 09:29:05 maybe you make it from the bark ;) 09:29:11 try chopping it up, let it dry, keep chopping it up, etc? 09:29:37 doh 09:29:41 this explains it 09:29:46 nm 09:29:59 what's carob powder good for? 09:30:05 * XeF4 just discoevered that these are baobab, not carob 09:30:45 futhin: tastes good 09:50:30 carob is used like chocholat (and tasts somewhat simular) 09:53:01 I think my primes thing is printing all the answers up to 10^31 09:53:21 unless 22222222223 is one 09:54:02 It is. 09:54:19 10^31 oe 2^31? 09:54:22 or* 09:54:37 10^31 09:55:14 there can't be any between 10^11 and 10^31 because there are too many digits to add up to 23, and not enough to add up to 223 09:55:51 how did you check that 22222222223 is one? 09:55:52 Ah, right... 09:56:01 calc :) 09:57:10 my code checks everything that fits in 32 bits 09:58:27 there's only 2 between 1G and 4G 09:58:29 How do you pick the numbers to check? 09:58:56 hey, is there a proof somewhere that that digit-checking prime tester works? 09:59:02 --- join: joonas (jpihlaja@kruuna.helsinki.fi) joined #forth 09:59:02 * XeF4 wants to see this 09:59:15 iltaa 09:59:15 Digit-checking prime tester? 09:59:17 Hi all. What's up? 09:59:19 Hi joonas. 09:59:43 Digit-checking prime tester? 09:59:51 * joonas checks the logs 10:00:14 Robert: your/Herkamire's prime lister 10:00:19 Oh. 10:00:22 that recursive thing ("digit") that tathi was trying to describe. it puts together each number (of a given number of digits) that is made up of only the digits 2,3,5,7, and calls my check function on each one 10:00:42 XeF4: I'm not into proofs sorry. 10:00:44 Well, it only returns primes whose sums of digits also are primes, whose sums of digits are primes, etc. 10:01:04 And all decimal digits should also be one-digit primes. 10:01:12 On top of that, it does a normal primality check. 10:01:21 But 17 is a prime and 1+7 = 8 10:01:36 joonas: right, so 17 isn't what we're looking for 10:01:43 Yup, that's why it doesn't print it. 10:01:59 23, 2+3 = 5. 10:02:01 these are: 2 3 5 7 23 223 2777 7727 27527 33377 10:02:03 223, 2+2+3 = 7 10:02:04 etc. 10:02:20 Oh, sorry. Thought you were looking for all primes. 10:02:48 so did I :) 10:03:41 heh :) all primes made of digits that are primes, and who's digits add up to 2,3,5,7 or 23 10:04:01 there is only one such number that does not fit in 32 bits :) 10:04:23 What a strange problem. Where does it come from? 10:04:26 Well... actually you can use the original definition. 10:04:38 Herkamire: How do you know that? 10:04:49 joonas: Actually, I was playing with my nick on another IRC server, and I told people to change nicks to this kind of primes. 10:05:13 2,3,5,7,11,13,17,19,23 10:05:29 19 adds to 10, 17 adds to 8, 1 is not prime 10:05:42 Robert: why? 10:05:52 joonas: I made a program that finds all the ones that fit in 32 bits, and once you have 12 digits, there is only one odd number where the digits are as small as 23 (22222222223) and Robert checked that it's prime with calc 10:05:52 joonas: Because I was bored :) 10:06:27 Herkamire: Ah, so you know there exists at least one such number that doesn't fit into 32 bits. ;) 10:06:48 Actually, the definition of a Dunder Prime(tm), is that it (a) should be a prime, (b) all its decimal digits should be primes, (c) the sum of its decimal digits shoud be a Dunder Prime. 10:06:55 So, the numbers could be larger. 10:07:20 --- join: ASau (~asau@158.250.48.197) joined #forth 10:07:27 Privet :) 10:07:33 yep. we've just found all the Dunder Primes that are less that 10^31 10:07:36 Good evening! 10:07:44 hi ASau 10:08:12 I've changed my soft in major part. 10:08:34 Now I avoid m$ if it is possible. 10:08:37 Robert: thanks for the definition. Makes much more sense now. 10:09:10 No problem :) 10:11:04 So how many Dunder Primes are there <10^31? Someone mentioned a number ~1000 or so. 10:13:21 joonas: there is exactly 1 number too big for 32 bits, that is prime, with prime digits, that adds up to 23, and it's 22222222223 10:14:10 yeah, it's around 1080 lemme check 10:15:53 sorry, 207 10:15:54 Herkamire: But there might be others that are larger, according to the definition Robert gave. Namely, defn doesn't say the digits have to add up to 23, just that the sum is also a Dunder Prime. 10:16:22 I believe there are 208 that are less that 10^31 10:16:43 So a prime whose digits add up to 22222222223 would qualify. 10:16:53 Yes. 10:17:02 --- join: KOHTPA (~asau@158.250.48.197) joined #forth 10:17:04 joonas: yes, and the next higher Dunder Prime is 223, and to have the digits add up to 223, you would have to have at least 32 digits 10:17:08 That would sure be a nice number. 10:17:12 Kontra? 10:17:22 ;) 10:17:29 What's that? 10:17:30 Ah, good point. 10:17:42 I'm testing my new soft... 10:17:58 An error happened... :( 10:18:09 KOHTPA: what software? 10:18:17 Hmm.. I don't see how I could code that routine to generate the "prime digit" numbers. 10:18:27 Can you give me a hint, Herkamire? 10:18:49 Herkamire: I'm testing my new IRC client. 10:19:02 KOHTPA: use irssi 10:19:09 KOHTPA: or are you writing one? 10:19:25 : appdig ( u1 digit -- u2 ) swap 10 * + ; 10:19:27 Robert: use base-4 to count, and then map base-4 digits like so: 0->2, 1->3, 2->5 3->7 10:19:27 No, I'm beta-testing 10:20:23 Ah! 10:20:24 Thanks. 10:20:54 Robert: we used recursion. we defined DIGIT ( base x -- ) which drops base by 10x and recurses 4 times (first time putting a 2 as that digit, then with a 3... 10:20:57 Now, I'm running DOS + TCP/IP + IRC client 10:21:26 Robert: when base reaches zero, it checks x to see if it's a Dunder Prime, and returns. 10:21:40 KOHTPA: Nice :) 10:21:55 Robert: I was thinking of doing a base-4 thing like joonas is talking about, but this works great, and it's gotta be faster 10:22:37 Robert: That is why I am one under two names :) 10:22:45 But it is rather strange 10:23:43 : digit ( place n -- ) swap 10 / swap over 0= if check drop exit then 10:23:43 ddup over 2 * + digit 10:23:43 ddup over 3 * + digit 10:23:43 ddup over 5 * + digit 10:23:43 over 7 * + digit ; 10:23:43 when I sat under Win95 my duplicate used to disappear by this time... 10:24:15 Herkamire: So you keep a list/hash/whatever of all previously found Dunder Primes and then check primality only if the sum of the candidate's digits is one of the earlier found ones? 10:24:29 call like so: 1000 0 digit and it will check all 3 digit numbers made from 2,3,5,7 digits 10:25:32 joonas: you could, except all but the first 6 and the last 3 that are < 10^31 add up to 23, so it's easier to just check against 23 10:26:12 Ah yes, you mentioned that. 10:26:17 Herk: voihanherrajumala why don't you just make a table of digit pairs 0..100 (or digits 0..10) and 10 /mod @ if mightbedunder else then ; 10:26:18 Way faster. 10:27:06 XeF4: I did something like that yesterday 10:27:49 was there a problem with it? 10:27:59 as tathi pointed out that way to check up to 1G I'm checking 10^9 numbers instead of 4^9 10:28:49 and actually, *nod* 10:29:59 turns out to be a few magnitudes faster. it went from a few minutes to < 40ms for up to 1 million 10:30:47 and now it checks up to 1 billion in about 720ms 10:32:24 Hm. 10:32:24 rrr... 661ms 10:32:43 320ms for 10 to 10^9. 10:32:45 :) 10:32:48 Thanks Herkamire. 10:33:27 Robert: sure :) it was tathi's idea to get the permutations recursively 10:33:42 tathi: You get a hug, too then. 10:34:12 2.53 seconds up to 4*10^9 10:34:28 Variable tmp Create primedigs 2 , 3 , 5 , 7 , : 0 dup tmp ! 262144 ?do i 0 18 ?do dup 3 and cells primedigs + @ tmp @ 10 * + tmp ! loop loop ; 10:34:31 or so 10:34:42 : gennums 0 ... even 10:37:23 Robert: that's about right :) when I went up to 4 billion, it took 1.7 secconds or something vaguely like that. the different is probably the speed of our computers now :) 10:37:49 XeF4: May I ask, what are you calculating? 10:38:21 KOHTRA: list of Dunder prime candidates 10:39:35 I.e. you're looking for big primes? 10:39:45 no 10:40:18 ignore that version, it's buggy. 10:46:17 KOHTPA: definition of a Dunder Prime: i) one of {2,3,5,7} or ii) a prime whose digits sum to a Dunder Prime and are in {2,3,5,7}. 10:49:43 Create primdigs 2 , 3 , 5 , 7 , 0 10:49:44 Create rprimdigs -1 , -1 , 0 , 1 , -1 , 2 , -1 , 3 , -1 , -1 , 10:49:44 : nextcan ( u1 -- u2 ) 10 /mod cells rprimdigs + @ 10:49:44 1+ cells primdigs + @ dup if swap 10 * + else drop 1+ 10* then ; 10:49:49 slightly opvercomplicated , but ... 10:51:43 How well does your sqrt() work with the recursive number generator? 10:52:46 variable lsqr 10:52:46 : sqrt lsqr @s begin 2dup dup * swap lt if 2 + [ swap ] 0 until then nip dup lsqr !s ; 10:52:55 joonas: You mean, number (ab..cd) is a Dunder prime, if a+b+c+d is in {2,3,5,7} 10:53:01 AIR? 10:53:28 ... a+b+...+c+d ... 10:54:03 KOHTPA: each digit has to be prime, and the sum of all digits has to be a Dunder Prime 10:54:05 KOHTPA: No, the definition is recursive, so that 223 is a Dunder Prime because 223 is a prime, and 2+2+3 = 7 is also a DP. 10:54:28 KOHTPA: Similarly, any prime whose digits are in {2,3,5,7} and sum to 223 would also be a Dunder Prime. 10:55:29 Aha! You mean (a+b+...+c+d) is DP <=> (ab..cd) is DP. 10:55:35 Now it'd be interesting to play with Dunder Primes using other bases than 10. 10:55:56 oook 10:56:01 one last time :) 10:56:24 Create primdigs 0 , 2 , 3 , 5 , 7 , 0 10:56:24 Create rprimdigs 0 , 0 , 1 , 2 , 0 , 3 , 0 , 4 , 0 , 0 , 10:56:24 : nextcan ( u1 -- u2 ) 10 /mod cells rprimdigs + @ dup 0= if exit then 10:56:24 1+ cells primdigs + @ dup if swap 10 * + else drop 1+ 10* then ; 10:56:26 Robert: pass in whatever base you want to DIGIT, and change 10 u/mod to base u/mod 10:56:35 Yes. 10:56:52 Actually, I've written a C program now ;) 10:57:27 bad Robert ;) 10:57:29 KOTHPA: yes, except the recursive defn needs to "bottom out" at single-digit primes, so it includes {2,3,5,7}. Without including those, the definition would be incomplete. 10:57:35 I've finally had enough. I stuck my prog in the examples folder for fpos, and I'm going to do someting slightly more usefull now. 10:57:38 I hope... 10:58:18 OK. I hope I've understood you right. 10:59:38 Th.1. For all D.P. a: a mod 9 ={2,3,5,7}. 10:59:53 Proof. Obvious. End. 11:00:11 : testall begin 2 while isprime? repeat ; 11:00:25 : testall begin 2 while isprime? nextcan repeat ; 11:00:59 XeF: ... 2 while ... <-- infinite loop. 11:01:24 yes it is :) 11:01:49 : testall 2 begin dup while isprime? nextcan repeat ; 11:01:57 brb, coffee 11:02:40 Th.2. Another base, p. Each D.P. a(base p) is: a mod (p-1) = {2 mod p, 3 mod p, 5 mod p, 7 mod p}. 11:02:49 Proof. 11:03:15 Using finite integer ring...obvious. 11:03:21 Proved. 11:04:45 KOHTPA: Ah, yes, right. You got it. 11:06:35 KOHTPA: Although, that proof wouldn't fly in an exam. :P 11:06:51 Now you can look (worst case) numbers that are (modulo p-1): (2 mod p),.. 11:07:14 joonas: I'm not passing exam right now! :) 11:07:28 joonas: uh oh, you're a schoolteacher? 11:07:29 I'm solving a problem! 11:07:36 KOHTPA: what's with p-1 11:07:39 XeF4: no 11:07:50 if it's base 10 you do "10 mod" 11:08:11 XeF4: just thinking what would happen if *I* put that kind of proof in an exame paper. :) 11:08:33 Hm. That square root word of yours, does it increase the square root by 2 until it squared reaches x? 11:08:58 joonas: I'm not a mathematician, I'm a chemister ;) 11:09:15 XeF4: had a little trouble with KOHTPA's theorem at first. 11:10:19 Th. #1 is a particular case of th.#2, isn't it? 11:10:27 Yes. 11:11:09 Consider finite ring with elements (modula) {0,1,2,..., p-1}. 11:11:19 Just that you saying "obvious" had me thinking for a bit. :) 11:11:40 Addition is addition modulo p. 11:11:55 Multiplications is multiplication modulo p. 11:12:15 I see it now: any number in base-p is written as \sum_i a_i*p^i, then in mod p-1 this reduces to \sum_i a_i. 11:12:28 Right. 11:12:45 \sum_i a_i must be a Dunder Prime by defn, so apply the theorem again until the base case is hit. 11:12:46 Now it's oblvious. 11:13:50 Using this feature you can optimize brute search. 11:15:41 Hmm. If one uses that (^^^high above) definition, one has to conclude, 11:16:18 that all numbers that are {2,3,5,7} mod p are D.P. 11:16:33 That is strange to me. 11:16:45 Are you sure in your definition? 11:16:49 KOHTPA: It also has to be a prime. 11:17:03 Ah! 11:17:22 Than everything is OK. 11:19:19 3-2=1; 5-3=7-5=2; 2-7=p-5 in our ring. 11:21:37