mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > jasong

Reply
 
Thread Tools
Old 2007-11-01, 04:11   #1
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

5×701 Posts
Default Picture primes

I'd like to learn how to find picture primes, and in the process, help others to accomplish this. For those of you who don't know, a picture prime is a prime number where when it is displayed at a certain number of digits per line, a picture, word, or many words is formed. I will describe what I think is the best method for doing this and hope that people can help me find programs that can accomplish each task.

First, we need to know the picture or sentence we want. For this we'll use "PRIME NUMBERS ARE SUPER-COOL!!!" Cheesy, but then again, a lot of people think prime number searching as a hobby is cheesy.

Next, one needs to find a program that can represent the bit-map of that sentence. Another problem is how big a square to use for each pixel, a square that will be represented by digits. And will the "pixels" all be one digit with another digit representing white space? What if one decides they want to list a lot of peoples names as prime pictures and the combination of the white space digit and the dark pixels digit is the person's age? Lot's of choices in the particulars.

Anyway, if we've got the bit-map and it's saved as a file, then we need a program that can take as input the bit-map, the size of the grid, and possibly the places in the picture that can be any number, since the odds are against our picture being prime right off the bat.

After that, it's a matter of sieving a range of numbers, the size of the range being decided by the size of the number. Then you should have a list of possibilities which you can PRP. If luck is on your side you'll get at least one PRP.

At that point, the resulting number may be so big that it would be foolish to try to test it to achieve a 100% certainty that it's prime. The place that I got this idea used a method where they knew for a fact that a 100,000 digit number was prime, but without having the necessary math skills, one can only hope to prove a number under 5,000 digits as absolutely prime, and in reality, the limit is probably much, MUCH less than a 5,000-digit limit. Unless, of course, you're reading this a few years after I actually wrote it.

I'm prepared for the possibility that this thread post won't achieve it's intended goal and either stay an orphan, or maybe people will be super-enthusiastic, and many posts later give up on the task. But...fingers crossed.

And if anyone wants to help the great unwashed use the super-cool, but mysterious n+/-1 method to generate massive primes, that would be fabulous.
jasong is offline   Reply With Quote
Old 2007-11-01, 11:15   #2
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

5·23·67 Posts
Default

We're not sure how your method works, but here is a "picture prime" of M27.
Attached Thumbnails
Click image for larger version

Name:	gabrielle.jpg
Views:	147
Size:	131.0 KB
ID:	1999  
Xyzzy is offline   Reply With Quote
Old 2007-11-01, 12:33   #3
m_f_h
 
m_f_h's Avatar
 
Feb 2007

24·33 Posts
Default

Quote:
Originally Posted by Xyzzy View Post
We're not sure how your method works, but here is a "picture prime" of M27.
It seems your method truncates the data:
it seems to display only the MSB (or LSB ? a matter of interpretation in this context ?)
If you cannot avoid truncation, try another data layout (LittleEndian vs BigEndian...)
m_f_h is offline   Reply With Quote
Old 2007-11-01, 12:38   #4
m_f_h
 
m_f_h's Avatar
 
Feb 2007

24·33 Posts
Default

Quote:
Originally Posted by jasong View Post
I'd like to learn how to find picture primes, and in the process, help others to accomplish this. For those of you who don't know, a picture prime is a prime number where when it is displayed at a certain number of digits per line, a picture, word, or many words is formed. I will describe what I think is the best method for doing this and hope that people can help me find programs that can accomplish each task.
For a given Mersenne prime there is only one way to arrange the binary digits in a rectangular square, and the outcoming pictures are quite similar for all primes of that kind...
m_f_h is offline   Reply With Quote
Old 2007-11-01, 14:47   #5
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

5·23·67 Posts
Default

Quote:
It seems your method truncates the data...
No truncation. The entire prime is in there.

Think like a terrorist. (Seriously!)
Xyzzy is offline   Reply With Quote
Old 2007-11-01, 15:16   #6
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

344610 Posts
Default

I think Jason is referring to a "primeform e-group" "picture prime".

Although a message in encoded in the prime, you can hardly call it encryption

"Picture" is probably not the most apt term. It would be nice to have a picture prime of M27 (above.) The possibilities are endless

We used some kind of "banner" program -- "man banner" on your Unix/Linux systems. "banner" was used on our continuous stationary at Uni to separate users' print-outs with their account names etc. I will get back to you with the name of the program we used if you cannot find a suitable one with Google. You need an "alphabet" -- a set of letter files -- which are used by the program to turn a message source text input file into the required output. It is an easy task for a budding computer science undergraduate to write such a program.

Last fiddled with by paulunderwood on 2007-11-01 at 15:50
paulunderwood is offline   Reply With Quote
Old 2007-11-01, 15:18   #7
petrw1
1976 Toyota Corona years forever!
 
petrw1's Avatar
 
"Wayne"
Nov 2006
Saskatchewan, Canada

3·52·59 Posts
Default

Is this what you are talking about?

http://hjem.get2net.dk/jka/math/egroup/picture.htm
petrw1 is online now   Reply With Quote
Old 2007-11-01, 15:35   #8
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

3·23·43 Posts
Default

I suggest using the gif image format, since you can put arbitrary number of characters as "comments" in a gif-file, so just fill in stuff until your image is prime.

check under "Comment Block Extension"
http://www.u229.no/stuff/GIFFormat/

Last fiddled with by ATH on 2007-11-01 at 15:35
ATH is offline   Reply With Quote
Old 2007-11-01, 21:11   #9
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

350510 Posts
Default

While we're on the subject of picture primes, does the fact that the prime was generated using the 15 N-1 factor files(I have no idea of how these were used, so I may be ignorantly referring to something that doesn't matter) disqualify it from the "no special form" category? I'd always thought that that only applied to the final number. Since I'm pretty sure the "no special form" record is significantly less than 100,000 digits, I guess I'm wrong.
jasong is offline   Reply With Quote
Old 2007-11-01, 22:54   #10
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

344610 Posts
Default

Yes, it has a "special form" because of the 30% factorization of N+1.
paulunderwood is offline   Reply With Quote
Old 2007-11-02, 02:58   #11
Xyzzy
 
Xyzzy's Avatar
 
"Mike"
Aug 2002

5·23·67 Posts
Default

Quote:
Think like a terrorist. (Seriously!)
Code:
$ apt-cache show steghide
Package: steghide
Priority: optional
Section: misc
Installed-Size: 484
Maintainer: Ola Lundqvist <opal@debian.org>
Architecture: i386
Version: 0.5.1-8
Depends: libc6 (>= 2.3.6-6), libgcc1 (>= 1:4.1.0), libjpeg62, libmcrypt4, libmhash2, libstdc++6 (>= 4.1.0), zlib1g (>= 1:1.2.1)
Filename: pool/main/s/steghide/steghide_0.5.1-8_i386.deb
Size: 174420
MD5sum: 0adc54c1e8783cf5282f0873ea911e5f
SHA1: 8556b3f25cbfdaa08dc8a2474b74b05d7cd7e31e
SHA256: ba780805044a239b638e8460360c22f3a86c95836ce8ada9d62e84b37c10dceb
Description: A steganography hiding tool
 Steghide is steganography program which hides bits of a data file
 in some of the least significant bits of another file in such a way
 that the existence of the data file is not visible and cannot be proven.
 .
 Steghide is designed to be portable and configurable and features hiding
 data in bmp, wav and au files, blowfish encryption, MD5 hashing of
 passphrases to blowfish keys, and pseudo-random distribution of hidden bits
 in the container data.
Tag: interface::commandline, role::program, scope::utility, security::cryptography, works-with::image, works-with::image:raster

$ steghide info gabrielle.jpg 
"gabrielle.jpg":
  format: jpeg
  capacity: 7.3 KB
Try to get information about embedded data ? (y/n) y
Enter passphrase: 
  embedded file "27.txt":
    size: 13.2 KB
    encrypted: rijndael-128, cbc
    compressed: yes

$ steghide extract -sf gabrielle.jpg 
Enter passphrase: 
wrote extracted data to "27.txt".

$ cat 27.txt 
8545098243036338031933007053184030365099015913040210583432692582822900647821676358562005000144576458
6148131529525322367493834050222564143679429483628661393367192283872234928618505445379948491970281406
6298682412853022594582702532253637046393573819102339382603546705057592743425373988510067594258489091
8826528169842304813392310893705975224296579622210236253897868384762225627009375728494936567783097098
4890261155981748182164856299141430118685263110991962801450689187993826991987637504147605457048039381
7802067642573802934320804004689212061263134937191146939217967863913998340450302066353316060446899821
9600169651494552474512568661204164558377852378894427367166228636947990631479724219151372811852236394
8553093908070070396563052428480369632952259456017856523100642835591426445580953590482718456788197075
2815068646412535212946406293446404577519747900684536609902072584992617981311048365318249332003277695
7273342392487560229193230298811170427442121068224481670906888162680584196178230503628068716441950949
8916402784273120031353652875289877862567447354927840677318519712072487344098119928604499876105419523
1373956949189989191876556229344730115045091462226103168618834097344609997156610133228831405954118698
3973608678369384512670266266590918439881807732794360864901796502843005576922341834764429846463091830
7275723297410022229911638949193869166402682161095387003213374949182998363445625100201876791107734199
8982406542117192442961159639187837594167906896813306451433188950986000602255947701445471051471124124
8484336829214745749720575068214150684678501124818809203316307200136273429717962200981466252531259013
3798038623481762989871070817615829869313314921416639943165627723116460023752736726677667987086578579
7830236117277818351059865801588376786510903900434642861824307368660843525509146180113489215970253073
1345369323345932633434286573386273784921786777977849042729418318134604348292381228571121858661612351
7337989610273076776142355839317816622471562095275865359123258606513093161223596102449595505257631378
5415587572218003004463096123010675460429586233582774784375746614062343087428887376655420063237888060
8631989480040604357707271032540165516719809796709244397686970277891575974508206254271409670848762533
3043290708236261620805834317734513801881283302993366020041817811306799871942628267417602953705694667
6010743381949863248322018120347951203883971813116798180480041145250934319940195212376997070020403473
2406184275123955659940176392676423875903522706234038414093987781979650528188804941226798796374509829
2987255988062388451466219669456774402794013003817992018259524822002996054583606843783653722042115186
5495276144874163510998224619086027469138960543563366461310280362835876324827709909151758836738659026
3469833549071585337411720085573472891918341188743445072117063997284882801647199419185485969964100640
7411283551674645401444064014769996679200163664907849204949729999203701072250276712361467457020832508
5786203978913246013088500640052780403783197363796495378941014322353383867757116808444859236033884177
5034886947463602630810775184952786726730076877146338146750740814039277084490525823622419436972062872
3658720856229364135609456618525515788779451753217328311183300030202561300521340548225287814907026520
5440373545426910161611341185559050988906020137614109481965847736796392112521375419675323000779270489
3409238065430509568275590321367288284256499163231600415098932399539296505895448646461690095681259701
2933138966840997303390729744599907618665109576531031106104368289656901620969453699613626647019156940
8033323541694057386738735231465391417715857531488577897250851792909910169470724853261427849940549334
3058964755928239926564583479938842145750742968146768744649711972156499745067240589160415089160491697
0745516543868362735182402123217384765017500956924684458533976433144403987971559593528051564089748125
7047884715263635621831312250733095244741473379412994928937246504471873360093422945901669688636733052
8722151883926683438705183322173579806860706093205544809105237955539422589009486006438315537851273821
9699254333814414178419800245490027144309168275657461668575324056608338450591198664472083873879654075
4497874824089314354427768560390125821906974331377915589874833096832220364826214637532467443257219325
3735425956321688681968456623145352577457405406900887212589323757269267807660429605225702623919447422
9182750052471961815220470664128935352703925044595167438714096420297977152569166792363551533312824086
8122085666451405605834956472406582298196815961996323161565850516941679845809803706388743206005082498
2879088284471424686126989425137754171119488405175107174441584153114258722355049122929009315302945400
1252926062522394758418678709106527099702611938642240709905768752269224344552855980436514951929936636
0636524787812055597948447738733157386435933019181691527123300142439165132639220658338166882600717005
9460570681095081902891690778005898550309398494143056099383244210656853427873351226289438932247375588
0095529123016235447370366826941824687645005145909872994968642761699131034625846780771420049329463495
4267280195055460982624792493147249023081291160699372476860084646890874325382990275414749482976830377
4199372534673576388659135081802866054097682406409048786086872846905780970841899439669912035763271629
8183447375694667990279960155640322703599773340846305188287804064860590348994350099009042881728213656
2244543138227751934870681977529470093118307377797864388134866337375506717466865840299561391687595163
8148710732575162371389530847397413210465125198987830559851375629099868628228214186979092186183758247
7624359612963557679935999936934408592348071769869957349194726691723831613659469751574888413284439681
4671847273719744879357852879547726224395778018791817246412295326838150979939296919653496539270225341
8260377147555923015002062793661603211014334765381682118777782892363824928395078163090541019968078819
6599025114406053158326966733250363984727128933120543136606406953088382089986870670943683648184878969
0764673023862695740597045358606957928324456815766130005846385401900094395353684780895776336253796523
7820756796130249683392901758138653877932553617428477840299921105889493405567416436638468697750184781
1839444336525079329981750624460353640851581050445608565668118348476690963250411915910185778621308437
0375778253371993950568270608368720255920096107484259695785002799244185251870094775729333995933499076
2573796010750259397593822826144847102862555499327453759526961092930411189297941237551683542757193673
6514115422368257727475698693980166635387898271241967204789582795142156360130421935293920161728194513
0711444593498910500078357202775578698708417758650476732444321615389586337183178052363104577036667976
9817943797751372549746991255216638059996525455419360357233898260568126176467797542779450476441166098
2832973679043639351741328825155889804551474944590642319432370630641411936662974790748128737394083284
2913969451233186914869606743291916409591019592632025299628197611384253264924748540717955006148011213
1963309733381733583507313303588011766870558206670073162064851742949807196815806110075763663155668179
8867667662981806971432222685171350105667670369369188242468994823428299097568967222651834347055097417
4195976295776513379484342672440028765751071277361281234011824451864987118511900268023620660925537819
5990171232232401952220370271615597853719682023122892223797160232801997625032033458423644758731654437
1199612163721865601407710993828763446264191123764366149873092499747847779830730610797297576502169776
4315038032227248049476011713075846328424181343680728329020299532724418468785014598773583912750973647
9023344560531033472369566796064821721452643071566985599262860471785037419495135404480386049800581348
0331896186784731792410641130542882206045545703462399347808187311204087994928431869910641686552149261
4531231783253320962518186939715705143181582332451403715983077334128673665133436729743874451580776248
8332762870033909012172610363645349459485975782670691972896161422548910350952459164841206860352903159
2421400424622285171578002623050220001230490565459980804438329363993061071276845276218827213552684893
7482560309725734239359041881081604932493295818851065897194460578664420343244668944218859930843009169
1514164397478549961324803846428232393751042656908296033137639788776335924436811564872260340070478649
5505539617149452362493152601086524782868042224415382751787492829862274260527578571918679985950597930
8352491593626969988121413269340766953822202945692532342274077693139016760771380343305198289191630235
1238881304565004457729729465185343376474903501651701465433251022023459059517209380633415221328658256
0015904004321317422594037838516233510525493306002477377116720950900933852100523276958876659251816569
7175352104674517670696569105465127985627784868398418070770887556648506376679874586510201116038731912
1126143819829890151732518870692245960148193122767296725734654580645493650155001153284486777121793572
8692517276380912171040501275955833675779498789506191997771297574643200496889810068611837684823691781
8928054045219935018646614556888891673782521226109539876603853518249396964141573474411786178864152187
2310728726818324266174080415618260832770829965049799051215767297618826741660629819618402059289921495
0312206879134805947011095817651142326991327603773468175374573342815663708943893273993369643235668266
8732464139632035094818062195320955001580567851453434840805453125631107205858205890026353091573367671
7201250162439835733969563931157528056463253080117072765336420863845049611806746981391709205170605180
6492090557249292205719608119623768274516420584600103231342031968653727643254034507136763227405490746
6295796072834575234227652980765772996039382235258886338751540189442236614051487377368191871254652241
5405283338036709315811863986807318354486657595424761671804533753551507284143823957942127454371661155
3536704826395776844150504731973490317617635358399969327109947107001685544248857454693282542472940866
6367431733711263035317370459792311926982579362304589031818587148975192530703366798574784205700976688
9751371707027040921225655610675353985610477702881428913336435405860941919428810988858611706766144952
1621766322496962560449474975284152680956233270513059522769466413667023345788017792725435789228028350
1771674153340181295757185220624956488625960241342854349445359997526435561960392392589534148436324133
2210480855642128380304168376633357409493890237676304106677561959230002896010317005074065957512847787
1461794181740799514399674478628742043156165431460153631641977372208677789390230055781454469072615352
4427504853234241083524047092443029212029099057510938541927161209092151527496660113715920637523480328
4309897427448101182751788022732499443796719418346610498104248244843355548543003324547523823825753877
8536250396934904820722802237860032107724242727355957759621670595497838557747683248176769869101996936
3764124908054104431258135562309403229995669410507869061560001668799471259677428825587266421236272771
3565489667319209259358276058955259449583905577751881825994307739763294373606272628694645372713954111
2763529510255310608863064434889524537804698808228199130012543570698057775838274869632065171062988937
8007269601604348150095922464466723718089944069302233407247100092030141634979668048628892544474704539
9806779592530453776900899174919209421357940673310691748358780473557630699169105058567448672284788195
5207651022032122114422511531155690262132015158094063153145482356620752891978753896071073113439725144
6863301951561400004159243550508846994979870220021654014363061263907055278823448015537418189345262220
8321010548621939009827567809666827984882618626030734065904671811486769852779206493767177802783209669
5841735916368644160360633818829211450682109163209140660219178347576786394979819192039130303782363544
0366852329792530304401282072217590937306513920702609468017126262860885494045694567006749197056309580
6433729851779889390295662390144586316599244433816941255298376494346005659811924248441449405962071321
6449057751576923920635773463356745250842575808551807372250074578891032927608366217430799701982166239
6368784000485410203494746501418379420966077237082321290470478615887034185693579996771486215404804695
4811224815715137042808526270121862674699916359816856408894733734758940978719075353512731556612952607
1537275678278036642085419722459622393183247728386085055697841075161667957040120297919579350867922927
0695813501332563153166070154095763822082051684399748732729553965958532985987911797902110713318155368
5582662145899183160733704894572221864142486412665825779350197782684268805844425849723735061349824699
6015375908375824333322026588931739469866674271743046763475349764550691147301750827205012232508882550
3782634226189081418110360232044483094917122073348832945196558930045450606186630066464264923682396019
1461235578204944100110411053520292483089413567596910929888137080832814722692866272761520718175205260
2364293079005160296017109669826614588795244671497270962312133608880028746971546134419514434347667783
2930394086124235564902368800329544881012516861962147429738421449344065429019424751594247732152478118
4534081072433775293642743525019042965658368990034893453680130529207756776266385588874578263062489301
7160824929027362119214757845842027575404193436428087327757634834088383087778995235185173536842583770
4493979337701560295930387002196518418354534911347404051951004651581481820521681180801097862520366245
1525352534451739134415034240926832206564016893505156584693553954080172185471910744296397835990948993
20410039863575946472558059877105808942471773922977396345497637789562340536844867686961011228671
Xyzzy is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Silly, picture thread Xyzzy Lounge 805 2020-10-06 05:04
Scenic picture thread MooMoo2 Lounge 91 2020-07-31 06:58
just a test of uploading a picture - please ignore mahbel Homework Help 1 2017-06-24 19:20
Silly picture thread Brian-E Forum Feedback 3 2014-08-30 16:39
The Man and the picture mfgoode Puzzles 3 2006-01-24 21:23

All times are UTC. The time now is 02:21.

Mon Oct 26 02:21:57 UTC 2020 up 45 days, 23:32, 0 users, load averages: 2.04, 1.85, 1.82

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.