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Trurl

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Everything posted by Trurl

  1. Trump did shut down businesses even if it meant hurting the economy.
  2. Keep it simple. Use Photoshop. Almost everyone has it and you can draw anything you want. Also use layers is simple and can display many different screens. I don't know how to view your screen on Skype, but it should be possible. You can share the Photoshop files and no one needs to download more software. You can export to gif or jpeg.
  3. This is a young person that ask why we need a fast computer. I was in graphics school in 1997 and the computers were state of art at the time, and storage was the main factor. If you made a graphic in Photoshop you had no media to back up your file. Thirty people printing at a time made the network crawl. It used to be you had to buy a computer every year because yours went out of date. Now I have 12 cores. I think the problem is programming so those cores work as one. But I am more interested in using less processing power to solve tasks. From what I know of programming it is more complex to programming cores. Does anyone know any good sites on C++ and Python that discuss this? Many cores made the Sega Saturn and PlayStation 3 hard to program. Games were delayed for the PS3. Xbox 360 games were smoother. So even with 7 cores of the Cell processors, if you cannot program it efficiently it does not get used. On the other hand, programmers complained the Nintendo Wii wasn’t powerful enough.
  4. Well I think this guess is relatively close to the smaller factor. Notice that I gave you a way to recreate the work. I also gave you a way to check y=(PNP^2/q) + q^2)/ PNP Does anyone know what the actual PNP is? I can approximate but when dealing with such a large number it is difficult for me to have a check without error. The next step is statistics. N - Nguess If you graph the N minus the guess N there is a Bell Curve (The normal distribution). This distribution also allows the use of calculus to make better math structured guesses.
  5. I agree with curious layman. If you are a believer or not, it has nothing to do with rather you a scientist or not. It could be that more Nobel winners are believers because they are trying to change the world. It is the Nobel Peace prize, after all.
  6. Can anyone identify if these factors are close?

    i realize that the numbers are huge. I am facing the same problems as you trying to see if this works.

    The goal is not to destroy RSA and those ciphers that rely on factoring. That would cripple SSL certificates. We probably don’t have any encryption the NSA can’t break.

    Instead finding patterns in factorization finds new patterns and series.

    I would like to find patterns in biological organisms, but I no little of genetics or cell biology.

    There are mathematicians and physicists looking for patterns in diseases. I am neither of theses, but finding pattern is the most basic math. If if you don’t understand the theories or notation you can still visualize the series. I am not saying it is easy to add to the field, put anyone can understand patterns.

    That is how I feel. Let’s find patterns in factoring.

    1. Show previous comments  1 more
    2. Trurl

      Trurl

      While it is only my speculation of the NSA. But I always picture them being very powerful. I never read all that stuff Snowden released. I listened to some os his book and he says stuff like the NSA nows you personality and how you think just on Internet habits. Most crypto algorithms are open source. I see intelligence agencies having the best of both worlds: if someone invents something they get it and if they invent something we don’t even know it exists.

    3. Sensei

      Sensei

      Quote

      The goal is not to destroy RSA and those ciphers that rely on factoring. That would cripple SSL certificates.

      You should not send something confidential through HTTPS/SSL. Properly (professionally) made websites hash passwords on client-side in JavaScript HTML Form validation code.. So even if SSL is compromised (e.g. SSL Strip) password is still encoded.

       

      Somebody bothering about security should archive the all data using 7zip with password. It is using AES 256. But it is not allowing to enter IV by user..

      Quote

      We probably don’t have any encryption the NSA can’t break.

      AES has been approved by NSA for encryption of non-classified data, later extended also to classified data. With enough power e.g. supercomputer cluster or botnet with gpu acceleration, or better custom made hardware cluster for 10 bln usd, if there is known IV (init vector), or simply leaved zero by incompetent programmer, not knowing what he or she is doing, or using wrong mode, it is possible to find out password (especially 128 bits long) in some reasonable amount of time. Therefor to decrease of chance of brute-force attack on transmissed data the key is to frequently change IV (randomize?) and transmit it together inside of already encoded packets (or alternative route). If somebody (gov) will intercept transmission in the middle, won't be able so easily use plain brute-force algorithm if IV can be anything having 128, 192 or 256 bits and changing. Ordinary hackers don't have ATM patience nor resources to brute-force pass through the all possible passwords even if they know IV.

       

      Example of what can happen if raw picture is encoded using silly insecure mode is on this website on the right.

      https://en.m.wikipedia.org/wiki/Block_cipher

       

    4. Trurl

      Trurl

      What if authentication through SSL, Sites could not prove they’re who they say.

      This post reminds me how much more in crypto I have to learn. But what if the NSA doesn’t have to brute force. Every cipher has public algorithms. What if we thought something was solid and it is just a facade that the math behind it is solid? Seems unlikely; but possible. The British claim to created RSA 7 years earlier. I have read open source ciphers make stronger schemes, but with factoring it may not have a definite pattern, but it doesn’t mean educated guesses can’t defeat it. Brute force may be impossible, but patterns exist in everything. I just think with the knowledge available to the NSA their researchers are ahead of civilian researchers. (Not that I have any knowledge of crypto research.)

      I admit I still need to learn about block chains and hashes. With RSA, p and q are in the enciphering and deciphering key. I am taking a given N and factoring it. But as you explained I need to find N from the enciphering and then break the message—where brute force is needed. But the only reason N is available is because it is the public key.

      The next step for me is to try and decipher messages with public keys and test to see if it is the true N.

      I have some names of ciphers that factoring can’t break. I am not familiar with them. You are right about brute force being useless. But one way functions are hard to make. As long as there is a public key brute force may not be needed.

  7. If you view my feed you most wondering about my factors project. Most likely you wonder why I’ve been at it so long. I keep chugging along because it is such an important problem. It has a high probably of failure but if it works it is gold dust.

    But the problem is more than plugging numbers. It is factoring, cryptography, geometry, calculus, statistics, and number theory. So even if my equation turns out to be wrong, I have learned a lot.

    Also you can help me by sending me large N’s.

    And remember RSA now stands for “Reveal the Secret Asap”

  8. Oh, and y=((PNP^2 / q) + q^2) / PNP And I invite you to look at my profile. (For things that don’t fit here but add to the conversation.)
  9. If you change q then PNP actual will not equal PNP estimate. This equation is PNP estimate: (Sqrt[((((q^2 * PNP^4 + 2* PNP^2 * q^5) + q^8) / PNP^4) * ((PNP^2/ q^2)))]) I subtract it by the actual PNP. N = N or 0 =0 q is imputed as a guess. Large numbers but usually less than 10 guess to get the right magnitude. If you change PNP to some other integer you get a different answer. You can experiment. Follow the fist set of code and substitute different n and q. (Sqrt[((((q^2 * PNP^4 + 2* PNP^2 * q^5) + q^8) / PNP^4) * ((PNP^2/ q^2)))]) It should give the location of the least factor of any PNP
  10. Yes if q is close PNP/q would also be close. I am only guessing at q. It comes close to the smallest factor of PNP. The remaining factor should also be close. But the error would be slightly greater. But I do have equation for the larger factor also. I put it in scientific notation so that it is easier to read. I like seeing the magnitude, like 409. I am doing semiPrimes but I don’t see a reason it can’t be used to factor any number. You can help by giving me large PNP’s to test. I only have 3 such numbers. Again this number needs verified. Some people own the factors. I have to find a method to verify. Finding the larger factor, even by division is a good place to start.
  11. 1.00111140657194927673100202970050001121410737599782781945816245736513\ 1278468842516733150612150020222444199271535713836705106165363816940972\ 7852961341531082700951250374290657534893907437882494339828790027283967\ 8323968773124658157519009514402613556863757843081318031549066464063464\ 8903637088626834871049426813651449824514934961323715586782698519267036\ 4136957297127727185659878862942307510915960740199425171606099*10^409 This is just to clear up the difficulty reading all the input. This is my best work. I believe it is a factor in many 2048 bit Primes. 2048 was worth $200,000. To bad the prize expired, but I still want to decipher this. So as I mentioned earlier in the post the moderators don't like me posting endless code. Here is my best work so far.ou It should be close to the integer that factors the 2048 bit number. But if someone could verify this I would appreciate the help. And I looked it up the product is a 2048 bit number. It has 617 digits. And if you can break a 2048 number RSA is compromised. But we must see if it works first.
  12. Well I found the reason I couldn't get accuracy was because you have to have the accuracy in all numbers you use. For example when I plugged it into the equation and say divide by q, q needed more "accuracy". It makes sense but makes it more difficult. But I will post my numbers here. Tell me if I am in reasonable estimate. It is probably guaranteed to fail, but I did put some effort and though into it. Here I used the full size. Also there is a normal distribution between PNP and estimated PNP. This normal distribution will help when guessing q. Yes, you are guessing q, but it is an educated guess. But if I did do a correct factorization this should equal the smaller semi-Prime. But there are no guarantees in math, especially when I wield the chalk. In[87]:= PNP = \ 5998490465869535958493457351726585769768780414997827819458162457365131\ 2784688425167331506121500202224441992715357138367051061653638169409727\ 8529613415310827009512503742906575348939074378824943398287900272839718\ 1012226608631723752258738079635407385665857943917136911564807480973854\ 0477603441448614459671016259991520028750578991648135327261214372672798\ 0903767703277168633339347967002362666965628644859661675221629352149974\ 9737800846524363691459902238665732702744582185179531226365443974338304\ 5939787842818642200160191894955133225326542363885702300787221019449943\ 58570309218509180305727137122851736117179378654706701977 q = 100111140657194927673100202970050001121410737599782781945816245736\ 5131278468842516733150612150020222444199271535713836705106165363816940\ 9727852961341531082700951250374290657534893907437882494339828790027283\ 9718101222660863172375225873807963540738566585794391713691156480748097\ 3854047760344144861445967101625999152002875057899164813532726121437267\ 2798090376770327716863333305727137122851736117179378654706701977 (Sqrt[((((q^2 * PNP^4 + 2* PNP^2 * q^5) + q^8) / PNP^4) * ((PNP^2/ q^2)))]) Out[87]= 5998490465869535958493457351726585769768780414997827819458162\ 4573651312784688425167331506121500202224441992715357138367051061653638\ 1694097278529613415310827009512503742906575348939074378824943398287900\ 2728397181012226608631723752258738079635407385665857943917136911564807\ 4809738540477603441448614459671016259991520028750578991648135327261214\ 3726727980903767703277168633339347967002362666965628644859661675221629\ 3521499749737800846524363691459902238665732702744582185179531226365443\ 9743383045939787842818642200160191894955133225326542363885702300787221\ 01944994358570309218509180305727137122851736117179378654706701977 Out[88]= 1001111406571949276731002029700500011214107375997827819458162\ 4573651312784688425167331506121500202224441992715357138367051061653638\ 1694097278529613415310827009512503742906575348939074378824943398287900\ 2728397181012226608631723752258738079635407385665857943917136911564807\ 4809738540477603441448614459671016259991520028750578991648135327261214\ 372672798090376770327716863333305727137122851736117179378654706701977 Out[89]= 3598289120705448492680059328834150322334448001622207912714128\ 6270306210690982540842543166403185241528795593766557486803136707938239\ 9271568942784642138646253353005635251855229982611082096617495327278988\ 6034138314595363712227903179098321332099042432094688889127255335934193\ 9910144822398803499036502791144788509725289029463011569872361246547341\ 6704558693865441793928494373571600592379630273961383590475105039969803\ 4486006253937796053837292199526847062983929041955904851574667653698032\ 3857793905098071574856310703189698344331355376605289838666116963502002\ 6997060484687691461523482749370524184741214446654994931729474157718575\ 2841702466111288399698046811183489665378322814876150691592558659206780\ 2286418935629292572033313994010480687164705289161159744459388883459593\ 5417694325251091407974625486305114294619946100659923237342349281588128\ 5015922425899569331395553047909343109656577179687855701640487791877470\ 2183218224730158957774351157867826711168016592832118240706695248547427\ 3761140291569496246525045715862623693727981640129087695758751448931583\ 9404145850115356336230295181816945324724356322936413641186755171066366\ 3522872281703641670265347320445417438356191517766072467035543617922477\ 292918483946522593224083703496041911554568355770362/\ 5998490465869535958493457351726585769768780414997827819458162457365131\ 2784688425167331506121500202224441992715357138367051061653638169409727\ 8529613415310827009512503742906575348939074378824943398287900272839718\ 1012226608631723752258738079635407385665857943917136911564807480973854\ 0477603441448614459671016259991520028750578991648135327261214372672798\ 0903767703277168633339347967002362666965628644859661675221629352149974\ 9737800846524363691459902238665732702744582185179531226365443974338304\ 5939787842818642200160191894955133225326542363885702300787221019449943\ 58570309218509180305727137122851736117179378654706701977 In[90]:= PNP - 3598289120705448492680059328834150322334448001622207912714128627\ 0306210690982540842543166403185241528795593766557486803136707938239927\ 1568942784642138646253353005635251855229982611082096617495327278988603\ 4138314595363712227903179098321332099042432094688889127255335934193991\ 0144822398803499036502791144788509725289029463011569872361246547341670\ 4558693865441793928494373571600592379630273961383590475105039969803448\ 6006253937796053837292199526847062983929041955904851574667653698032385\ 7793905098071574856310703189698344331355376605289838666116963502002699\ 7060484687691461523482749370524184741214446654994931729474157718575284\ 1702466111288399698046811183489665378322814876150691592558659206780228\ 6418935629292572033313994010480687164705289161159744459388883459593541\ 7694325251091407974625486305114294619946100659923237342349281588128501\ 5922425899569331395553047909343109656577179687855701640487791877470218\ 3218224730158957774351157867826711168016592832118240706695248547427376\ 1140291569496246525045715862623693727981640129087695758751448931583940\ 4145850115356336230295181816945324724356322936413641186755171066366352\ 2872281703641670265347320445417438356191517766072467035543617922477292\ 918483946522593224083703496041911554568355770362/ 59984904658695359584934573517265857697687804149978278194581624573651\ 3127846884251673315061215002022244419927153571383670510616536381694097\ 2785296134153108270095125037429065753489390743788249433982879002728397\ 1810122266086317237522587380796354073856658579439171369115648074809738\ 5404776034414486144596710162599915200287505789916481353272612143726727\ 9809037677032771686333393479670023626669656286448596616752216293521499\ 7497378008465243636914599022386657327027445821851795312263654439743383\ 0459397878428186422001601918949551332253265423638857023007872210194499\ 4358570309218509180305727137122851736117179378654706701977 Out[90]= -(\ 1003337926762389049221126796215583044111287392509572407957361630075276\ 9505131574604802375389492124492898548849744921866438826479970845253166\ 5286371164639751196966576858129600921807606026358615662532610138182538\ 3636765498759821676246069237032957534374432336610334560127204527283356\ 3999143594559687482446004256128329553814501088092018965233439791910082\ 2846991619424657099049350300585147978932265245231395879838950171324512\ 2970817464138978364753024470618424771102246294259091573015051471283229\ 1081100169373970495499690724467160987209063036567035108939022149134886\ 2517355182826636423935614329522097000601647962594541064070461627390134\ 7536657230472436382754096021417129062587067688590412252385403913508714\ 1961325083408245209320940098986654344561959190907809042686958196441030\ 3899437797648943140246355017712110654807887087624921809884308040202223\ 9996383269290296202903487456758097609903645061411424222739152682711747\ 0322353005743890894510415982298620570596253483316856775695754866581314\ 3664508949852483173726698633100818473785829707870858896643911724929114\ 4859482370915211019498575494065439836529883870306766859074115080141713\ 8666208933121978732291153355129507645934297155764596339013578313268902\ 46560926762406703208585328968060061833/ 5998490465869535958493457351726585769768780414997827819458162457365\ 1312784688425167331506121500202224441992715357138367051061653638169409\ 7278529613415310827009512503742906575348939074378824943398287900272839\ 7181012226608631723752258738079635407385665857943917136911564807480973\ 8540477603441448614459671016259991520028750578991648135327261214372672\ 7980903767703277168633339347967002362666965628644859661675221629352149\ 9749737800846524363691459902238665732702744582185179531226365443974338\ 3045939787842818642200160191894955133225326542363885702300787221019449\ 94358570309218509180305727137122851736117179378654706701977) In[91]:= q - (10033379267623890492211267962155830441112873925095724079573616300\ 7527695051315746048023753894921244928985488497449218664388264799708452\ 5316652863711646397511969665768581296009218076060263586156625326101381\ 8253836367654987598216762460692370329575343744323366103345601272045272\ 8335639991435945596874824460042561283295538145010880920189652334397919\ 1008228469916194246570990493503005851479789322652452313958798389501713\ 2451229708174641389783647530244706184247711022462942590915730150514712\ 8322910811001693739704954996907244671609872090630365670351089390221491\ 3488625173551828266364239356143295220970006016479625945410640704616273\ 9013475366572304724363827540960214171290625870676885904122523854039135\ 0871419613250834082452093209400989866543445619591909078090426869581964\ 4103038994377976489431402463550177121106548078870876249218098843080402\ 0222399963832692902962029034874567580976099036450614114242227391526827\ 1174703223530057438908945104159822986205705962534833168567756957548665\ 8131436645089498524831737266986331008184737858297078708588966439117249\ 2911448594823709152110194985754940654398365298838703067668590741150801\ 4171386662089331219787322911533551295076459342971557645963390135783132\ 6890246560926762406703208585328968060061833/ 599849046586953595849345735172658576976878041499782781945816245736\ 5131278468842516733150612150020222444199271535713836705106165363816940\ 9727852961341531082700951250374290657534893907437882494339828790027283\ 9718101222660863172375225873807963540738566585794391713691156480748097\ 3854047760344144861445967101625999152002875057899164813532726121437267\ 2798090376770327716863333934796700236266696562864485966167522162935214\ 9974973780084652436369145990223866573270274458218517953122636544397433\ 8304593978784281864220016019189495513322532654236388570230078722101944\ 994358570309218509180305727137122851736117179378654706701977) / q Out[91]= 6005157227595078439406835238794066464166217361556872908440991\ 1282976544749217352966095305064260976131204390106416093998394042208854\ 7593647838596486806269285487124538411876902031290465184358522934882710\ 7468932015125430085020735266385041418658401844011223865199560944341434\ 4382977176112915945427311858818259246049722738902468149157934513552061\ 9997688297974236046666408569893388019019418263378453571233264289205298\ 0480472873653140396089108178522939945009442689406711806507044965048418\ 8748542472073681797599573830861480964578658197776249730088320427676273\ 6418233713375287621166773563131993803042568857955930966082301794497535\ 4422340480161776806362976983653377730194820252303936196500528833754719\ 9077913968987780900871348721284098276417837541324502971810887802119298\ 3741091413474024436422904784647114333872970673475514338028366026036503\ 6450734925328262248208337288071391792959821279837279132465988631047083\ 9237550307052196288077036452576036598708270768314556635456479313448765\ 326486828739519000000000000000000000000000000000000000/\ 5998490465869535958493457351726585769768780414997827819458162457365131\ 2784688425167331506121500202224441992715357138367051061653638169409727\ 8529613415310827009512503742906575348939074378824943398287900272839718\ 1012226608631723752258738079635407385665857943917136911564807480973854\ 0477603441448614459671016259991520028750578991648135327261214372672798\ 0903767703277168633339347967002362666965628644859661675221629352149974\ 9737800846524363691459902238665732702744582185179531226365443974338304\ 5939787842818642200160191894955133225326542363885702300787221019449943\ 58570309218509180305727137122851736117179378654706701977 In[92]:= N[%91] Out[92]= 1.001111406571949*10^409 smallest factor
  13. I think it is me calling it the wrong thing. I still confuse how many bits a key is long. But I have the number I used here in this post. If I can get the digits of accuracy I believe I can factor this number. I know I can factor smaller numbers within a margin of error. But to prove I can factor I have to break this number. That is why when I said "the right magnitude" I mean the factor will occur at 410 digits. Obviously that is a lot still to use recursion to divide. But if I can maintain the entire 410 digit number I could factor within a smaller margin of error. You see the only way to prove that I can factor is to factor a large number. But large semi-Primes are hard to find. And yes the nomenclature of this math confuses me. But I hope to clear it up in this post. 5998490465869535958493457351726585769768780414997827819458162457365131\ 2784688425167331506121500202224441992715357138367051061653638169409727\ 8529613415310827009512503742906575348939074378824943398287900272839718\ 1012226608631723752258738079635407385665857943917136911564807480973854\ 0477603441448614459671016259991520028750578991648135327261214372672798\ 0903767703277168633339347967002362666965628644859661675221629352149974\ 9737800846524363691459902238665732702744582185179531226365443974338304\ 5939787842818642200160191894955133225326542363885702300787221019449943\ 58570309218509180305727137122851736117179378654706701977 This is the semi-Prime I used. You are right that it is shortening my value in Mathematica and making it displayed as a float point. But the thing is Mathematica does have the precision. I tried to get to use the accuracy, but even though Mathematica can have the accuracy, it again comes out in scientific notation. But did I make the magnitude? I am saying that 1.165633406571949 is the first 16 digits or the smallest factor that has 410 digits. So if anyone knows anything about Mathematica and how to keep the precision let me know.
  14. First I am surprised no on replied to this topic. Secondly I’m not a biologist. CMU has sensors of the local air pollution. The hospitals have the cancer demographics. But the problem is the average user only has access to the local news. The only way that I know to get data would be to survey the local families who are in the polluted air area. The fact is they know who the polluters are, but it would impact industry. So instead of closing a chemical plant they place emissions on automobiles. I don’t mean to sound political, but conservation biology often is. If those biometrics you are looking to compare were known, people could judge for themselves the condition of the environment.
  15. I know the moderators don’t like it when I post blocks of numbers. However, I am only asking if this number is the correct factor. I know I should know if I could actually factor. But to prove my method I tried to factor a 2048 bit number. This is what I got in about 15 minutes work. 1.165633406571949X10^409 Is the smallest factor of 5.998490465869536X10^615 Need more accuracy Let me know if I have successfully factored So so I need more digits accuracy than just 15 digits. But this gives the first 16 digits and the magnitude of 1.1*10^409. So it does eliminate possibilities. Not perfect, but let me know if it is close.
  16. Thanks for the links and programming advice 😊 Seems like it is pretty involved to do this kind of thing. I will use it to strengthen my programming. I was taught that that something written as say: 28/7 is in exact form. It is when you divide it is an approximation in decimal form. I read the article and they prove that the fractions are infinite. Here is what I was trying to do is invert the quotient and factor both the numerator and denominator. Divide and reduce those factors; then decide if there is any common modulus where the factors will reach a whole number. I guess you could say the fraction will terminate where the factors multiplied together will equal. (If they don’t terminate at a smaller modulus). I know you are thinking how do we know by division that this modulus will be reached. But it would simply be the modulus of the numerator by the denominator would tell how many iterations, until the infinite fraction terminates. We know the numerator and denominator will terminate at their original product. However there is no guarantee that the inverse quotient of those factors will terminate. I know this is flawed. But in the article they were testing fractions for accuracy. They prove the accuracy. But I am arguing that with infinite iterations the decimal may terminate. Yes, I know they went to Oxford and I went to Point Park, but this hypotenuse is why I was interested in this process in the first place. Hope this makes sense.
  17. If you know your exact position and magnitude of explosion (how long the sound took to reach you) the direction you were looking at the explosion, you may be able to determine the location based on arc length. You are at the tangent of that arc length. But the arc length is unique to you who measured it. Different magnitudes would have different arc lengths. I need someone to verify this. But I believe if you have your exact position you may be able to tell. It would be like finding the trajectory of someone shooting at you. The shot is a straight line and the angle. Reverse those and the arc lengths along the tangent to you is where the shooter is. The distance from you to the shooter would depend of the magnitude of the bullet. But to keep the same tangent the shooter would have to move along the same angle. If he shot with greater magnitude and a different field of vision it would be an entirely different arc. I believe what you are trying to say and a question I will asks is: With different positions having different arcs, do you have enough information to determine the location (knowing your current location) to solve the shortest distance you are from that arc? If you used that magnitude to measure from you to the original explosion? I hope this makes sense. Correct me if am wrong. But it seems you are asking can you find the distance without enough known.
  18. Does anyone know of any research or math records on determining when a decimal number will terminate based on the inverse of its factors? Yes I know that I would be working with whole numbers not integers. But for integers what if you took the factors of a quotient, say circumference divided by diameter and factored the numerator and denominator. The equation would be = to itself, but if you multiplied the factors together you already know that those factors terminate at the product. Someone has probably done a similar technique. But factoring large numbers is recursive and then you add to the process recursion again to do the multiplication and you get a problem you can’t solve. Also can someone explain the process that was used when they solved Pi to a trillion digits and don’t know where it stops. The stopping point is what I would describe by the multiplication of the factors. The factors multiplied together still equal the original number, but the product determines where the factors stop. Hope this makes sense.
  19. Would such sets be more tangible if related to computers? Like pointers which point to a memory address but are used to store a value they represent but are not equal to. I have had an idea of a computer algorithm to sort. Test a value s, to see if an element of array R. If s is not an element then set s equal to R. s is not an element of R but the equivalent of R. I hope I made sense. But I think there is model that helps picture the paradox.
  20. In[118]:= PNP = \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211 x = PNP * (1/ 833333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3) Sqrt[((((x^2 * PNP^4 + 2* PNP^2 * x^5) + x^8) / PNP^4) * ((PNP^2/ x^2)))] Out[118]= \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211 Out[119]= \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211/\ 8333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333 Out[120]= \ 1119462642967601379625749889949236065777407216363091843656817758630897\ 2822004013012808616251428523303469194983368339224288931527755260370593\ 4564726982165021366914927214391866070447793539124105460668568853618924\ 3132905693874616958336079958862242579650280812660512453816275628067977\ 7721150419713278365400937039926619418164741229089532498330068239309776\ 1690074453198227284210005164670550843915175125291348603192500942129571\ 2160296397474642360130036975254240806723286365854612676445799004846266\ 7602028680911873106587947193189889293999449715734241944639662748710845\ 3864217222758522411029165882690689971923777751749568939373903823332879\ 0347862820497821662686301328739580127103593058742239980461079578843089\ 8938404770001288892056326897984920834525603021493609403571623845097415\ 9269047818150038841906826639724779147047347019045703317553593717846683\ 7809250765440348545752291612966122145077943669090956833677756556314535\ 3415742755622794040068289994068630691327156047081726660842339291269766\ 7917971187981886248629293392246074136458310437500753586451933193176668\ 2313587611783431933780044950953903564442478335965847599970260746987255\ 0731160508492599759339823308128315559840203913178785278415738419343860\ 320599550946803281571941063514234186096009901328/\ 5787037037037037037037037037037037037037037037037037037037037037037037\ 0370370370370370370370370370370370370370370370370370370370370370370370\ 3703703703703703703703703703703703703703703703703703703703703703703009\ 2592592592592592592592592592592592592592592592592592592592592592592592\ 5925925925925925925925925925925925925925925925925925925925925925925925\ 9259259259259259259259259259259259259259259259259259259259259259537037\ 0370370370370370370370370370370370370370370370370370370370370370370370\ 3703703703703703703703703703703703703703703703703703703703703703703703\ 7037037037037037037037037037037037037037037037037037037037037 In[121]:= N[%120] Out[121]= 1.934431447048015*10^616 Hopefully the code is readable. I need to use such operations in the guessing game. It is still trillions of digits off. But calculus can be used. I will need help with the calculus. I will also need advice on how to approach the programming to get large numbers into usable figures. But I hope you agree this definitely eliminates potential values. And is the large number a 1024 bit number?
  21. I am using Visual Studio 2017. All of my skills in C++ are just out of school and learning how to make useful programs. I have seen how to import libraries (mainly C++ libraries). I know classes, but again I have the theory of overriding but not much experience. I am attempting to learn the Flint library. This is a library I have a book on, but I am not experienced to use it. I figured using the library is separate from understanding it, but I have found no clear-cut program that will let me plug and play large numbers. Obviously, this isn’t very easy, or I would have found a program that will let me plug and chug my 128-bit key into a mathematical equation. This is a learning process. I want to do this to show my math project works. I have the 128bit numbers if I could factor them it would be gold dust. Is there no ready-made program that will do this? Cheap is important. I don’t want to spend several hundred dollars. Is there something in Linux? If something like this isn’t ready made it should be. Obviously, someone before has faced this problem. There is a worthy project here for someone with programming skills. With limited expertise what are my options? I need to be able to complete the equation in the previous posts. It has N^6th power and then adding and diving it. So, I would take a 128-bit key and multiply it by itself 6 times creating a large monster. But it still needs only the 4 arithmetic operations of addition, subtraction, multiplication, and division. No recursion. I also only need to test 2 to 8 values in the equation. I need one below the factor and one above the factor. It will be a math guessing game for the factor.
  22. Ok Sensei, How do I put a very large number into this program? I am not sure why a large number would cause a memory leak. I know that computers can handle many digits. But programs like Mathematica are max at x^100 power. If I am only using the 4 arithmetic operators: addition, subtraction, multiplication, and division, why wouldn’t the computer just take more time. Yes, I have researched it myself. I will not be using recursion to factor. That is where computers crash. But it is possible. People have factored Pi to a billion digits. I am only using a workstation. I have looked at libraries that handle large number digit operations. I believe C++ console cannot handle larger than double, because of the way it manages variables. You can’t put in a large number and expect it to go through many functions. But if I could limit it to just arithmetic operations. So after reading that, my question is: How do I approach working with a 128 bit number? I did not learn this in school. And it appears it is a continuing computer puzzle. Oh and, Sensei and Sensei only, view my profile for the latest updates.
  23. Obviously Tomlin is a great coach and the other 48 are knowledgeable professionals. I'm not saying that I know the game more or could outcoach them. I'm saying apply science and math. There is something simple everyone is overlooking. Well Game Theory explained the Cold War and I saw an example where a goalie uses it to block left instead of right. But even though this is also strategy, Game Theory still applies. If Game Theory couldn't help make sense of complex decisions it wouldn't be useful. I have many other ideas to measure but I do not have access to game footage. So if anyone has access to any such game footage
  24. Thanks for the input, but I'm not far in left field here. But you are right I have to put it into something calculable. How bout this. I just heard you have to put pressure on Brady (the Patriot's quarterback), but he releases the ball too fast. So the game theory "decision" is to determine when Brady is throwing fast and when he needs more time for his receivers to get down field. The decision to make is stopping the small gains. The Steelers usually take away the deep allowing the short, but this doesn't work. The Pats march up the field with short passes. But the only way to stop such an offense is to solve when the Pats are short or long plays. My solution (recommendation (not mathematically proven)) is to make the receivers go deep. I say this because Brady is relying on his receivers to get open. The receiver goes short when the defender goes deep and will go deep if the defender tries to stop the short pass. So rush Brady if receivers go deep and don't rush Brady when you give up the short. This strategy correlates with Brady decision and time to release, and how he is allowing his receivers to dictate the march down the field. I know this sounds simplistic but I think we could test it scientifically. From my understanding game theory is simply decision making. I know not all football is logic, but the strategy is game theory even if it is too complex for math. But you guys insisted on a concrete example. Let me know if this is a more fundamental approach. I chose this example for a clear choice of when to rush Brady. Obviously the offense has the advantage. A few recivers going different routes and going deep or should would complicate the math. But I include this example if the Pats go undefeated this season this forum may be interested in how they are doing it once again.
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