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Yes I know you say the graph doesn’t show anything we don’t already know. That is why I showed you the graph. But testing 10^49 to 90^49 you clam is tribal to testing numbers 10^100. You could argue why don’t I just test the bottom half of 10^100. You may be successful or maybe not. But the point is I just did it mathematically in real time. And if I could estimate the error in the expression I could do it in one calculation. But the purpose is not to destroy RSA anyway. The Pappy Craylar conjecture might not destroy RSA. It is a pattern in factorization. It is a significant step in the pattern. If you look at the database numbers on error I posted, you will see the error has potential to find patterns. And if you followed along I think you know the equation isn’t trivial. So I don’t mind if you say I can’t break RSA. But you have to admit it was a good attempt. And you don’t know what other ideas I have. But I appreciate the critic. You tested the problem. Before it was an idea which no one I know could test. Supposedly Primes are impossible. Right or wrong I needed someone to test it. And it may not be wrong just not precise enough. For future explorations It is important to note the statistics of the curve of the graph of those values with a y axis value of zero.

You only have to test those odd numbers whose y value is less than one. I know the graph isn’t very descriptive. I need a “real time” plotting software. But as I show by cheating, I arranged the test value to the answer. As you can see y equals zero when x is the answer. I understand you say that numbers below 25% are too small. But they also have y-axis values below zero. So if you are crunching numbers you would start on the right and divide into N until a factor is found. Instead of numbers of 10^10 you are testing 10^50 and most of the time the right most y-axis zero value is the number. If you want a more mathematical explanation you would have to analyze the zero y-axis values with calculus. RSA is still protected because of the computation of the values on the number line. But as long as you can square pnp, RSA is significantly less secure. But don’t believe me. Test the number line. Look for y-axis equals zero. Start on the right and divide into N. RSA can hide in security of large numbers, but the reason the Pappy Craylar Method works is because it works on all Prime numbers. The small numbers test and so should the large. x = plot[ (x^4/(1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139^2+x)), {x, 0, 37975227936943673922808872755445627854565536638199 }] https://www.wolframalpha.com/input?i=x+%3D+plot[+(x^4%2F(1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139^2%2Bx))%2C+{x%2C+0%2C+37975227936943673922808872755445627854565536638199+}]

The plot is the answer. The y axis is expression x^4/(N^2+x). When the expression equals zero the y axis is also zero. So when the y axis is between zero and one then x at that values of the y axis that are less than one is all that needs tested. Start at the right of those x and divide N by x until you find the correct Prime factor x. The graph does in seconds what takes hours. No. We see the answers on the plot because we are testing x in the equation. The graph will show an answer knowing only N (pnp).

Here the link is. https://www.wolframalpha.com/input?i=x+%3D+plot%5B+%28x%5E4%2F%281522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139%5E2%2Bx%29%29%2C+%7Bx%2C+0%2C+10%5E51+%7D%5D Here where y = zero x^4/(N^2+x) = y x on the graph where y = 0, is the smaller factor q So it should work with large numbers. I know I know the answers before computation, but where y = 0, x is a possible Prime factor. Loads in seconds. According to Wikipedia “It takes four hours to repeat this factorization using the program Msieve on a 2200 MHz Athlon 64 processor. “ Note. Look at the graph. I not sure about all the numbers.

You are correct. I am simply calling the difficulties of factoring N the one-way-function. The difficulty of the Prime number factorization is what makes RSA work. I claim the Pappy Craylar method can make it 2 way. That is the claim of breaking RSA. I believe you call that one way or trap door function. Or N or NP. RSA seems impenetrable because we can’t find a pattern in Prime numbers to test. The PC method says forget for a moment in testing all known Primes. Instead look at how numbers are factored. Prime numbers can hide but factors can’t.

I will explain better. I keep talking about Prime numbers because I focused on the N=p*q part of RSA. It is where my work began. I focused on p and q. If p is so large that would determine the size of q. In RSA we are given N and it is a challenge to factor, thus a one way function. This is my focus. I figured let’s put N in terms of p alone. So I wrote an equation that would use N and compare (subtract N -N calculated) N in terms of N and p. And it worked. Except there was always a slight error when subtracting N - Ncalculated. An error between zero and one. So eventually I solved the error or at least found how it was calculated. This error is why the expression is between zero and one. That means the expression to be useful in breaking RSA there is a need to test all values between zero and one. (I don’t know how complex that is with hundred digit numbers.) That is how many p’s (you know p as x) there are when the main equation (or expression) results in a value between zero and one. (Again N-Ncalculated approaches zero.) I believe factoring N is the key to find a pattern in Prime numbers. Because a pattern in factoring correlates with a measurable pattern that can be graphed. Picture this: If p is small q is large. If p is large q is small. I made an equation that would approximate N with an unknown p. And since N is the know we will match unknown p’s until the value makes the known and unchanging N true. Because of the error the N=N is between zero and one.

Division Is 0.25 your lower limit because y approaches pnp? To me it seems like we are solving something different. 3 in my equation would be smaller and smaller as the SemiPrime increases. But 3 has infinity large SemiPrimes. That is why in a status update that if you could factor SemiPrimes you could test for Primality. But the trouble is all the 3s then the 5s and the 7s all lead to infinity SemiPrimes. But you would only need one number to factor and graph. So if 3*Prime# is between 0 and 1 then they are Prime. However the problem is that the expression often has many values between zero and one. That is why it isn’t perfect. But that doesn’t mean it isn’t useful. RSA uses large Primes but SemiPrimes use all Primes. But remember I’m a graphic artist not a cryptographer. I have done some reading. Basically the code is open source. My method is not mathematically complex. I am simply isolating x as compared to pnp. That expression between zero and one is just pnp minus pnp estimate. That is why with 100 digit numbers x of 3 is very small and falls into the test area but if x of higher values don’t test to be the correct factor 3 is possible. Download the complete spreadsheet and test for yourself. I’m am glad you are challenging my work. That is why I put it here. I very likely could be wrong. But look at the stumbling block our ancestors gave us. They want a pattern of Primes but it’s impossible. But once you start down the rabbit hole you can’t stop. But it means everything to computer science. While I was in school I did busy work with a cryptographer. I really didn’t appreciate his job. But it was pretty serious stuff. He had to get a polygraph and testing for weeks. I think I’ll stick with open source crypto.

For values where the expression (the main equation) will equal a number between 0 and 1. As pnp gets larger the x value will become smaller. For example if an x=5 is less then 1 when put into the expression for a pnp test value of 85 and we keep the pnp=85 but try x=3 the expression is still between 0 and 1. That is what I show in the spreadsheet. That smallness is the error (distance from zero of the expression) that occurs. Sure we can have a million digit SemiPrime with a factor of 3. But as pnp increases the expression becomes close to zero which in turn y becomes larger. But y cannot become larger than pnp.

That is fair constructive criticism. It is a bold claim to make to break RSA. If the Pappy Craylar conjecture was true RSA and any ciphers that relied on factoring, Prime numbers, or logarithms would have to have larger keys. Yes I know that as pnp gets larger the number of values less than zero, increase. I don’t see this as a flaw. It is just how the numbers fall. If pnp was a hundred digit number it is still possible 5 could still be a factor. So does it apply to the pnp value of RSA? It isn’t perfect, but I am not aware of any other tool to take its place. But it is useful in RSA factoring because there are 4 times less numbers to test. Maybe even less number are possible if a pattern is found. You would test lager odd numbers first. But as you test values there are hints to how large the test value should be. For example with a pnp of 85, 3 would be between 0 and 1 but 85/3 isn’t a whole number. If I was crunching numbers, I would test the higher numbers first. But the second thing to note is what happens with larger numbers. Will the distance between large numbers become smaller or will there be more zeros with more numbers to test? That is why I post this thread. I think I have a simple enough pattern that may challenge RSA. I post this picture to show the less than zero values of the Prime number 3. Yes it approaches zero as pnp increases. But you forget as x approaches zero the corresponding y value approaches pnp.

Pnp is known. Which happens to be x*y. The question is what x with known pnp will be close to or moving away from zero. The given pnp will only be true (within error) when x puts the equation near zero.

Should say x is smaller factor of SemiPrime pnp.

You are correct. I haven’t changed the equation. The semiprime is still pnp. But notice that pnp is known and does not change. Test 5, pnp equals 85. Test 11, pnp is still 85. It should only be true when x equals the smaller factor of pnp. My hypothesis is if we can factor a semiprime you can predict and find higher value Primes where x the smaller Prime factor forms another semiprime. So 3 * 5 make semiprime 15 and 3 * 7 make semiprime 21. I show a pattern in the table of values in the previous post. I show the error in the first 1000 Prime numbers. I believe if you graph the equation knowing x and finding a pnp (which is x*y), where the graph equals zero then y is Prime. I don’t understand how the Riemann hypothesis finds Prime numbers. Finding zeroes either proves or disproves it, but why cannot we have a pattern of Primes before it is proved? If the zeta function minus the values at zero in the Riemann hypotheses fits the logarithm function to match the Prime number distribution, I wonder how the Pappy Craylar conjecture finds zeros. The PC conjecture has the error of the equation. But the PC conjecture is not a line but a modified circular function. The past 2 posts before the current posts where I listed a bunch of numbers is a pattern. There are 2 equations I offer as a proof as a pattern. I have shared the Pappy Craylar conjecture with as many people that I could. One person is an engineer, but says he isn’t schooled in number theory. I posted the new post, just to reiterate that it is just the simplest of equations. I never got a chance to get a doctoral degree. However, this is my dissertation. That is why I put so much effort in it and why I work so hard to prove it.

This picture sums up my work. If you wonder why I put so much effort and posted so much about this problem, it is because the application of this problem. This is several problems and techniques. Every post has been to address something in the breaking of RSA. Now the problem is applied to Prime numbers and their distribution. If you graph the equation, Prime numbers will occur around zero. Any known Prime number multiplied by test value should result in zero when the test number is also a Prime number. If you graph the equation of the Pappy Craylar conjecture and graph the inverse of this graph, it may very well be that it is a Tracy-Widom distribution. There are many applications. I only list some new ones here. I once stated back in 2006 that a logarithmic spiral could be used to represent Prime numbers. I still believe that even though how original that idea may be. I see the graph as a resonating circular function. This circular function would increase in value but with harmonics that occasionally dampen it. If the equation does not convince you I completely understand. I must find the ultimate proof by breaking RSA. Breaking it will improve my programming skills. If you wonder why I did not just do that at the start. The fact remains I have the math, but crunching the numbers takes considerable programming skills. But the RSA numbers are still available, even though, the prize money for solving them has expired.

Well I used the word speculation to mean I don’t have a scientific study. I was basing my view on facts of my education experience and what situations I know and what other teachers have told me in discussions. But you miss understand me. Being an online teacher is to avoid the disciplining of the classroom. Picture Arnold Schwarzenegger on the first day of class of Kindergarten Cop. Teachers to there credit are managing classrooms and students behavior more often than the art of instruction. I want to practice instruction without the headache of bad student behavior. Teachers salary was discussed because you mentioned it. My original question was to find legitimate places for teaching adults or high school online.

Story time: When I was in 5th grade 3 students were sent to an empty classroom to take a make up test. Soon one came back and said the other 2 just left the building. Then a kid in the classroom pointed them out and the class came to the window and watched them for minutes as they ran through the woods. How does a teacher teach while they are trying to get the kids back? That is a mild example. And you can’t use traditional methods today like when there is a fight; let them use boxing gloves to wear it out of them. You don’t want a military type of discipline but those are mild disruptions in my stories. Kids like the school shooting profiles start this way. I don’t know how to fix it. I figured if an online student interfered with the feed it would be recorded and I could just block them. Again from just speculation: teaching is more managing the classroom than the instruction of students. Teaching is a leadership position. (Especially in secondary school) That is why I’d prefer to teach adults where there is a emphasis on instruction and not classroom management. I want a classroom where the students know how to behave as students.

I’m speaking with speculation, but one of the worst things I have heard goes back to discipline. Teachers aren’t given methods to control the classroom. When teaching adults the usually want to be in the classroom. If not grades and money (in tuition) will motivate them. Adolescents are not motivated the same way. When rewards don’t work and class is still disrupted how do you handle it? Money is important. But if you aren’t given tools to stop disruptive behavior you can’t teach. And thing like test scores and graduation rates is your fault. Again in speculation, higher pay will not correct this problem.

You sound like a teacher. I guess it differs state to state but in my area teachers make a decent wage. It is the substitute teachers that don’t and they use them to fill teachers’ positions. All a substitute teacher needs is a bachelors degree. They lowered the certification to fill openings. But you are right that does lower wages. I felt that working online would be easier to control the classroom. I am not skilled at giving detentions and unruly kids. I’d rather work with adults. I guess now is the best time to find a job in education. If I was going to take a class, I agree that in person is better. I have taken online classes and all the work was left up to me. The professor just graded me telling me I did it all wrong. I had nothing such as other student’s work to compare. The comments did not show what was wrong except minor grammar. The videos on YouTube are way more educational. But you don’t earn a degree watching YouTube. I have some ideas that I would use to improve online courses. Online courses are not cheaper than in person but the instructors usually don’t give instruction. With modern internet technology this should not be so. You made a good point that math instruction is difficult remotely, but why doesn’t the classroom share a document in real time in a chat room? What is your take on this?

There is a shortage of teachers. What would be a legitimate online school to teach for? I am not a secondary school teacher but I am asking about cyber schools both secondary and post secondary schools. What are trusted employers? How do you apply? One challenge to secondary schools is disciplining the classroom. I assume the online format would correct this. But if anyone knows of teaching positions in a legitimate online school post it.

iNow, I know it seems link a cowardly response. I am just saying NATO should have done more before it escalated. Sometimes you can’t just talk, you have to back it up. Well the Ukraine has backed it up and stood up to the bully. But how can NATO help them? I ask that question because it is this thread’s question? I don’t know what you can do but talk to the other side. Did you study the Vietnam War in high school? Both sides blew each other up until the U.S. left. Now we’re friends. They don’t teach the part on how peace happened. Could it all just have been avoided?

That isn’t a source. It is my speculation. I think NATO failed the Ukraines. The U.S. says the Russians are going to invade. We’re are the peace talks? We send weapons and intelligence. Both won’t stop the Russians. We should have flooded the country with humanitarian aid. What is Ukraine’s plan to win this war? Now the woman and children are displaced. I believe for the world to maintain peace both Ukraine and Taiwan would have to be released from NATO in a bargaining agreement. I know the Ukraine and Taiwan are not part of NATO so they only receive aid. But I think the NATO countries know they can’t protect them without disaster. So NATO is forced to slow the progression of war and hope a solution presents itself over time. I stated that the world can be as safe and peaceful without the entire world being a democracy. We can spread democracy peacefully through the people changing their own country. But there is a fine line between peaceful influence and pissing off Russia or China. Again this is all my speculation. I don’t have any intel other than the media and internet. But this is my view of the positions of Ukraine and Taiwan.

Ok. I was reading this thread and someone rant on a rant about the left and communism. Maybe this reply can be moved. But I remember somewhere I say something somewhere else that described the World was safer when there was a balance of power throughout the World. I speculate that NATO didn’t act in Ukraine because it was the safer think to do.

I love freedom and democracy but is it right for every country? Strategically probably not. Did George W. Bush do this with Husain? Sure it would be great to give democracy and stop the spread of communism. But wasn’t that be Vietnam? Every country is to blame. Let’s “spread democracy” and kill thousands on both sides until it isn’t profitable. And what is the purpose of Pelosi of ticking of China? That is no better than rocket man launching or Iran threatening to building a nuclear program. I would say the people of other countries would love democracy. But the leaders are threatened by it. To put it in relation to psychology, it is like having an atheist believe. How will a country react to the fact outsiders want to change the rules? Not a smart move to force beliefs on anyone. On both sides.

I have attached a PDF to view. I know it could be formatted more clearly. But if the Pappy Craylar Hypothesis is true: We can verify a number is Prime by multiplying it by a known Prime number and see if a Semi-Prime results. And we may be able to take a known Prime and see which consecutive number will result in a Semi-Prime, thus establishing a pattern. This pattern is seen in the PDF I posted by taking the error of the equation when (p^4 / ((p*Data)^2 + p)). I know it is hard to see in my PDF. I’m working to make it easier to read. I have been reading a book that said if there is a pattern in Prime numbers the Riemann Hypothesis is false. And if Prime numbers are completely random the Riemann Hypothesis is true. But the question is do you have a pattern if you can predict where the next Prime number occurs? I ask this because there may be a computation to find the next Prime number, but the overall placement of all Prime numbers may be arbitrary. @studiot : This is what I was describing in my status update. 20220622ProofSFN.pdf

I think the situation worked out as best as it possibly could. As far as lives not lost. Any effort to stop the rioters would result in massive casualties. Killing your fellow Americans doesn’t make sense. Trump doesn’t call of the rioters because if he does he has to admit he is in control of them. I think the only reason he makes a statement is to save the rioters lives. More firepower was on the way in my speculation. Whatever was planned didn’t work. And the game becomes more dangerous to prolong the riot. I know it was bad but the dems say it could have been worse. As for future security I don’t know. It is just like gun violence issue with no easy answer. I say we ban Biden and Trump both from the next election.

I am for supporting the Ukraine. But I come to the conclusion that they should have avoided war and surrendered to Russia. Yes I know it is more honorable to fight. But I don’t think fighting was in its best interest. They could fight a battle they can win. But more importantly look at the loss of life. At least with surrendering civilian lives are saved. And there would be open peace talks. I don’t like to see them be given ineffective weapons because airplanes and missiles are what they need. From what I hear on the news the can’t attack Russian soil. I want them to prevail but I don’t like to see all these people dying for lack of diplomacy.