Trurl 9 Posted April 30 Ok, so 40,000 people have seen this post. Does no one agree the equations show a pattern in factoring. I’m serious in my approach to this problem. I am not trying to deceive anyone. As my instructor in college would say this is a 5 second problem. Plug in N and x can only be a Prime factor. I know it isn’t difficult solving knowing both x and N. But these equations show where x must be knowing only N. Many have seen it but does anyone believe me? You see no one believes me that an amateur found a pattern to Prime numbers. And they would be correct. These equations and patterns are based on patterns in factoring. So if N was 10 an x of 2 would prove the equations true. So has anyone actually tried what I proposed? Or, did it just sound impossible and not worth the effort? I ask because I must not be explaining it correctly. Does anyone have any questions? This was the first time I wrote so much about a set of math problems. I have learned it can get out of control; not knowing how to describe something that isn’t completely finished. So let me know good or bad what you think. Like in show business no comments is worse than criticism. My question is, “Does no one see it?” A pattern in Primes may be impossible, but a pattern in factoring is possible. And is important to reverse public key cryptography. 0 Share this post Link to post Share on other sites

Trurl 9 Posted June 6 http://m.wolframalpha.com/input/?i=Sqrt[((((6911^2*7823^4%2B2*7823^2%2B6911^5)%2B6911^8)%2F7823^4*(7823%2F6911^2)))] Compare to http://m.wolframalpha.com/input/?i=Sqrt[((((6911^2*(6911*7823)^4%2B2*(6911*7823)^2%2B6911^5)%2B6911^8)%2F(6911*7823)^4*(6911*7823)^2%2F6911^2)))] Compare these 2 Wolfram Alpha links. There is a pattern here. Easy knowing both x and n. But the pattern is there. There is more to the patterns I am working on. I am compiling a Kindle book. If you believe there is a pattern post here or check my profile. 0 Share this post Link to post Share on other sites

Trurl 9 Posted June 18 Ok so no response means that no one sees my pattern. I know my equations are cumbersome, but there is a pattern. In fact I have about 3 distinct equations that show patterns when solved. I know it isn’t a perfect solution where x is found knowing only n. You have to use test values of x to determine where n’s least common multiple is. There is a pattern and I am trying to show that pattern of the least common multiple. I will post again a simplified explanation. My goal was to show the pattern before just plugging a chugging an answer. I will show this pattern, but it is labor intensive to organize all 4 equations. I just wish I was getting more feedback. Over 5 years ago I posted to the Wolfram community. This problem is not designed for their boards. But I did receive some good feedback that knowing n and x the equation checked. However that is not useful. So as I refined my idea where the equation would show a pattern knowing only n. The only problem was it was such a complex nth degree polynomial, I could not solve it. I could only use it in a computer program to compare test values of x. I mean, I led me to work what was known about solving polynomials and if there was anyway to solve it graphically. But I still feel my equations though rugged, showed important patterns. My equations had a range of error, but I now know this was due to the limitations of the calculator. But will my average coding skills I do not know how to program for over 100 digit numbers. But in my future attempts to show my work, I will show my patterns and where you can learn more about them. But until then don’t just look at this equation of finding the least common multiple. Look at the equations with the factors known and see those factors as forming a pattern as they are multiplied together to form n. A pattern in Prime numbers sounds impossible. But that is not what my equation does. It takes n and finds it factors according to an equation that will solve for the least common multiple. I remember a previous comment that solving a Prime pattern was not serious. I argue that it may be impossible, put finding an equation describing the least common multiple is a serious endeavor. 0 Share this post Link to post Share on other sites

Trurl 9 Posted July 7 (x^2 * (N^2 + 2 * x^3)) / N^2 x^2 = ((N^4*x^2*N^2*x^5) +x^8) / N^4 ((N^4*x^2 + 2*N^2) * x^5) / (N^4*x^2) (((N^4/x) + 2*N^2*x^2 + x^5)/N^3) / N) * x^3 = x^2 Where y = ((N^4/x) + 2*N^2*x^2 + x^5)/N^3) Each of these 4 equations is separate. I just wanted to post and show just how fun plugging and chugging can be. It doesn’t mean every equation is a useful solution. But plugging and chugging is fun when working with series. It is a place where computers and automation of equations does prove useful. I recently read a journal entry where it described brute force as a way to prove or disprove. I am not worried about that debate, but I am interested in using computers to look for patterns. I hope I typed these equations correctly. It is late so if you get any typos let me know the equations can be extremely hard not to create mass confusion. But I challenge you to test these equations and try your own creations. There are infinitely many, but I want one that is useful to describe the patterns of factorization. I don’t care if the equation simplifies to zero equals zero. I would prefer it didn’t but the quest for the useful equation begins. Oh, N is the known product of 2 numbers x and y, where x is the smaller factor 0 Share this post Link to post Share on other sites

Trurl 9 Posted July 9 See attached PDF. Here is a bunch of patterns when trying to substitute and find x knowing only N. Again, a lot of zero equals zero; and a bunch of high degree hard to simplify polynomials. But if you look at the fraction Mathematica has created (while knowing both x and N) you see there is a simplification of the polynomial. No guarantees, but it may just be possible to simplify the polynomial equation to make it way more useful. For example, the equations and fractions are of the form: (N^4 * x) / x^5 = y y^4= N^4 / x^4 So these fractions are: (Something Simplified) / (x^5y) The right combination might just simplify a large, cumbersome polynomial into something more useful. Or not. You be the judge. Download the PDF and test for yourself. 20190204VeryImportantPatterns20190330.pdf 0 Share this post Link to post Share on other sites

Trurl 9 Posted July 10 Reduced this polynomial: {(((((N^4 / x) + 2 * (N^2 * x^2) + x^5) / n^3) * x^3) / N} to ((N^4 / x^5 + 2 * N^2 / x^2 + x) * x^3) / (N4 / x^4) Sqrt{((N^4 / x^5 + 2 * N^2 / x^2 + x) * x^3) / (N4 / x^4)} =x Need some math help. I reduced the polynomial. However, the result does not seem any easier to solve. The black is the original the red is reduced. N is known. And x is to be solved. Can anyone solve this simplified polynomial? 0 Share this post Link to post Share on other sites

Trurl 9 Posted Monday at 06:37 PM I hope someone responds. I am serious. And to show that I am serious I offer the equation as far as I can simplify. [ x^4 + (2*x)/N^2 + x^10/N^4 ] ^(1/4) = x The brackets are the 4^{th} root of We know N = 85, so solving for x should equal 5. It works when you know both N and x, but is this enough to solve for N? This is my best attempt so far. So if you are curious please respond with your own polynomial simplifications. Respond if you fill that I am serious and on the right path of solving the least common multiple. 0 Share this post Link to post Share on other sites

Trurl 9 Posted Thursday at 02:08 AM [ x^4 + (2*x)/N^2 + x^10/N^4 ] ^(1/4) = x The brackets are the 4^{th} root of N = x * y , the product of 2 Prime numbers x is the smaller Prime factor Example N = 85, x = 5, and y = 17 I apologize for the blunder above. But you need to understand I literally tried thousands of equations. So far this is my best. Check it for errors. Is anyone having any luck with other combinations? x^3 + 2*x^4/N^2 + x^6/N^4 = x^2 0 Share this post Link to post Share on other sites

Phi for All 5478 Posted Thursday at 05:21 PM On 2/23/2018 at 1:19 PM, Trurl said: Ok, this is my final post to this thread, unless someone asks a question. On 7/24/2018 at 3:17 PM, Trurl said: I don’t know if anyone believes me when I say this series is significant. On 7/24/2018 at 3:17 PM, Trurl said: So, if you think there is any meaning to my equations, please post me a message in this thread to let me know. I will respond with more information. On 6/17/2019 at 7:15 PM, Trurl said: Ok so no response means that no one sees my pattern. ! Moderator Note I'm afraid this is something only YOU see. If you find a way to persuade others, let me know and I can open this monologue up to discussion again. 0 Share this post Link to post Share on other sites