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Trurl

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About Trurl

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    applied mathematics

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  1. 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”

  2. 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.)
  3. 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
  4. 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.
  5. 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.
  6. 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
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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?
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