Brimstone for cracking RSA. (jk)
[CENTER][COLOR=#000000][FONT="][B] Story of tails, windows and how it impacts integer factorization.. [/B][/FONT][/COLOR]
[COLOR=#000000][FONT="][B]In other words, MILESTONE has been done :D[/B][/FONT][/COLOR][/CENTER] [LEFT][COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="]From the very start of my journey to discover the innards of stubborn IF, the prime goal was to have [/FONT][/COLOR] [COLOR=#000000][FONT="]developed binarysearchtree algos. At some point, it seemed utterly impossible. But here we go..[/FONT][/COLOR] [COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="]Actually, algo consists of three stages..[/FONT][/COLOR] [COLOR=#000000][FONT="] [/FONT][/COLOR][/LEFT] [LIST][*]it picks initial (probable) Z’s (pZ_L and pZ_R) up (Z = P + Q, N = P*Q). So, now algo needs to guess which one is closest to original Z.[/LIST][LIST][*] for pZ_L, it generates N_L which is closest to N from left/right and the same way for N_R of pZ_R.[/LIST][LIST][*] for N_R/L, it collects statistics of bit windows against N (their positions, widths..)..[/LIST][LEFT][COLOR=#000000][FONT="] [/FONT][/COLOR][/LEFT] [CENTER][COLOR=#000000][FONT="]Window(N, EntryPoint, Width) == NOT Window(N_L, EntryPoint, Width).[/FONT][/COLOR][/CENTER] [LEFT][COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="]For instance, let Window(N, EntryPoint, Width) == “010”, then Window(N_L, EntryPoint, Width) == “101”. And now it’s possible to choose probable Z according collected statistics for given iteration.[/FONT][/COLOR] [COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="]For tests, RSA150 ([URL]https://en.wikipedia.org/wiki/RSA_numbers#RSA150[/URL]) has been taken, criterion to go left/right is widths of greatest windows. Output…[/FONT][/COLOR] [COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="] test mode gets activated[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 1[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 2[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 3[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 4[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 5[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 6[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 7[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 8[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 9[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 10[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 11[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 12[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 13[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 14[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 15[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 16[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 17[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 18[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 19[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 20[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 21[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 22[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 23[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 24[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 25[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 26[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 27[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 28[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 29[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 30[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 31[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 32[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 33[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 34[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 35[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 36[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 37[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 38[/FONT][/COLOR] [COLOR=#000000][FONT="]Wrong turn @ 39[/FONT][/COLOR] [COLOR=#000000][FONT="][B][COLOR=#ff0000][COLOR=red]Wrong turn @ 40[/COLOR][/COLOR][/B][/FONT][/COLOR] [COLOR=#000000][FONT="][B][COLOR=#ff0000][COLOR=red]Wrong turns == 40[/COLOR][/COLOR][/B][/FONT][/COLOR] [COLOR=#000000][FONT="]nice turns == 208[/FONT][/COLOR] [COLOR=#000000][FONT="]Total iterations == 248[/FONT][/COLOR] [COLOR=#000000][FONT="] [/FONT][/COLOR] [COLOR=#000000][FONT="]In short, algo doesn’t do gaps (good and bad turns ain’t shuffled/mixed) even with such rather primitive criterion.[/FONT][/COLOR] [COLOR=#000000][FONT="]Archive: https:// sourceforge . net /projects/fastprimecruncher/[/FONT][/COLOR][FONT="Arial Black"][COLOR="Red"]Mod note URL intentionally broken. Sourceforge reports it as malware.[/COLOR][/FONT] [COLOR=#000000][FONT="]Password for archive: ᬓꨒꛏ78🁶 [/FONT][/COLOR][/LEFT] 
Fantastic! Unfortunately, Aoki, Kida, Shimoyama, & Ueda already factored RSA150, so it's not a good way to show that your method works. Could you demonstrate it with this smaller number, please?
3817396723515136582858035291731476702231874047478035390874743899933916107585885458479075057627686466112442032963859000272684225286856787555319737 I promise that it was (pseudo)randomly generated* and that I've kept the factorization a secret (even from myself). This number isn't considered hard to factor, and so it won't of itself demonstrate a breakthrough, but it would make a better example. (Of course if you could factor such examples quickly enough it would suggest either collusion or a breakthrough, either in factorization or RNG cracking.) * Brent's XORGEN. 
[QUOTE=CRGreathouse;553095]Fantastic! Unfortunately, Aoki, Kida, Shimoyama, & Ueda already factored RSA150, so it's not a good way to show that your method works. Could you demonstrate it with this smaller number, please?
3817396723515136582858035291731476702231874047478035390874743899933916107585885458479075057627686466112442032963859000272684225286856787555319737 [/QUOTE] for now, it's just a test mode, so it takes original P & Q :smile::blush::cmd::rolleyes: 
[b][color=red]MODERATOR NOTE: Thread moved to Miscellaneous Math[/color][/b]
[QUOTE=SarK0Y;553107]for now, it's just a test mode, so it takes original P & Q :smile::blush::cmd::rolleyes:[/QUOTE] In other words, your "method" depends on already having the factors (P and Q). :tank: 
...so the "MILESTONE" is that, if you know the factorization, you can find it again very quickly?

[QUOTE=SarK0Y;553107]for now, it's just a test mode, so it takes original P & Q :smile::blush::cmd::rolleyes:[/QUOTE]
Well golly, my own topsekrit factoring method for RSAstyle moduli has that beat by a mile. You see, given a semiprime n = p*q, I only need *one* of p or q in order to quickly produce the other prime factor. 
strictly speaking, it's not an actual factorization method, it's test bench to expose possible vectors of attack to crack IF.. so, yes == it takes P & Q to collect info for new methods. why "MILESTONE"? :) for instance, the're no division and no modular arithmetic, thereby test bench is rather fast. In fact, we use modular arithmetic for pseudorandom numbers, so it provides too wobbly ground to construct useful criteria + big matrices ain't good for multithreaded solutions. in short, current methods already approached its deadline by algorithmic limits & hw ones as well.

[QUOTE=SarK0Y;553192]strictly speaking, it's not an actual factorization method, it's test bench to expose possible vectors of attack to crack IF.[/QUOTE]
Could you give an example of what such a vector would look like? [QUOTE=SarK0Y;553192]why "MILESTONE"? :) for instance, the're no division and no modular arithmetic, thereby test bench is rather fast.[/QUOTE] Could you give an example of a similar algorithm that already does the same thing (or a comparable thing), but which uses heavier operations like division or modular arithmetic? (Not that those are particularly costly, but I digress.) It would help us understand what, exactly, you're trying to do. [QUOTE=SarK0Y;553192]In fact, we use modular arithmetic for pseudorandom numbers, so it provides too wobbly ground to construct useful criteria + big matrices ain't good for multithreaded solutions.[/QUOTE] Are you saying [LIST=1][*] That your algorithm uses modular arithmetic, in particular for the generation of pseudorandom numbers (but I thought you said it didn't use modular arithmetic?), or[*] That some algorithms for generating pseudorandom numbers use modular arithmetic, and your method, not using modular arithmetic, is superior (but how does your method compare to generating pseudorandom numbers? seems like apples and oranges, or am I missing something?)[/LIST] And what is this about big matrices? [QUOTE=SarK0Y;553192]In short, current methods already approached its deadline by algorithmic limits & hw ones as well.[/QUOTE] Current methods for what, exactly? 
[QUOTE=SarK0Y;553061][COLOR=#000000][FONT="]Archive: https:// sourceforge . net /projects/fastprimecruncher/[/FONT][/COLOR]
[LEFT] [COLOR=#000000][FONT="]Password for archive: ᬓꨒꛏ78������ [/FONT][/COLOR][/LEFT] [/QUOTE] SourceForge says "Malware detected. Download at own risk." Somebody here with a virtual machine at hand including virus and malware scanner wants to try to open it? 
[QUOTE=Till;553292]SourceForge says "Malware detected. Download at own risk."[/QUOTE]
Thanks for catching that. I broke the link. If someone want to get it they can do so with full knowledge. 
[QUOTE=Till;553292]Somebody here with a virtual machine at hand including virus and malware scanner wants to try to open it?[/QUOTE]
The file contains: [CODE].: total 16K drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 . drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 .. drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 FastPrimeCruncher rwxrwxrwx 1 oliver oliver 15K Aug 9 20:49 MILESTONE.odt ./FastPrimeCruncher: total 160K drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 . drwxrwxrwx 1 oliver oliver 4.0K Aug 11 17:56 .. drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 bin rwxrwxrwx 1 oliver oliver 23K Jul 25 22:20 BuildLog.txt drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 .clang drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 .codelite rwxrwxrwx 1 oliver oliver 287 Aug 3 00:33 compile_commands.json drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 Debug rwxrwxrwx 1 oliver oliver 1.1K Jul 19 23:59 FastPrimeCruncher.cbp rwxrwxrwx 1 oliver oliver 176 Jul 20 00:53 FastPrimeCruncher.layout rwxrwxrwx 1 oliver oliver 4.2K Aug 8 18:26 FastPrimeCruncher.mk rwxrwxrwx 1 oliver oliver 4.7K Aug 5 19:42 FastPrimeCruncher.project rwxrwxrwx 1 oliver oliver 39 Aug 8 18:26 FastPrimeCruncher.txt rwxrwxrwx 1 oliver oliver 594 Aug 8 06:01 FastPrimeCruncher.workspace rwxrwxrwx 1 oliver oliver 165 Jul 19 23:56 FastPrimeCruncher.workspace.layout rwxrwxrwx 1 oliver oliver 45K Aug 8 18:26 gears.cpp rwxrwxrwx 1 oliver oliver 5.2K Aug 4 00:29 headers.h rwxrwxrwx 1 oliver oliver 5.7K Feb 20 2019 konsole1.txt rwxrwxrwx 1 oliver oliver 14K Feb 20 2019 konsole.txt rwxrwxrwx 1 oliver oliver 2.4K Feb 20 2019 main0.cpp rwxrwxrwx 1 oliver oliver 1.8K Feb 20 2019 main1.cpp rwxrwxrwx 1 oliver oliver 4.4K Aug 8 17:50 main.cpp rwxrwxrwx 1 oliver oliver 267 Aug 8 18:26 Makefile rwxrwxrwx 1 oliver oliver 1.7K Aug 8 23:55 milestone.txt rwxrwxrwx 1 oliver oliver 11K Jul 28 04:56 out.txt rwxrwxrwx 1 oliver oliver 18 Aug 8 23:39 pswd.txt drwxrwxrwx 1 oliver oliver 4.0K Jul 25 22:19 Release rwxrwxrwx 1 oliver oliver 581 Aug 8 18:14 run.gdb rwxrwxrwx 1 oliver oliver 193 Feb 20 2019 txt.txt ./FastPrimeCruncher/bin: total 0 drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .. drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:47 Debug ./FastPrimeCruncher/bin/Debug: total 0 drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:47 . drwxrwxrwx 1 oliver oliver 4.0K Jul 20 00:07 .. ./FastPrimeCruncher/.clang: total 0 drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .. ./FastPrimeCruncher/.codelite: total 524K drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .. rwxrwxrwx 1 oliver oliver 7.0K Aug 8 18:26 compilation.db rwxrwxrwx 1 oliver oliver 539 Jul 25 22:17 compile_commands.json rwxrwxrwx 1 oliver oliver 3.5K Aug 8 06:01 FastPrimeCruncher.session rwxrwxrwx 1 oliver oliver 300K Aug 8 18:26 FastPrimeCruncher.tags rwxrwxrwx 1 oliver oliver 156 Feb 20 2019 FastPrimeCruncher.workspace.someone rwxrwxrwx 1 oliver oliver 210K Aug 8 16:44 refactoring.db rwxrwxrwx 1 oliver oliver 3 Feb 20 2019 sftpworkspacesettings.conf rwxrwxrwx 1 oliver oliver 44 Feb 20 2019 subversion.conf drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 tabgroups rwxrwxrwx 1 oliver oliver 142 Feb 20 2019 .ternproject rwxrwxrwx 1 oliver oliver 3 Feb 20 2019 tweaks.conf rwxrwxrwx 1 oliver oliver 0 Feb 20 2019 valgrind.memcheck.supp ./FastPrimeCruncher/.codelite/tabgroups: total 0 drwxrwxrwx 1 oliver oliver 4.0K Feb 20 2019 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 .. ./FastPrimeCruncher/Debug: total 2.1M drwxrwxrwx 1 oliver oliver 4.0K Aug 8 18:26 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .. rwxrwxrwx 1 oliver oliver 1 Aug 8 18:26 .d rwxrwxrwx 1 oliver oliver 594K Aug 8 18:26 FastPrimeCruncher rwxrwxrwx 1 oliver oliver 980K Aug 8 18:26 gears.cpp.o rwxrwxrwx 1 oliver oliver 50 Aug 8 18:26 gears.cpp.o.d rwxrwxrwx 1 oliver oliver 500K Aug 8 17:57 main.cpp.o rwxrwxrwx 1 oliver oliver 48 Aug 8 17:57 main.cpp.o.d ./FastPrimeCruncher/Release: total 220K drwxrwxrwx 1 oliver oliver 4.0K Jul 25 22:19 . drwxrwxrwx 1 oliver oliver 4.0K Aug 8 23:55 .. rwxrwxrwx 1 oliver oliver 1 Jul 25 22:19 .d rwxrwxrwx 1 oliver oliver 73K Jul 25 22:19 FastPrimeCruncher rwxrwxrwx 1 oliver oliver 121K Jul 25 22:19 gears.cpp.o rwxrwxrwx 1 oliver oliver 53 Jul 25 22:19 gears.cpp.o.d rwxrwxrwx 1 oliver oliver 20K Jul 25 22:19 main.cpp.o rwxrwxrwx 1 oliver oliver 51 Jul 25 22:19 main.cpp.o.d[/CODE] 
[QUOTE=Uncwilly;553296]Thanks for catching that. I broke the link. If someone want to get it they can do so with full knowledge.[/QUOTE]
Actually, the Sourceforge project link does not seem to be the problem, it is rather the download link which appends "files/latest/download" to the project link. But if I understand correctly, kruoli had no warnings opening the archive. Btw, I do not really understand why the author creates a passwordprotected archive and then publishes the password on a public forum. Why not a plain open SourceForge project? 
I guess SF says it's malicious [I]because[/I] it is password protected and cannot be checked against malware etc.
The password is not shown correctly on my end, but I still could copy and insert in into my archiver. 
[QUOTE=Till;553299]Actually, the Sourceforge project link does not seem to be the problem, it is rather the download link which appends "files/latest/download" to the project link.
But if I understand correctly, kruoli had no warnings opening the archive. Btw, I do not really understand why the author creates a passwordprotected archive and then publishes the password on a public forum. Why not a plain open SourceForge project?[/QUOTE]As a bozo filter? Anyone can download an unprotected project. A certain minimum level of cluefulness is needed for one which is passwordprotected. 
[QUOTE=xilman;553305]As a bojo filter?
[/QUOTE] Great one :razz: :grin::grin: 
I am always keen to learn some crowd psychology.
The question that I had is  why do folks get compelled to download a code that does something wrongly? We [I]already [/I]know that it does its own job wrongly. What does it matter [I]how [/I]it does it? One wants to marvel the coding style or the number of lines or something? Very curious. _____________________ The algorithm starts with N, P and Q, then... [QUOTE=SarK0Y;553061]At some point, it seemed utterly impossible. But here we go.. Actually, algo consists of three stages.. it picks initial (probable) Z’s (pZ_L and pZ_R) up (Z = P + Q, [B][COLOR="Red"]N = P*Q[/COLOR][/B])[/QUOTE] Full stop, don't need to read further. The algorithm now computed P*Q and if it equals N: stop, all done. Else: stop because there is no point in going further :) Arguing that it is better because "it doesn't use division and (untrue) doesn't use modular arithmetic" is false because it competes with the Algorithm 2: "Compute P*Q. If equal N, stop. Done" and loses. 
[QUOTE=Till;553309]Great one :razz: :D :D[/QUOTE]Clever misquoting. :tu:
By and large I disapprove of editing quotes but on this occasion I will make an exception. 
[QUOTE=xilman;553312]Clever misquoting. :tu:
By and large I disapprove of editing quotes but on this occasion I will make an exception.[/QUOTE] Thank you sir :smile: 
[QUOTE=Till;553313]Thank you sir :smile:[/QUOTE]You're welcome.
As a nitpick (I spend a significant amount of my time picking nits) I will point out that BoJo is conventionally BiCapitalized, 
[QUOTE=xilman;553317]You're welcome.
As a nitpick (I spend a significant amount of my time picking nits) I will point out that BoJo is conventionally BiCapitalized,[/QUOTE] Is this a riddle that someone could crack who does not know british language or culture to a really large extend? I am quite clueless about it, but I think that those two capitalized letters are a distraction. 
[QUOTE=Till;553322]Is this a riddle that someone could crack who does not know british language or culture to a really large extend? I am quite clueless about it, but I think that those two capitalized letters are a distraction.[/QUOTE]"BoJo"is a common contraction of "Boris Johnson".
"Bozo" is the name of a historically famous circus clown. I used "bozo" whereas you misquoted it as "bojo". 
[QUOTE=xilman;553327]"BoJo"is a common contraction of "Boris Johnson".
"Bozo" is the name of a historically famous circus clown. I used "bozo" whereas you misquoted it as "bojo".[/QUOTE] I understood that much... Good night :cool: 
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[QUOTE=xilman;553327]"BoJo"is a common contraction of "Boris Johnson".
"Bozo" is the name of a historically famous circus clown. I used "bozo" whereas you misquoted it as "bojo".[/QUOTE] Spot the difference 
[QUOTE=xilman;553327]"BoJo"is a common contraction of "Boris Johnson".
"Bozo" is the name of a historically famous circus clown. I used "bozo" whereas you misquoted it as "bojo".[/QUOTE] Uh I think I got the last bit... "de" vs. "bi" is the pun? 
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[QUOTE=Batalov;553311]I am always keen to learn some crowd psychology.
The question that I had is  why do folks get compelled to download a code that does something wrongly? We [I]already [/I]know that it does its own job wrongly. What does it matter [I]how [/I]it does it? One wants to marvel the coding style or the number of lines or something? Very curious. _____________________ The algorithm starts with N, P and Q, then... Full stop, don't need to read further. The algorithm now computed P*Q and if it equals N: stop, all done. Else: stop because there is no point in going further :) Arguing that it is better because "it doesn't use division and (untrue) doesn't use modular arithmetic" is false because it competes with the Algorithm 2: "Compute P*Q. If equal N, stop. Done" and loses.[/QUOTE] You really want too much :rolleyes: this algo been going for research matters == it collects statistics how numbers permutates with Z. password is indeed simple filter for kickingaround folks :smile: 
[QUOTE=Till;553338]Uh I think I got the last bit... "de" vs. "bi" is the pun?[/QUOTE]Nope. You are overanalyzing.
"BiCapitalization" is a pejorative attack on corporations who use weird capitals within a word so that they can (try to) trademark common words. So no pun at all. 
[QUOTE=xilman;553467]Nope. You are overanalyzing.[/QUOTE]
Yep :/ [QUOTE=xilman;553467] "BiCapitalization" is a pejorative attack on corporations who use weird capitals within a word so that they can (try to) trademark common words. So no pun at all.[/QUOTE] Thanks for the explanation. There is so much to learn... 
new record w/ S0T
1.0000446813071602893494976452652620620272901612870562716159161685257140761382896257095479097774775786455255056866367729546439460748470940020192907863495110249 28454879317331762049771484736268086850579340310166395586498323803260792907800077463922559676313168204797474729443423059391492806223905521108490077250478 [URL="https://sourceforge.net/projects/fastprimecruncher/"]Src here[/URL]. this function is some kind of mystic == result oscillates quite close to 1 :) [COLOR=Red]LaurV: link edited, see my post below[/COLOR] 
I clicked the link and was automatically downloading a compressed file. I'm not a fan and automatically sluiced it out the backdoor. For anyone else looking at this link beware of this behavior or at least have a few safety features in place to contend with anything nasty.
For the OP, I looked at what I could and couldn't discern any milestone and if you spot anything else that is mystical consult one of the many oracles that can dissipate the smoke..google..duck duck.. 
[QUOTE=jwaltos;556455]I clicked the link and was automatically downloading a compressed file. I'm not a fan and automatically sluiced it out the backdoor. For anyone else looking at this link beware of this behavior or at least have a few safety features in place to contend with anything nasty.
For the OP, I looked at what I could and couldn't discern any milestone and if you spot anything else that is mystical consult one of the many oracles that can dissipate the smoke..google..duck duck..[/QUOTE] learn basics about computers & security, then your questions + concerns shall be eliminated for good. :smile: it's very sad that discussion has become so boring offtopic. 
:modhat: :flex:
Hiding a sourceforge link to an executable file behind an amd forum link won't do you any good either. Together with the scratchy answer above, that resulted in me editing the link. No, I didn't try to download it. I will take your advice for good, and I will not open it before learning some more about computer security, whenever that will be :razz: 
direct link to a file has the sense, because even slight changes of algo have affected results + i add more statistics + weed bugs out. And if archive is malware, it doesn't matter you download it manually or automatically == infection will be activated during opening. Actually any archive can be easily checked for malware..
[url]https://www.virustotal.com/gui/[/url] google drive other online services virtual machines offline antiviruses +++++++++++++++++++ in short. the're no sense to push malware that way. :smile: 
[B]Yet another remarkable result == FPC11 [/B]
S0T_guided doesn't provide more precision to estimate Z, but anyway result is rather curious... number of loops: 100 0, 1, guided '2' Please, enter version of S0T: 2 max Z to orig [CODE]0.6372928473642518323379782288209547690425255443149893931893843535970792784175827341996320445052560478699298601839443533476029251438056391372609841262742385638132526154494125575509613040804480112920323565670709588246405288404908622894629709445337 3438821172788817007077339573053851240563147377315517345065198070950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[/code] Mean Z to orig [CODE]0.847816521663485657814133837914497020755162842047555820546465597072997806836376666909889217573427171732060213664709636126472666235082149940337731722430296321900550428764812235598509955603712461573414220897963933429496883501654422702168241902579 76761323958691878245912386572902803522455618816353527839870935888620000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [/CODE] min Z to orig [CODE]0.9899022558143058079156912361317448150859862978254655589273759906236828905373638276408135040588895053841490325450704413770152873445232075816563257398247839495905241594389007703128728139981129486315948151838363626365347525996501078194027536481540 9773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [/CODE] closest Z to orig [code]0.989902255814305807915691236131744815085986297825465558927375990623682890537363827640813504058889505384149032545070441377015287344523207581656325739824783949590524159438900770312872813998112948631594815183836362636534752599650107819402753648 15409773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[/CODE] number of loops: 1000 0, 1, guided '2' Please, enter version of S0T: 2 max Z to orig [CODE]0.6372928473642518323379782288209547690425255443149893931893843535970792784175827341996320445052560478699298601839443533476029251438056391372609841262742385638132526154494125575509613040804480112920323565670709588246405288404908622894629709445337 3438821172788817007077339573053851240563147377315517345065198070950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [/CODE] Mean Z to orig [CODE]0.847254227884694871840210282646655859595988024436944967483139972442796707903333791436934964257186571865906945732866754293783827697653512151204043811848902883579696369741256577272607407808388339428622875723682619255196023276606284720922557147192 42324452492007603826245486175440403294895115476090344925759358260020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [/CODE] min Z to orig [CODE]0.9899022558143058079156912361317448150859862978254655589273759906236828905373638276408135040588895053841490325450704413770152873445232075816563257398247839495905241594389007703128728139981129486315948151838363626365347525996501078194027536481540 9773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [/CODE] closest Z to orig [CODE]0.989902255814305807915691236131744815085986297825465558927375990623682890537363827640813504058889505384149032545070441377015287344523207581656325739824783949590524159438900770312872813998112948631594815183836362636534752599650107819402753648 15409773578928729900104958869190201416265909610810311382805296301175410000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000[/CODE] Number of loops doesn't affect output + ratio doesn't jump over 1. src: [URL="https://community.amd.com/externallink.jspa?url=https%3A%2F%2Fsourceforge.net%2Fprojects%2Ffastprimecruncher%2Ffiles%2FFPC11.7z%2Fdownload"]https://sourceforge.net/projects/fastprimecruncher/files/FPC11.7z/download[/URL] Plus, the're QSORT 4 GMP, I wrote it as dynamic code w/ function pointers. PS actually, if I'll be having some more time, rsa can be cracked :smile: 
What, exactly, is curious about this output? What are you trying to tell us?
You say "crack RSA" like it's one thing. Which RSA number do you think you can crack? I mean, I can crack RSA100 in a few different ways, using a wide variety of tools; but most of them fail to help me crack RSA768. 
[QUOTE=VBCurtis;561289]What, exactly, is curious about this output? What are you trying to tell us?
You say "crack RSA" like it's one thing. Which RSA number do you think you can crack? I mean, I can crack RSA100 in a few different ways, using a wide variety of tools; but most of them fail to help me crack RSA768.[/QUOTE] for now, i've been toying w/ rsa150 == the very goal ain't just crack rsa numbers, but is to find polynomialtime techniques. heh.. it sounds ambitious, but crude approximation of Z (Z == P + Q) has been already possible w/ S0Ts :D 
now fpc has very good result for mean value == report here: [url]https://sourceforge.net/projects/fastprimecruncher/files/Outputs/FPC14/S0T2Head%20makes%20record%20for%20mean%20val%20_%292.txt[/url]
src here: [url]https://sourceforge.net/projects/fastprimecruncher/files/FPC14.7z[/url] actually, it's already possible to crack rsa == it takes the array of samples generated w/ S0Ts (for instance, S0T2Head) & then play w/ function "means" to reduce noisy data. meanwhile, i'd like to improve the speed of convergence:smile: 
[url]https://sourceforge.net/projects/fastprimecruncher/files/Outputs/FPC14/cut%20the%20means1.txt[/url]
[url]https://sourceforge.net/projects/fastprimecruncher/files/Outputs/FPC14/cut%20the%20means.txt[/url] 
[QUOTE=SarK0Y;562316]now fpc has very good result for mean value == report here: [url]https://sourceforge.net/projects/fastprimecruncher/files/Outputs/FPC14/S0T2Head%20makes%20record%20for%20mean%20val%20_%292.txt[/url]
src here: [url]https://sourceforge.net/projects/fastprimecruncher/files/FPC14.7z[/url] actually, it's already possible to crack rsa == it takes the array of samples generated w/ S0Ts (for instance, S0T2Head) & then play w/ function "means" to reduce noisy data. meanwhile, i'd like to improve the speed of convergence:smile:[/QUOTE] What does any of this mean? How do you factor one of the RSA challenge numbers with your method? 
[QUOTE=mathwiz;562330]What does any of this mean?
How do you factor one of the RSA challenge numbers with your method?[/QUOTE] He doesn't. But, he *could*!! You know, when his thingies converge. If he explained his method, someone might steal it! So, please just give him attention. You won't learn anything, since he can't actually do anything. 
[QUOTE=mathwiz;562330]What does any of this mean?
How do you factor one of the RSA challenge numbers with your method?[/QUOTE] just download output (txt files) == the're step by step == approximate Z & then you have.. N = P * Q Z = P + Q 
[QUOTE=SarK0Y;562316]now fpc has very good result for mean value == report here: [url]https://sourceforge.net/projects/fastprimecruncher/files/Outputs/FPC14/S0T2Head%20makes%20record%20for%20mean%20val%20_%292.txt[/url]
src here: [url]https://sourceforge.net/projects/fastprimecruncher/files/FPC14.7z[/url] actually, it's already possible to crack rsa == it takes the array of samples generated w/ S0Ts (for instance, S0T2Head) & then play w/ function "means" to reduce noisy data. meanwhile, i'd like to improve the speed of convergence:smile:[/QUOTE] [QUOTE=SarK0Y;562336]just download output (txt files) == the're step by step == approximate Z & then you have.. N = P * Q Z = P + Q[/QUOTE] Please show, step by step, how you would factor (say) RSA200. 
[QUOTE=SarK0Y;562336]just download output (txt files) == the're step by step == approximate Z & then you have..
N = P * Q Z = P + Q[/QUOTE] Just factor this: [CODE]22881674130987296817369335083505533792239602706912929845514703469287126491267727124570402660433186186250608348826913204513283590140161157396044966038359555681362347423[/CODE] 
[QUOTE=mathwiz;562339]Please show, step by step, how you would factor (say) RSA200.[/QUOTE]
like any other rsa number. just look into outputs. 
[QUOTE=Batalov;562340]Just factor this:
[CODE]22881674130987296817369335083505533792239602706912929845514703469287126491267727124570402660433186186250608348826913204513283590140161157396044966038359555681362347423[/CODE][/QUOTE] any one can try on their own. since then my task has been to reduce number of samples for given numbers. 
There's nothing to try. You can't get factors yourself. We certainly aren't going to be able to either.
You haven't demonstrated any factoring. Just a bunch of BS. Factor something. 
[QUOTE=VBCurtis;562360]There's nothing to try. You can't get factors yourself. We certainly aren't going to be able to either.
You haven't demonstrated any factoring. Just a bunch of BS. Factor something.[/QUOTE] bs? :) curious "synonym" for approximation. actually, i have no time to crack any number for [B]NOTHING[/B] + it has no sense. so far here i have met laughable stock w/ deep phobias to open 7zip archive. So it was extremely naive for me to wait adequate dispute :grin: 
[QUOTE=SarK0Y;562366]bs? :) curious "synonym" for approximation. actually, i have no time to crack any number for [B]NOTHING[/B] + it has no sense. so far here i have met laughable stock w/ deep phobias to open 7zip archive. So it was extremely naive for me to wait adequate dispute :grin:[/QUOTE]
Except you haven't actually demonstrated any sort of method or algorithm whatsoever. 
[QUOTE=SarK0Y;562366]bs? :) curious "synonym" for approximation ...[/QUOTE]If it isn't all just BS then [b]show[/b] us why it isn't. Produce an actual result, instead of the endless pontificating and meaningless random numbers.

[QUOTE=mathwiz;562369]Except you haven't actually demonstrated any sort of method or algorithm whatsoever.[/QUOTE]
my point has been perfectly clear from the very start == I've researched the ways to approximate Z for polynomial time. I've shared sources & examples/results how to operate w/ those methods. So, i'd like to ask very naive question == is this forum for math & researchers or wtf here is going on :question::exclaim::sad::confused: it would have been purely understandable, if indigenous community would have shared alt methods to approximate Z w/ more speed (for instance) or would have provided some clues to improve shared algos. But [B]NO ABSOLUTELY[/B], my thread has been flooded by just absurd offtopic... So, you want superb algo(s) & want to do [B]NOTHING[/B] for :) so, any not magical algo is only bs for you :grin: 
[QUOTE=SarK0Y;562466]my point has been perfectly clear from the very start == I've researched the ways to approximate Z for polynomial time. I've shared sources & examples/results how to operate w/ those methods. So, i'd like to ask very naive question == is this forum for math & researchers or wtf here is going on :question::exclaim::sad::confused: it would have been purely understandable, if indigenous community would have shared alt methods to approximate Z w/ more speed (for instance) or would have provided some clues to improve shared algos. But [B]NO ABSOLUTELY[/B], my thread has been flooded by just absurd offtopic...
So, you want superb algo(s) & want to do [B]NOTHING[/B] for :) so, any not magical algo is only bs for you :grin:[/QUOTE] People on this forum generally care about (1) efficient algorithms to factor large integers, or (2) efficient algorithms for finding large primes (and proving them prime). You've demonstrated no meaningful algorithm for doing either. 
[QUOTE=mathwiz;562469]People on this forum generally care about
(1) efficient algorithms to factor large integers, or (2) efficient algorithms for finding large primes (and proving them prime). You've demonstrated no meaningful algorithm for doing either.[/QUOTE] really? :rolleyes: how could you have efficient algo, if you have done no research??? perhaps new algos appear out of the blue, right? :) 
[QUOTE=SarK0Y;562466]So, you want superb algo(s) & want to do [B]NOTHING[/B] for :) so, any not magical algo is only bs for you :grin:[/QUOTE]
To prove that your algo is not BS I will give you 3 tests for it, each harder than the previous. You need to solve the first one before your next post (and you must post the solution in your next post), or you may be banned (because you fail to show that your method works and just want to be a troll). Then you must solve the next one (and post the answer) to continue posting. After you have posted the answer to the third, then we will believe that you are on to something. First test. Factor this semiprime (using your method): [C]3870092038884345663779821427477643475136534002402905753076769909311217[/C] Second test Factor this semiprime (using your method) [C]150996579069406676849328254452885095204370060219736837010494868333342863322970462956706063[/C] Third test. Factor this semiprime (using your method) [CODE]4735324369078304459849659757648833978535825054585241886997488631830939162381565490995222405517413444400835669[/CODE] 
[QUOTE=Uncwilly;562471]To prove that your algo is not BS I will give you 3 tests for it, each harder than the next.
You need to solve the first one before your next post (and you must post the solution in your next post), or you may be banned (because you fail to show that your method works and just want to be a troll). Then you must solve the next one (and post the answer) to continue posting. After you have posted the answer to the third, then we will believe that you are on to something. First test. Factor this semiprime (using your method): [C]3870092038884345663779821427477643475136534002402905753076769909311217[/C] Second test Factor this semiprime (using your method) [C]150996579069406676849328254452885095204370060219736837010494868333342863322970462956706063[/C] Third test. Factor this semiprime (using your method) [CODE]4735324369078304459849659757648833978535825054585241886997488631830939162381565490995222405517413444400835669[/CODE][/QUOTE] You lost very point == the task ain't been just solve (it has no sense) == the task is to solve (at least approximate as much as possible) for [B]POLYNOMIAL TIME. [/B]can you do it? :smile::rolleyes: so, don't feed me numbers == the're a hella lot of them w/o such help :grin::wink: 
[QUOTE=SarK0Y;562470]really? :rolleyes: how could you have efficient algo, if you have done no research??? perhaps new algos appear out of the blue, right? :)[/QUOTE]
Here's the issue many forumites have with your approach and why you may consider responses to your research hostile: [LIST=1] You claimed to "have a milestone" in integer factorization and continue claiming that you will "crack rsa, if you have time". These are not light things to make claims for and, in fact, the bigger the claim, the more skeptical people are. It is no wonder, then, that to test your theories, people demand even basic results that will demonstrates tangible results people can work with. [*] You then refuse to demonstrate (or even explain!) your method in a significant way  after reading things on the forums, my best guess is approximation of the sum of P and Q given the product? Not even particularly how you do it, just that you'd rather like to? I am not very well versed in the topic, but I'm pretty sure you need the exact sum, and not just an approximation, and while being off by 0.000000001% would be promising, for a 200 digit number, that leaves you out by a number that is about 190 digits  absolutely no progress at all, really. I may be wrong about your accuracy, but it is not as if you've worked particularly hard to explain your accuracy in the first place, other than some confusing source code and text documents. [*] Most egregiously, you now have chosen to walk back the importance of your research, and scoff at us for expecting really anything at all for a thread that starts with "MILESTONE has been done :D".[/LIST] If you wanted any cooperation, it would have been more helpful to ask questions about the topic  "Has there been any work done on factorizing RSA numbers with approximations of the sums of the primes in the product?"  rather than to announce "big results" and then be gleefully sour when people are doubtful. It would have saved us a lot of time, and it's likely there's already been a lot of research into the topic  with a good reason as to why it's failed so far. 
[QUOTE=SarK0Y;562473]You lost very point == the task ain't been just solve (it has no sense) == the task is to solve (at least approximate as much as possible) for [B]POLYNOMIAL TIME. [/B]can you do it? :smile::rolleyes: so, don't feed me numbers == the're a hella lot of them w/o such help :grin::wink:[/QUOTE]
And you earned yourself a timeout. PM me or any supermod with the factorization of the first test to have posting privileges restored. 
@Gelly
Always good to see a decent criticism.. well then, let's be clear upon that AMAP :smile: [QUOTE]You claimed to "have a milestone" in integer factorization and continue claiming that you will "crack rsa,[/QUOTE]First & foremost, we need to look into canonical definition of «MILESTONE».. [QUOTE][B]2. [/B] a significant event or point in development. [URL]https://www.thefreedictionary.com/milestone[/URL] [/QUOTE]it doesn't mean «final point» & definitely it doesn't mean something magic. It just means that project has had some positive/promising results to proceed further. 2nd moment, Polynomial time doesn't mean you can crack everything in no time. For example, O(N*lgN) & O(N²) are both polynomial time, but (w/ growing N) gap between those speeds becomes Abyss. [QUOTE]You then refuse to demonstrate (or even explain!) your method in a significant way[/QUOTE]actually, there ain't been questions ontopic.. some guys struggled w/ their deep fears of malware & others just have wanted a magic out of the Blue :shock: [QUOTE]but I'm pretty sure you need the exact sum, and not just an approximation,[/QUOTE]from the POV of Practice, we need approximation a way down to the point, where it's possible to use brute force for getting exact sum. Well, this link will answer your questions, if you really want them... [size=2]https://alg0z.blogspot.com/2020/12/majorupdatefpc15rev3.html[/size] [color=red][b]MODERATOR NOTE: Link disabled pending evaluation of software downloads thereat[/b][/color] 
[QUOTE=SarK0Y;566326]actually, there ain't been questions ontopic..[/QUOTE]
Actually, there have been: "Can you factor this composite to demonstrate your algorithm isn't complete BS?" 
[QUOTE=mathwiz;566388]Actually, there have been: "Can you factor this composite to demonstrate your algorithm isn't complete BS?"[/QUOTE]
say me, please, what do you mean with phrase «complete BS». For now, the're no algorithms of integer factorization for practical use == they're too greedy for memory & cpu + they're bad for concurrency too. And actually I have shared everything about my researching. my goal hasn't been to crack occasional rsa numbers, just been researching possible ways to approximate Z. at the very least, it's curious from the POV of theoretical matter :wink: 
Initial investigation of the file: VirusTotal reports that the URL is clean.
The file that that link takes me is clean, [URL="https://www.virustotal.com/gui/file/7bcd6bd258535edf164edec4cd368a88859e831ab6d81b2a8c73ea07c3234794/detection"]according to VirusTotal[/URL]. Attempting to run the program sandboxed in Windows 10 doesn't work (needs the bash shell to work, plus Start.exe fails to start). Attempting to run it in a Linux VM, gets me this far when I run the first bit of code in the pdf you linked: [CODE]./fpc ver poweredby bye sh: en: command not found see seed: 682257166327978917907309860240882231625049719486075477905198 bits: 199 Please, enter a coef 4 Z: [/CODE]Which is not the expected result. So I thought, maybe I should recompile. Except that doesn't work, as the stuff in the makefile appears to be hardcoded, due to the software used to make the makefile. This of course makes it impossible for one to just download the source and compile, unless they go through the trouble of making the file themselves (which I am not going to do). 
[QUOTE=Dylan14;566401]Initial investigation of the file: VirusTotal reports that the URL is clean.
The file that that link takes me is clean, [URL="https://www.virustotal.com/gui/file/7bcd6bd258535edf164edec4cd368a88859e831ab6d81b2a8c73ea07c3234794/detection"]according to VirusTotal[/URL]. Attempting to run the program sandboxed in Windows 10 doesn't work (needs the bash shell to work, plus Start.exe fails to start). Attempting to run it in a Linux VM, gets me this far when I run the first bit of code in the pdf you linked: [CODE]./fpc ver poweredby bye sh: en: command not found see seed: 682257166327978917907309860240882231625049719486075477905198 bits: 199 Please, enter a coef 4 Z: [/CODE]Which is not the expected result. So I thought, maybe I should recompile. Except that doesn't work, as the stuff in the makefile appears to be hardcoded, due to the software used to make the makefile. This of course makes it impossible for one to just download the source and compile, unless they go through the trouble of making the file themselves (which I am not going to do).[/QUOTE] what is version you downloaded? actually, i use codelite to edit sources & build 'em. P.S. [QUOTE]sh: en: command not found[/QUOTE] my bad :) in the main.cpp [QUOTE]system("TZ='Europe/Moscow' en date");[/QUOTE] delete it or change to.. [QUOTE]system("date");[/QUOTE] 
[QUOTE=SarK0Y;566403]what is version you downloaded? actually, i use codelite to edit sources & build 'em.[/QUOTE]
Rev 3, the latest one in this thread (ie the one where the hyperlink is disabled due to potential malware risk). 
[QUOTE=Dylan14;566404]Rev 3, the latest one in this thread (ie the one where the hyperlink is disabled due to potential malware risk).[/QUOTE]
what is funny sourceforge has shown no downloads and all archives are healthy (except directory for encrypted ones). :ermm: 
https: //sourceforge.net/projects/fastprimecruncher/files/Build/FPC15/build.sh/download
this script builds stuff... [QUOTEmkdir ./Debug export compiler=$1 $compiler c "./main.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/main.cpp.o I$2/include I. $compiler c "./gears.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/gears.cpp.o I$2/include I. $compiler c "./vars.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/vars.cpp.o I$2/include I. $compiler c "./S0T.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/S0T.cpp.o I$2/include I. $compiler c "./alt_funcs.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/alt_funcs.cpp.o I$2/include I. $compiler c "./taltws.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/taltws.cpp.o I$2/include I. $compiler c "./S0T_v0.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/S0T_v0.cpp.o I$2/include I. $compiler c "./gears2.cpp" g g3 O0 pedantic Wall std=gnu++20 o ./Debug/gears2.cpp.o I$2/include I. $compiler o ./Debug/FastPrimeCruncher @"FastPrimeCruncher.txt" L. L$2/lib64 g lgmp lpthread chmod u+x ./Debug/FastPrimeCruncher echo "path to program is ./Debug/FastPrimeCruncher"[/QUOTE]just put it into project's directory, then chmod u+x ./build.sh & run ./build.sh /path/to/g++ /dir/of/gcc Ex. ./build.sh /gcc10/bin/g++ /gcc10 
made some renew for guide to add the more detailed remark about disadvantages.

[QUOTE=Dylan14;566401]Initial investigation of the file: VirusTotal reports that the URL is clean.
The file that that link takes me is clean, [URL="https://www.virustotal.com/gui/file/7bcd6bd258535edf164edec4cd368a88859e831ab6d81b2a8c73ea07c3234794/detection"]according to VirusTotal[/URL]. Attempting to run the program sandboxed in Windows 10 doesn't work (needs the bash shell to work, plus Start.exe fails to start). Attempting to run it in a Linux VM, gets me this far when I run the first bit of code in the pdf you linked: [CODE]./fpc ver poweredby bye sh: en: command not found see seed: 682257166327978917907309860240882231625049719486075477905198 bits: 199 Please, enter a coef 4 Z: [/CODE]Which is not the expected result. So I thought, maybe I should recompile. Except that doesn't work, as the stuff in the makefile appears to be hardcoded, due to the software used to make the makefile. This of course makes it impossible for one to just download the source and compile, unless they go through the trouble of making the file themselves (which I am not going to do).[/QUOTE] [QUOTE][FONT=monospace][COLOR=#000000]./fpc [/COLOR] date Fri Dec 18 00:28:56 MSK 2020 see seed: 17298806269879287989854479267472249225451484322313065116803 bits: 194 Please, enter a coef 4 Z: 1 n = 155089812478348440509606754370011861770654545830995430655466945774312632703463465954363335027577729025391453996787414027003501631772186840890795964683 origP = 348009867102283695483970451047593424831012817350385456889559637548278410717 origQ = 445647744903640741533241125787086176005442536297766153493419724532460296199 zero = 0No luck, cycles 247, bits in numero 496 max delta 496, min delta 482 pvt 452481620476707434240172611436088862775136030162941194679675157584264838795 bits in pvt 249 fctr0 452481620476707434223143780492380366100056287714190241526593877347970056190 fctr1 342777029041274693209436393106254960601139864285139500599868342747434696109 delta of pvt & fctr0 17028830943708496675079742448750953153081280236294782605 Enter '1' to run test Enter '2' to try factorization Take a look in windows deeply '3' [/FONT][/QUOTE] it's old stuff. not sure of version.. perhaps, even 5th/6th one, if not older. the newest one is [FONT=monospace][COLOR=#000000]./Debug/FastPrimeCruncher ver poweredby[/COLOR] [/FONT] 
Side effect of research == [TEX]\sqrt{2}[/TEX] is the rational number [URL="https://alg0z.blogspot.com/2021/01/squarerootof2isrationalnumber.html?m=0"]https://alg0z.blogspot.com/2021/01/squarerootof2isrationalnumber.html?m=0 :smile:
[/URL] 
[QUOTE=SarK0Y;568160]Side effect of research == [TEX]\sqrt{2}[/TEX] is the rational number [URL="https://alg0z.blogspot.com/2021/01/squarerootof2isrationalnumber.html?m=0"]https://alg0z.blogspot.com/2021/01/squarerootof2isrationalnumber.html?m=0 :smile:
[/URL][/QUOTE]For once I am pleased that the linked target displays nothing without JS, because just the title makes it look like a crank worthy post. Would you like to summarise what it says? 
1 Attachment(s)
In a nutshell, he says:
Let's take a rational number p/q = 2/3. "but definition of the odd/even has absolutely no sense for rational numbers," (direct quote) so we cannot say that integer p=2 is an even number. it's neither even nor odd. It is 1.99999999999... End of proof. Is that right, Evgeniy? 2 is not an even number? Would it make you feel better, if p/q = 1414/1000, "we cannot prove that integer 1414 is an even number"? I attached his "proof". 
[QUOTE=Batalov;568165]In a nutshell, he says:
Let's take a rational number p/q = 2/3. "but definition of the odd/even has absolutely no sense for rational numbers," (direct quote) so we cannot say that integer p=2 is an even number. it's neither even nor odd. It is 1.99999999999... End of proof. Is that right, Evgeniy? 2 is not an even number? Would it make you feel better, if p/q = 1414/1000, "we cannot prove that integer 1414 is an even number"? I attached his "proof".[/QUOTE] Åctually, no :) 2 is 2, but when you deal with rationals you cannot treat them like natural numbers. for example.. [TEX]\frac{1}{9}\cdot9 \neq\frac{9}{9}\cdot1[/TEX] at 1st glance, looks strange, but... [TEX]\frac{1}{9}\cdot9 \eq0.11111111111111..11\cdot9[/TEX] according to the very principle of limits, approximation of continuous function cannot reach its final point. Here we could recall [B][URL="https://www.cuttheknot.org/WhatIs/Infinity/AchillesAndTortoise.shtml"]Achilles and the Tortoise[/URL][/B] 
No, 1/9 times 9 is 1, even in decimals.
0.9999repeating is equal to 1 yet you claim it is not, and make fuzzy reference to a limit. If it's not equal to 1, how far away from 1 is it? Or, what number can you fit between it and 1? 
[QUOTE=VBCurtis;568233]No, 1/9 times 9 is 1, even in decimals.
0.9999repeating is equal to 1 yet you claim it is not, and make fuzzy reference to a limit. If it's not equal [B]to 1, how far away from 1 is it? Or, what number can you fit between it and 1?[/B][/QUOTE] 0.9 < 0.99 < 0.999< .. < 0.999..99 it's continuous sequence/function. if you assume it can reach its final point 1 then you fall into bad situation like.. [CENTER][TEX]\lim_{x \to 1}\frac{1}{1x}\eq \frac{1}{0}[/TEX][/CENTER] :smile: 
[QUOTE=SarK0Y;568231]Åctually, no :) 2 is 2, but when you deal with rationals you cannot treat them like natural numbers. for example..
<<some red herring>>[/QUOTE] Don't get distracted. Observe: a p/q is a rational number, where p [B]is an integer[/B] and q [B]is an integer.[/B]. Done with rationals. Now all you have are integer numbers until the end of Euclid's proof. Now, are you saying that it's not true that all integer numbers are either even or odd? [SPOILER]Hint: they are![/SPOILER] 
[QUOTE=SarK0Y;568237]0.9 < 0.99 < 0.999< .. < 0.999..99 it's continuous sequence/function. if you assume it can reach its final point 1 then you fall into bad situation like..
[CENTER][TEX]\lim_{x \to 1}\frac{1}{1x}\eq \frac{1}{0}[/TEX][/CENTER] :smile:[/QUOTE] Neither side of your limit example exists, so your congruence is nonsensical and irrelevant to whether 0.9repeating is equal to 1. There is no sequence involved in the single number 0.9repeating, either. I didn't ask about 0.9, nor 0.99. 0.9repeating is neither of those numbers. Every member of your sequence is strictly less than 0.9repeating, anyway. You might figure out the flaws in your reasoning if you used words properly how do you define "continuous sequence"? 
(1) OP seems to be confounding "fractions" (rational numbers) and "decimal fractions," i.e. fractions that can be expressed with a poweroften denominator. Not all rational numbers are decimal fractions.
(2) OP also seems to think that invalidating a proof of A automatically proves ~A (notA). It doesn't. (Here, A is "The square root of 2 is irrational.") OP, of course, did not invalidate the proof. What he actually did was (1). Expressing the statement that the (positive) square root of 2 is rational as an equation in positive integers p and q, (*) p[sup]2[/sup] = 2*q[sup]2[/sup] invites a Euclidean proof that the square root of 2 is not rational, because the equation is impossible. Euclid also proved a result now known as the Fundamental Theorem of Arithmetic, AKA unique factorization. The equation (*) violates the Fundamental Theorem, because the left side is divisible by 2 evenly many times, while the right side is divisible by 2 oddly many times. 
[QUOTE=Dr Sardonicus;568248](1) OP seems to be confounding "fractions" (rational numbers) and "decimal fractions," i.e. fractions that can be expressed with a poweroften denominator. Not all rational numbers are decimal fractions.
[/QUOTE] don't confuse numerical system & numbers itself == any proper numerical system can express any number. Another moment is how efficient that expression could be. [QUOTE=Dr Sardonicus;568248] (2) OP also seems to think that invalidating a proof of A automatically proves ~A (notA). It doesn't. (Here, A is "The square root of 2 is irrational.") [/QUOTE] no, the very point is, you must uniform objects before you do operations on them. that proof messes w/ two different types of objects. for instance, 1/3 is odd or even? or let [TEX]p,q \in \mathbb{N}\; \frac{p}{q}=\epsilon,\; p=\epsilon\cdot q[/TEX] everything looks fine out there, right?:grin: But we have the damn grave problem, even two ones... [TEX] p=\epsilon\cdot q[/TEX] exists everywhere for any p & q. second form has two troubling cases == 1st one w/ q = 0 and 2nd one is that.. [CENTER] [TEX]\displaystyle \lim_{q \to \infty}\lim_{p \to \infty}\frac{p}{q}\eq????[/TEX][/CENTER] 
[QUOTE=VBCurtis;568242]Neither side of your limit example exists, so your congruence is nonsensical and irrelevant to whether 0.9repeating is equal to 1.
There is no sequence involved in the single number 0.9repeating, either. I didn't ask about 0.9, nor 0.99. 0.9repeating is neither of those numbers. Every member of your sequence is strictly less than 0.9repeating, anyway. You might figure out the flaws in your reasoning if you used words properly how do you define "continuous sequence"?[/QUOTE] so [TEX]\ln(x)[/TEX] and [TEX] \frac{d\ln(x)}{x}[/TEX] do not exist, right?:smile: [QUOTE=VBCurtis;568242] There is no sequence involved in the single number 0.9repeating, either. I didn't ask about 0.9, nor 0.99. 0.9repeating is neither of those numbers. Every member of your sequence is strictly less than 0.9repeating, anyway. You might figure out the flaws in your reasoning if you used words properly how do you define "continuous sequence"?[/QUOTE] Oh, boy, really?:cmd::ermm: [CENTER] [TEX]\lim_{n \to \infty}\left(1\frac{1}{10^{n}\right)\eq0.9999..99[/TEX] [/CENTER] 
The attempt to :deadhorse: (and resurrect a dead thread) detected.
:direction: Thread is closed. [COLOR="Red"]Mod warning: More wasting of people's time with BS will result in a ban.[/COLOR] 
\(\lim\limits_{n \to \infty}\frac{n}{n+1}=0.9999..99\); in fact, \(\lim\limits_{n \to \infty}\frac{n}{n+M82589933}=0.9999..99\) too... hihi
edit: whoops, sorry Serge, didn't see the thread is closed. (but this way I learned an important difference between \TeX and \MathJax (using the \limits when the formula is inline, otherwise the limits are placed as indices, and not compacted vertically). 
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