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  1. Prime Products just one last time

    PNP = 85 (((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/ x^2))) == PNP^2 85 (7225 (-1 + x^2/170 + (52200625 x^2 + 14450 x^5 + x^8)/52200625))/x^2 == 7225 Solve[(7225 (-1 + x^2/170 + (52200625 x^2 + 14450 x^5 + x^8)/52200625))/x^2 == 7225, {x}] {{x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 1]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 2]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 3]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 4]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 5]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 6]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 7]}, {x -> Root[-104401250 + 614125 #1^2 + 28900 #1^5 + 2 #1^8 &, 8]}} N[%3] {{x -> -24.3484}, {x -> 4.97889}, {x -> -4.2072 - 2.87925 I}, {x -> -4.2072 + 2.87925 I}, {x -> 1.71775 - 5.00069 I}, {x -> 1.71775 + 5.00069 I}, {x -> 12.1742 - 21.0804 I}, {x -> 12.1742 + 21.0804 I}} f[x_] := (((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2))) == PNP^2 f'[x] (7225 (x/85 + (104401250 x + 72250 x^4 + 8 x^7)/52200625))/x^2 - ( 14450 (-1 + x^2/170 + (52200625 x^2 + 14450 x^5 + x^8)/52200625))/x^3 == 0 g[x_] := f'[x] 1 + (85 - f[1])/f'[1] False 313875685/208889212 N[313875685/208889212] 1.50259 Again the above equation has 5 as a solution knowing only N. I know this is not enough until tried with all values, but it seems that Mathematica has a solution for this instance. I want to show what I was trying to do at the bottom (end) of the equations. I was trying to use Newton's Method. I studied the equations from Wikipedia and felt that maybe applying the method would simplify my equations. I used an y of 85 (a y of N, instead of zero) and placed the slope (the derivative of my PNP equation) in order to solve a test value of x. This test value x is intended to be an estimate, however I tried to find a modified the equations to find x based on a given number (start point; 1) and the slope (derivative) of the original equation (from the first post of this thread). I know this didn't work, but I share just to walk through the idea. If there was a way to find a given value of an equation using the equation and its slope, it would solve my original equation. Below is the equation. 0 = f ' (xn) *(x - xn) + f(xn) 85 = f ' (xn) *(x - xn) + f(xn) xn = 1 ---- This is the start value. 85 = f ' (xn) (x - xn) + f (xn) 1 + [85 - f(xn) / f '(xn)] = x I am aware this doesn't work. However I thought the idea was so simplistic it could work. This is what I am proposing: The slope is known and any start number can be used, so finding the value of x where the y-coordinate equals N can be found without the complexity of the original equation. Obviously, it has been done before. But I am asking for help in trying to apply it to my equation. 20170916SFNnewtonMethod008b.nb
  2. Prime Products just one last time

    Yes, imatfaal is correct those patterns are true for all numbers. I intend to redeem the mistake. Early in my work I was just finding different ways to represent “y” in terms of “x”. It led to a lot of x = x. But I did have several equations that were distinct and significant. Below are some patterns that are redundant, but I encourage you to look because if I do find one that is distinct it is gold dust. I believe the equation at the start of this post to be distinct. I know it cannot be solved. But I think it is a pattern. Yes, my equation solved N knowing x, which wasn’t significant. But if there a way to solve the equation N would be the only number needed. So here we go again: PNP= 85 x=5 {(((((PNP^4)/x)+2*(PNP^2*x^2)+x^5)/PNP^3)* x^3) / PNP } 85 5 {2160900/83521} N[{2160900/83521}] {25.872535051065`} Sqrt[25.8725] 5.0865 PNP= 85 x=5 {((PNP^4+2*(PNP^2*x^2)+x^5)/PNP^3)} 85 5 {420520/4913} N[{420520/4913}] {85.5933} N[{2102600/4913}] {427.967} 427.966619173621`/85 5.0349 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------___ ___ ___ ___ ___ ___ ___ _ Other Patterns related to above work 125/5 = 25 25* 52200625 = 1305015625 --------------------------- 52200625/614125 =N ___________________________________ 52200625 / 125 = 420520 _______ 85^3 = 614125 614125 / 125 = 17^3 = 4913 ________ 83521/ 4913 = 17^4 / 17^3 = 17 _____________________ 2102600 / 420520 = 5 MaybeSIGSFN20170813V02.nb
  3. Prime Products just one last time

    You are correct. That paragraph is garbage. I am not sure what I meant at the time I wrote it. These calculations will always be a perfect square root. Thus finding the product of 2 Prime numbers is equivalent to this equation being used to find a perfect square. Yes other products will also have a perfect square, but it will be a decimal and not a whole number These calculations will always be a perfect square root. I mean the patterns I just showed are always a square root. Which there is no arguments about. It may seem this is of no use, but I am only showing a pattern; A series of patterns that give use a feel for what is happening in the factorization. Thus finding the product of 2 Prime numbers is equivalent to this equation being used to find a perfect square. In the succeeding patterns of the first write-up only 85/7 equals a whole number. I know this again does not seem to prove anything, but here I am only listing patterns. I will give a better explain my example. Testing to see if 3 and 28.3333 are Prime multiples of 85: 1/(85 * 3) = 1/(0.0039215) = 255 28.3333^2 = 802.778 255 - 802.778 = -547.778 -547.778/ 28.3333 = -19.3334 28.3333 / 19.3334= -1.46551 1/-1.46551 = -0.682355 -0.682355 * -547.778 = 373.779 Sqrt[373.779] = 19.3334 28.3333 / -547.778 = -0.51724 19.3334/-0.51724 = -373.791 Sqrt[373.791] =19.3337 This is true that 19.3337 is not a whole number. Obviously. I know that 5 * 17 = 85 and I will square 17 in part of the following example. Obviously if I know this it doesn’t help me solving knowing only 85. I am only trying to find out what is happening in the factorization. But remember that: 1/(85 * 3) = 1/(0.0039215) = 255 255/(85 / 3) = 255/(28.333333) = 9 Sqrt[9] = 3 But it is interesting that 9 + 19.3337 approximately = 28.3333 It must be tested for all numbers and different potential Prime factors but know: 17^2 = 289 425 - 289 = 136 136 / 17 = 8 17 / 8 = 2.125 1/2.125 = 0.470588 0.470588 * 136 = 64 Sqrt[64] = 8 8/0.125 = 64 Is unique among other factors. It is the correct factor. This pattern does not solve that, but shows something interesting is going on. We must test for more for more numbers, but the same is true for 85/11. I am not solving a pattern in Prime numbers. I only care what happens when factored. I know it doesn’t seem like much but it is how I visual the equations. For example the factors of 85 have to be less than 85. And when you choose the smaller factor the second largest factor is limited in value. I know it has been tried and there are already algorithms. But I just want to show that my idea is unique. And I realize it uses test values. But these patterns are important in understanding how I derived my equation. The one that is ugly and slower than division. But again, what patterns are going on in the calculation of that equation. That is why I shared this. To reiterate: 85 *11 =935 935/(85/11) = 121 Sqrt(121) = 11 85/11 = 7.72727 Abs[(7.72727^2 - 935] = 875.293471 875.293471/7.722727 = 113.27322731 Abs[113.27322731 -121] = 7.7267 The solution of 7.7227 is similar to what happen with 85/3 as 28.333. The square 9 for 3 and square 121 for 11 shows a pattern in the factoring. That is if I just didn’t redundantly cause the pattern. I hope it is understood what I tried to present.
  4. Prime Products just one last time

    You should read further. I am aware of the simple pattern that cancels each other out. I canceled many of equations looking for the right one. 1/(85*3) 1/0.0039215686 = 255 255/(85/3) = 9 I know these patterns don’t seem like much, but they were the start of my last equation. The one that you claim will give factors but is slower than division. I argue it gives a position (a distance) from the Prime product. But I am not working on that here I just want to show patterns. I know this isn’t the best written explanation. And I know I have trouble describing my ideas to others. But if you decide to read further down the line there should be a pattern. It has been 6 years since I wrote this. I have to study it myself, because as I stated in my previous post, I have lots of data. Start at the 3rd paragraph of equations. Where 17^2 = 289 for relevant content. Remember = sign means they are equal, but the line below is a pattern where I mixed the numbers together. The below line is not always equal to the top. It is its own operation. This is probably bad practice. But I do not know of a better way to write it down.
  5. Prime Products just one last time

    The multiple of 2 "unknown" Prime numbers: 85 = 5 * 17 1/(85 * 3) = 1/(0.0039215) = 255 255/(85 / 3) = 255/(28.333333) = 9 Sqrt[9] = 3 1/(85 * 5) = 1/(0.00235) = 425 425/(85 / 5) = 425/(17) = 25 Sqrt[25] = 5 17^2 = 289 425 - 289 = 136 136 / 17 = 8 17 / 8 = 2.125 1/2.125 = 0.470588 0.470588 * 136 = 64 Sqrt[64] = 8 17/136 = 0.125 8/0.125 = 64 Sqrt[64] = 8 The last 2 calculations are loops. But it shows one thing. These calculations will always be a perfect square root. Thus finding the product of 2 Prime numbers is equivalent to this equation being used to find a perfect square. Yes other products will also have a perfect square, but it will be a decimal and not a whole number. So the idea is to find perfect roots below the product of 2 Prime numbers. We can easily find square roots and we know that this square root is less than the square root of the product. So the numbers we are looking for square root is less than the square root of 85 in this example. 20110818 These are just some interesting relationships I found in between doing class work. I do not know of any equation that finds whole numbers faster than division.The benefit is to find where the mod equals zero.These relationships can be subtracted to each other and set to zero in an attempt to find some meaningful equation. 20110527--- 20110818 The multiple of two "unknown" Prime numbers. 3.79424E6 = 2459 * 1543 and two non-Prime mutilples 3.79424E6 = 2132 * 1779.66 1/(3.79424E6 * 1543) = 1 / 1.70808E-10 = 5.854551E9 5.854551E9 - (2459^2) = 5.85451E9 5.85451E9 / 2459 = 2.37839E6 The last step is actually to find the modulus of the two numbers. Testing to see if 3 and 28.3333 are Prime multiples of 85: 1/(85 * 3) = 1/(0.0039215) = 255 28.3333^2 = 802.778 255 - 802.778 = -547.778 -547.778/ 28.3333 = -19.3334 28.3333 / 19.3334= -1.46551 1/-1.46551 = -0.682355 -0.682355 * -547.778 = 373.779 Sqrt[373.779] = 19.3334 28.3333 / -547.778 = -0.51724 19.3334/-0.51724 = -373.791 Sqrt[373.791] =19.3337 17^2 = 289 425 - 289 = 136 136 / 17 = 8 17 / 8 = 2.125 1/2.125 = 0.470588 0.470588 * 136 = 64 Sqrt[64] = 8 8/0.125 = 64 The preceding is my work from 2011. It proves nothing, but is an attempt to find simple patterns in Prime factorization. The trouble is that I now have hundreds of pages of Prime product patterns. What is the best way to assemble and organize my work so that it doesn’t get lost. I am not claiming all the patterns work or even are useful, but seeing them in one place may cause someone to have a brainstorm that actually solves something. I have probably a thousand pages of math work. Some works; some impossible; some practical. I have used my website to share are record some of them. And as I have done at SFN, I have sought input and direction. So I have hundreds of files that I don’t think I have time to organize. What is the best format or way to share the files? I thought about sharing everything, but much is incomplete or needs me to explain what I am trying to do. Has anyone ran into the same problem where good ideas have been consumed by too much data created? I saw on 60 minutes that Watson could find better medical therapies than a team of 30 doctors could in a lifetime. Is there no way for humans to decipher data? I know this is no breakthrough. It is just testing for patterns. WholeNumbersIdentifier_unknown_relationship_web_revisted.nb
  6. Finding large Primes using Standing Wave Harmonics

    I have read some of your factor work. I don’t admit to understand it yet. But here are my thoughts intuitively with no work yet. I claim that my equation can tell if you are higher or lower than the actual factor. In your pattern of exponents, I would say the pattern is in the position of the factor. For example, more 1’s would mean the distance from the factor is closer or further away from a product. It would tell you if you have one factor that is small and one that is larger. Or they could both be larger. This is hard for me to explain, but say you had a product of (7229 * 7757) = 56,075,353 and a difference of exponents from (7229 *7) = 50,603 your pattern would distinguish between the distance of 7757 and 7, because 7757 would be out of range of the exponent and 7 would require a smaller exponent. I don’t know how to word this, but I think your pattern of exponents allows the distance between factors to be found. Thus, eliminating test values to a smaller range. I did not think it would be related to my equation, but now I think they are both eliminating options. The equation relies on testing values, but I think they both speed-up the process. I know the argument exists that it is more work than division. But I have 5 or more equations that show patterns in division. I am uncertain that combining them would improve the problem of complexity. However, I think anything that shows a pattern is significant. After all there is not an answer to the Prime factorization problem. I thought that if the Prime numbers for an exponential range were known, you could eliminate test values. If you know that numbers raised to a specific exponent will be larger than the given N for your test factors, it may not seem useful at first, but if it were programmed into a computer it should be faster than division. It isn’t perfect because you would have to test values, but with those test values would have a theme; an organized search. I hope this makes sense. And I hope I understood you. I will continue to read this and see if I can come up with any good brainstorms. Oh, and let me know if my equation is useful to you eliminating factors and I will work towards understanding your work. But if nothing else, this will be a different look at the same problem. I need a different look, I have put a lot of effort into this project, but results are difficult.
  7. Finding large Primes using Standing Wave Harmonics

    I admire your ethics and integrity. I do not want to necessary break RSA to steal information. I just wonder if it could be done. I have really read-up on cryptography, including a couple of Bruce Schneier’s books. It is more of a competition to see who can encipher and who can decipher. After all, if there is a hole in the Prime factorization problem we should know. But you don’t think my work is close, do you? Of course not. After all, it is a one-way function and should be impossible to solve. If you can solve it, it is no longer a one-way. So, I try to figure it out, not to destroy public key cryptography, because it should be impossible for me to do so. I am after the mathematical answer and not the breaking of technology. Ironically, finding Prime numbers and their patterns is also a threat to security. Not necessarily a bad one, but if your standing wave harmonics works then new cryptography must be built. I know that is not why you are looking for patterns in Prime numbers, but it must be considered. It goes back to the enciphers vs. deciphers. I understand where how you are thinking. A pattern in Prime numbers is beautiful, where destroying RSA isn’t. Agreed. I don’t think I can crack RSA. I have only found patterns. But if a pattern did work, it may cause disaster, where math is meant to create. But for a pattern in Prime numbers I have always imagined it as a logarithmic spiral. But all end this post there, because I might make you interested in factoring instead of the Prime sieve.
  8. Finding large Primes using Standing Wave Harmonics

    (((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) * ((PNP^2/x^2 ))) == PNP^2 You don’t have to use this clunky equation. I have about 5 to 10 equations that could be plugged into the wave distribution. I will compile a list. But basically, in my old posts the left or right side will work when separated from the equation. So 2*(85^2*x^2) + x^5 = 0, where 85 = N and x is the smaller factor. If anyone is interested I will compile a list. I wrote the above shortened equation without testing it, so I hope it works. Over the next few days I will compile a list.
  9. Prime Products just one last time

    All right thread viewers, I know you probably don’t see much in my work with Prime numbers. But I assure you it was a sincere effort. What I ask is you look at this link: And find if there is any math problem of value. It is a mixture of work I have done from 2003 till now. Not all of it is about Prime numbers or RSA. Some is based on topics from school. What I need to know is would any of this be of any value for a portfolio? Remember not all my topics are as impossible as Prime numbers. And I would teach those interested in math more traditional subjects. I would not teach them math of the impossible. Though, I would not teach it, I would still post on message boards to those who would want to read. But even though my posts are just ideas, I would teach the curriculum instead. But I still believe that working on the impossible is very important. But it is extra and not the testable program objects that are measured on tests. So you may be asking yourself why I try the impossible. Well it was an idea that started with the possible. If you read-through my math write-ups you will see the concepts were simple. But this Prime number thread you are reading now, has made a full circle of all my work. There are many relationships between my standard work and my impossible work. Keep that in mind as you review my math portfolio. And I still have 2 math write-ups that relate to this thread you are reading now. I am trying to keep it realistic and logical. But until then visit the above link.
  10. Finding large Primes using Standing Wave Harmonics

    I mean, the product whose factors are 2 Prime numbers. Know the product find the factors, instead of finding the Prime placement along a modulus in a wave. Start with the product and use the wave to see if there are any patterns in the factorization.
  11. Finding large Primes using Standing Wave Harmonics

    (((((x^2*PNP^4 + 2*PNP^2 * x^5) + x^8)/ PNP^4 ) - ((1 - x^2/(2*PNP)))) * ((PNP^2/x^2 ))) == PNP^2 TakeItSeriously, I have a question. You are looking for a pattern in Prime numbers, where to predict larger and larger values. But have you ever tried it to work backwards to find factors? That is the products of large Prime numbers. I have an equation which I can’t solve, but I argue that it gives a linear progression towards the smallest of the two products of the large Prime number. I know that it gives y, knowing x. That isn’t very useful. However, with several test values it gives a feeling of where x is. I was thinking this “Standing Wave Harmonics” will be solved by using the wave harmonics and a form of my equation. I have no scientific proof. I am just stating an idea that may need testing. I do know a little bit about matrices. They are basically vectors. And vectors are why I designed my statement that a logarithmic spiral could show a pattern in Prime numbers and why I designed the ever-complicated triangles. Let me know if such an idea is feasible. My equation is a one-to-one, increasing function. Knowing as little as I know, I think your pattern of waves applied to my equation may do something. I just don’t know what. It may do nothing for all I know. Let me know what you think. See my Product Primes post.
  12. Prime Products just one last time

    These triangles are starting to look like a polygon. If this interest you, you can view my homepage…at the bottom graphic, click on it for a previous attempt I made back in 2010. Ignore it for now. I just thought a construction exists that will solve for segment FE. Maybe similar triangles between FEF’ and CEC’??? I don’t know. Forget about triangle syx ‘s relationship to Prime products. Concentrate on solving triangle FEC. If it can be solved, a one-way function has just been solved.
  13. Finding large Primes using Standing Wave Harmonics

    I don’t claim to understand this. But if you are using waves that have a frequency of the factor (say 2…4...6…8 and 4…8…12) than the next bracket (numbers above 9; in ten digit brackets) you would only have to use the Prime numbers for the next wave. (11…13…17…19) and any new waves would have to be Prime numbers since those are the only new waves. So, you use the factors of the non-prime waves and just add those numbers that do not fit the waves (which are Prime numbers) to the new waves. This is just my understanding. But is this how the sieve works? And is this what the matrices were trying to predict, in this way? I like the idea of waves. If the wave was harmonic, always having the same frequency, the starting point of the wave would always be at a Prime number. The problem is finding where those waves start because you must know the Prime numbers that came before. I do like the graphical depiction using waves. But it is the same as using the modulus. There would have to be an anomaly in the wave that finds Prime numbers. I think it would be hard to find Prime numbers by eliminating those that were not Prime. Of course, I am not claiming any of this is right. I am trying to learn. But a wave theory is interesting. It reminds me of a 3 stage alternator were adding waves equals a line. But knowing that the waves frequency is the modulus, the Prime number would be between all the non-Prime wave’s frequencies. Like in your diagram of the waves, the Prime number will fall between the sum of wave frequencies. But I don’t know if that makes anything in finding the Prime numbers easier, because of the computation of all the known, non-Prime waves. There may not be a pattern in the placement of the numbers in the sieve, however do you think it is possible for a pattern in the waves? Again, this is just how I understood it.
  14. “Absolutely Wrong” means you failed the test. The test was to see if you agree that tests are bad. You got the wrong answer and failed. How do you like tests now? Seriously though, I agree that tests have many flaws. Kids who study the answers or cram does defeat the purpose of leaning the material. Without going into all the details, we are already aware of I will say simply, that testing is like money in that no one can find a better system. Captain Kirk wondered how they built ships in Picard’s 24 century where money had been eliminated. You can do things to improve the testing frequency, but eliminating it requires the invention and implementation of an entirely new system. I have taken a few education classes and they swear by: create measurable objectives that support the topic being taught; then evaluated (test) based on those objectives. fay’s uncle did give a topic of great debate. The question isn’t if testing is good or bad, but what are the solutions to fix it.
  15. Computer science is not a science!

    I don’t know that you guys are helping hipmatt, other than giving him the debate he needs to answer. First, which class is this for? Is it a computer science class? Second, he needs to define using academic sources the criteria that define science. And then he needs to explain his position and defend it in an essay. My approach would be to find sources that label histories, such as the stone age, atomic age, and find all you can about if modern computer science defines science. But remember computer science is not new. I’m not sure exactly where it starts, but computer science is probably as old as math. I’m not sure where to find a journal entry that tries to disprove that computer science is not a science. I would start with a search within your school’s library. But is the purpose of the essay to argue a position or is it to do research? Obviously, there really isn’t a correct answer? At least not that anyone can agree. My tip is to search for “Is computer science a science?” in an Education Journal. That is where you might find some peer reviewed “opinions”. I can’t imagine a computer scientist debating that he is not a scientist in a journal. Remember do what the assignment says. Use the criteria of a scientist, you have found by research to support your belief that it is a true science. This is an English and not a science class essay correct? I could be wrong, of course. But I have had to write so many papers for academic writing that I learned they care that your writing is clear, meets the requirements, and is structured academically. If you are like me, you approach this problem thinking good and creative content will get you the grade. I learned the hard way that this is not how academic educators think. I’m just sharing what I learned and don’t like to write. BTW, if your teacher is not a scientist, it is easy to confuse her. Education academics don’t like it when the laymen can’t understand. Write the paper so your “audience” understands it. Also there may be a deference between what a college defines as computer science and what the profession stands for.