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There are no anomalies. When you graph the equation, the x of the graph (you just graphed) equals the smaller Prime factor where y of the graph is or around zero. There are no tricks. That is why I called it Simple Yet Interesting. The code I posted was generated by ChatGPT. It simplified the equation. You should try it in Mathematica. It is not meant to be efficient but the first function should break (and print) near zero and estimate the smaller factor x. I have already posted on this. Let pnp = 2564855351 When x = 41227, the (x*y) part of equation equals 2564855365.5 https://www.scienceforums.net/topic/124453-simple-yet-interesting/page/7/#elControls_1258420_menu Hope this explains what I was attempting to do. I need to post another, larger example. If the program from ChatGPT works you should be able to modify the testing steps ( from every odd number to x+=22 or larger) The one thing that needs checking is how GPT simplified the equation. That is why I said test for lager Primes. Because 2 known Primes multiplied together will equal zero in the equation if they form a SemiPrime.

@Ghideon And anyone interested Yes. I am still dividing and finding a square root in my calculations. How could it be faster than the original recursive division? Probably not faster, since when you start at 3 the unknown x is closer to zero than pnp anyway. But the advantage is you don’t need to test those values in my equation that don’t occur next to zero. This zero is unique to pnp. It also occurs in sequential order. So, if you subtract the left side of the equation by pnp and it is, say 5, you know that x is smaller than the tested x at that value. I know it has many faults, but it does provide a unique graph that may contain some useful analysis. I think it will prove more useful as pnp increases in value. But it is difficult for me to test. I will try to factor the largest semi-Prime posted earlier. But that is why I posted here in the first place for help testing. I realize my algorithm isn’t faster than plain division, but that isn’t what it was intended to do. I need outside eyes because I created the algorithm and am biased, but finding semi-Primes is not the only part. Instead, it is to exploit a pattern in factorization.

3x+1 if odd x/2 if even So why not create a sieve of multiples of 2, 4, and 8? When x equals a logarithm of 2, 4, or 8 then x/2 repeated equals 2. 2*2*2*2… 4*4*4*4… 8*8*8*8… These 3 logarithms of 2, 4, and 8 encompass all the numbers that reduce to 2 when repeatedly divided by 2. What am I missing? Did I break the rules of the pattern? I am trying real hard not to factor semiPrimes. I did not research the problem yet. I am only working with 3x+1. I realize that this is more complex with larger numbers. I am just stating a simple example.

@Sensei @Ghideon I had help on this program. A good Samaritan put the code into ChatGPT and it supped-up the code. I still don’t know if it will run faster with larger Primes compared to standard recursive division. I think it gives a picture of what is going on with the factoring. x will only occur around zero on the graph. Again, I don’t know how to measure any efficiency of the program. Obviously with small Prime products (pnp), it will not show any improvement with factoring the semiprime. Again, I am breaking a resolution not to enhance RSA. But I wanted to share some final thoughts on this project I have spent great effort on. I think my next project will be Microsoft Kinect or 3D Printing. A friend bought me a book on Nichola Tesla for Christmas. It has his messages. However, the messages are encoded in puzzles and cryptograms. I thought I could write a simple Mathematica program and decode them. If the program works, I will share every detail. Here we go again. LoL. At least it’s not RSA. Even video games would be a good break from RSA. I know what you are thinking why would I give such information away. That is if you really believe in my program. I know such information is valuable, but if no one attempts to find large Primes with it I don’t know if the program even works. That is why I shared everything in the message board. I have shown my case. Please prove it right by finding large Primes. p = 2564855351; x = 3; Monitor[While[x <= p, If[(Sqrt[p^3/(p*x^2 + x)] - p) < 0.5, Print[x]; Break[];]; x += 2;]; If[x <= p, While[x <= p, If[Divisible[p, x], Print[x]; Break[];]; x += 2;];], x]

One of my resolutions this year is to stop trying to enhance RSA cryptography. I have been at it as early as 2006. In my first attempts, I stated that a logarithmic spiral could define a pattern in Prime numbers. I still believe this. And it is inherently feasible because logarithms already explain many patterns. But my ideas are the same in all my posts: x * y = pnp. If I had just left the equation at: x * (pnp / x) = pnp ; it wouldn’t have been helpful. I had to find a way to put y terms of x and pnp that was useful and equaled more than 1 =1. The enhanced equation still may be difficult to solve, but with only x as the unknown I could substitute x along the graph and when that value minus pnp approximately equaled zero, the value of x that caused that zero is the smaller Prime factor. Well despite the fact if you believe me or not Or if this is even useful (I believe it is useful), you could set up an equation similar to this isolating x and testing it along a graph for any pattern. It may be a challenge to put y in terms of x and pnp that only solves the desired pattern, but it would be a shot to analyze the series in ways not done before. So, as I break or fulfill my resolution, I ask even though it would still be challenging to break RSA with this method, is the method itself useful in trying to find patterns where this is no pattern? x* y = pnp x * (Sqrt[ (pnp^3/(pnp * x^2 + x) + (x^4/(pnp^2 + x) )] ) = pnp x * (Sqrt[ (pnp^3/(pnp * x^2 + x) + (x^4/(pnp^2 + x) )] ) – pnp = 0 Let pnp = 2564855351 When x = 41227, the (x*y) part of equation equals 2564855365.5 Not bad for government work.

Thanks tor the links 😁

One of my New Years resolutions is to stop trying to enhance RSA. Where is there a list of copyrighted content that is now public? The first Mickey Mouse movie now is public domain. Also, I thought that all my data analysis on crypto would benefit me in bioinformatics. Even though I am not a biology major or know much about, I thought I could still work with the statistics. Is there any online database of open source data to try and crunch and find patterns in genetics?

The back of the book picture I posted says it will break RSA, DSA, and ECDSA. I have yet to read the book, but it proposes alternatives to modern encryption. The previous link you posted was the first I saw that said today’s encryption was safe. I have been listening to Michio Kaku’s book. I haven’t finished but he describes quantum computers as pattern solvers. Uses like mapping dna or folding proteins. He doesn’t say we can do that currently. He does mention Google and Microsoft building prototypes.

I guess there is some disagreement on quantum computing. 60 minutes made it sound like it was coming out tomorrow. And there is several sources that say it will break RSA, DSA, and ECDSA. I’ve heard 40 qubits was the highest. But I believe you that it is far off. I see quantum computing as producing too much information. We are going to get an answer and it will be so complex that we will have to assume it is correct. I mean something like how you can’t prove a math theory by crunching numbers. However expanding the amount of different crypto algorithms seems awesome. BTW, I have not read this book.

Several sources have a cliffhanger: quantum computers defeat modern cryptography. The book article of chapter 2: The Physics of Quantum Information, Bouwmeester, mainly says the man in the middle attack. If Eve has the public key she can use it to compare her plain text to the cipher text. The article goes on to say how secure quantum ciphers are. A lot of which I don’t understand. I still don’t know why modern encryption fails. I will research Shor’s algorithm. Thanks for the tip. There is currently much interest in A.I. and quantum computers. I am trying to branch out to other subjects than RSA. But both subjects may destroy humanity. I only say this as a fact of science, but isn’t a device that can manipulate atoms and have infinite processing power God?

Why does the invention of a quantum computer mean the end of RSA? I have seen many sources that claim this, but they never explain the “how.” The one explanation I have read is that they have one of the keys and the way quantum computers work they reveal the pattern only knowing the given part. My question is does this only imply to modern key sizes? What would prevent someone from using a quantum computer to make a gigantic semiprime to factor? And do quantum computers explain mathematical patterns? I don’t think by factoring the RSA semiprimes it would find a pattern. Isn’t the quantum computer still just crunching numbers? From my reading, it was said that quantum computers will design a custom key system every time. I understood it as being a sort of geometry that unique to all computers. Combine A.I. and quantum and you have a thinking machine that can manipulate the world through atoms. SFN will now be moderated by the quantum. But that is ok because we can’t keep track of the trillion-digit keys or us finding patterns is no longer needed. Worse yet, we have lost the argument that the world is a simulation.

I think the scientist’s view determines rather he proves if God does or does not exist to himself. Before the 20th century science and religion were on the same page. Scientists were only explaining what God created for us. Some scientists see the work of God in a mathematical series. Other scientists need more evidence. In fact they dedicate their lives to it. Why do we want more knowledge and discoveries? It is to create and unlock mysteries. But for what reason are we doing this? Technology doesn’t always equal improvement. And what are we doing with all this knowledge? Finding better ways to kill each other? Whatever you believe is a personal choice. Science can’t answer such questions. That is why we seek God.

I realize that I didn’t use an official tax system. I just wanted to illustrate that tax compounded makes more for the government than the amount of money they tax. I choose sales tax. In high school we are taught this is the most fair tax. The more you spend the more your tax. And everyone pays the same rate. But like most taxes I think the more money you have the less the tax affects you. But imagine a flea market with dealers buying from one another. Each spends $100 on an item from the other dealer and pays $6 tax on every $100. The $6 is additive. You still need $100 to purchase, but you must add the $6 tax. The tax is subtracted from the individual buyer each time they spend. The $100 is constant. I am trying to illustrate that the tax has the potential to generate more tax than the original payment of goods. I don’t think this is new. I think it is inherent in taxes themselves. I would say the inability for governments to track transactions of cryptocurrency is why they want cryptocurrency to fail. I know if you have tax it takes away from the amount of money you have left. But money transfers it is never destroyed. I am not an economics expert, but somewhere somehow someone has mapped the movement of money between taxpayers and the amount of tax revenue generated.

It isn’t a tax system. I am just raising the question is taxing money making more revenue. I used sales tax as an example. With every purchase or transaction there is 6%. The cost is $100 to purchase each time. So one person buys something for $100 and pays $6 sales tax. The person who receives the money makes their own purchase of $100 and so forth. So the same $100 generates revenue more than its original value over time. More transactions means more $6 in tax fees.

Sales tax Pyramid Scheme Ok say I buy something for$100 + $6.00 sales tax. Then the person I bought from buys something for $100 + $6.00 sales tax. And so on and so forth for n, the number of money transactions. Does that mean that on $100 the government just make $6.00 * n. And after $100 / $6 times the government is making more money than the original $100? So the act of saying $100 is worth so much in gold, actually makes more than the value of the gold? And then transfer of money is promoted because it generates more value? And you thought bitcoin was a scam.

p=2564855351 For[i = 3, i <= p, i+2, If[(Sqrt[p^3/(p*i^2+i)] - p) < 0.5, x = i, Print[i], i=p+1 ] ] While[x<= p, x+2 If[ Divisible[p,x], Print[x], p = 1]; ] This was an attempt to target the range of divisors into the semi-Prime. I know I am doing division in the second loop, but the range is smaller, where the test equation of the first loop equals approximately zero. I know you can argue the usefulness. However, I still argue that at large semi-Primes with this algorithm, the number of test values is significantly less. And a shout-out to Chat gpt. The reason I am a terrible programmer is syntax; too many languages; too many unknown classes. Now that I have uploaded my algorithm, gpt will render all public key encryption invalid 😜--- only kidding of course. No one believes my work anyway. That was until gpt …

Well that would mean that the human brain was still significant. After all the machines were created and taught by humans. But what would be the distinction of humans and machines? And would machines be as distinct in personality as humans? And would machines be as destructive as humans? Remember the Matrix was designed to create peace. Recall when Agent Smith said that the Matrix was originally a utopian world. The effort of the Matrix's design for peace is flawed. Obviously, the machines don't know how to achieve a perfect world.

Well freewill or predestined, we will find out. I know this is in psychology topic, but it is just as much computer science. Imagine Chat gpt learning hate speech or other crap that we have advertised, as the A.I. is being trained. Would it inspire to be an architect or academic or would it do something else? I don’t think there is a thing called artificial intelligence. It is just intelligence.

The shear difficulty in making a secure one-way-function that will produce a public and secure private key makes security based on intense computation impossible to test, verify, and rely on the system. It is one thing to create a one-way-function but how will that one-way-function define the cypher that encrypts the message. My example which I don’t know if it has been tried before is to use the addition of large numbers, relates to the odometer problem I proposed earlier in this tread. We are always plugging numbers into the functions by using counting numbers. But what if we start counting by the pattern before numbers are placed into the function. Instead of 1.2.3.4.5…. to infinity, we modify the numbers by a function and then place it into the function machine? I know I am talking very abstractly and this is difficult for me to explain. But what if you counted only those numbers in the odometer that had 2 or more instances of a digit. 101100. If you count by a function that solves those numbers than you only see the distance between the pattern. However, if you counted 1.2.3.4.5… it would not show a pattern. There would be arbitrary distances between reading of 2 or more digits. I hypothesize this is why we can’t see a pattern in Primes. ______________________- I wrote this last week. It doesn’t make sense, but I post it so someone might see the abstract idea it represents. On the odometer you count linearly. So, a number 90909 may occur at a greater distance from the current pattern number minus the previous repeating of the similar digit. Simply put 90909 would occur after 50505. But the distance between such numbers is dependent on counting linearly. That is the same way we look for a pattern in Primes. Is that what is making it so difficult to factor semi-Primes? Does this make any sense? Have you ever had an abstract idea that is hard to put to words? 90909 – 50505 = 40404 but does 50505 – 50500 greater occur before 90909 – 90900. It depends on how I am classifying repeated digits but do larger digits occur after the smaller digits of reoccurring digits? For example, 111111 is linearly faster that 999999, but 099999 comes before 111111. This was the original idea for the odometer example. I know it didn’t explain my idea. Can anyone put my thought into a workable idea?

I think the author is referring to the geometric symbolism of this pictures. Like Leonardo using the triangle to represent the trinity. But pictures tell a thousand words. And making these images in math as a universal language that is easer to share that translating a Bible and printing it. I have the Bible but I am no expert on math symbolism in the Bible. But I think the mathematics thread is the proper place to put this topic. The geometry here is complex. And we don’t understand it all. I wish the author would have used only one example and explained his thoughts. But this is Dan Brown’s territory.

I agree that 4+ thousand are not all “seen”. But the ads are targeted. They will guide your interest. So you do a search and get 1000 responses you wii be guided to one. It is an interactive process. Remember search engines control what is found. I’m not a psychologist but when you look at a page of content you make multiple decisions and assumptions in milliseconds. Also you are not aware of all your thoughts. That is just observations on how I approach advertisements. I would put effort in designing an experiment but the advertisers already know all this. I wish I knew the goal of such advertising. And I wonder how it effects our decisions. And why did we allow this internet evolve this way. @dimreepr Ads to other ads. But reviews are not reliable. If Google results in a sale they should care what you buy. That should make them neutral. But are they neutral? I became interested in this because so many people are calling this out saying it is negatively effecting us. We don’t have the means to beat it, but we can defend against it waiting on the world to change.

It is important to note that my Pastor brought up the advertisements we are exposed to. It is me that compared it to external influences. But my question can be answered by those who prefer Faith or strictly science. We could say everyone has their own beliefs. But what influenced these beliefs? My estimate of how many ads we saw a day was around 500. But I think 4+ thousand is probably right. If someone or something is influencing how you surf the web than everything you see is causing a decision reaction in your mind. I know you think that fool believes in God. The scientific method determines my decisions. But the influencers already know what you believe. So it comes down to did you mindfully make that decision or did some web content specifically geared to you help you make up your mind? And I am no different than you. I hope we have free will and can work together even if we don’t share the same views. I have been reading on this subject and I think people are now seeing the bad of social media. But it is not my idea behind this. This was known before in what Bruce Schneider writes. So you say your brain sees not what you’re eyes see. But this is subconscious isn’t it? If 4000 was legitimate Google should know. How do we test this scientifically in a practical way? I mean is there any way to count average ads per hour? What would you say is the minimal speed in that a news story or ad could make you “think” about it? I’m guessing milliseconds but that’s just a guess.

My Pastor said last Sunday that Google estimates that 4 to 10 thousand advertisements are seen by a person on a given day. That seems high, but I wonder if it factors the data tracing the user by computers like surf history and phone usage. I was taught that you design your according to the target audience. But this rule does not work backwards because I don’t always know who has me as their target audience. So we are subject to thousands of messages a day and we don’t know who created them or how they are trying to influence us. We don’t know what it is that they are trying to make as act. I hope free will exists in that we could make choices and not be controlled by ads. But it still has an effect of some sort that we are probably unaware of. My question is: “Are these ads a byproduct of communication or are the ads controlled to influence behavior? This topic was the theme of the Matrix. Neo is offered candy by the Oracle and replies, Do I have a choice?” That is does he make a choice or does the fact that he thinks a certain way means his choice is already determined.

I don’t understand. I have been on the opposite end of this in my simple yet interesting post. It just goes to prove my theory that a pattern of Primes will never happen. Not because there isn’t a pattern but because the thoughts that lead to a pattern cannot be communicated from one person to another. For my post it came down to if I could factor a large SemiPrime or not. I couldn’t do it efficiently. But could reflect my programming skills and not my equations. Just as I started, your write up is too complex. It would take months to sort it out and it could be wrong. I have the same troubles when explaining. Give me an example where I can plug and chug. I am always interested in Primes. Why don’t you elaborate on the diagram of the ellipse.

This is not an easy question. It could be reworded to say, “how to perform at peak performance?” Like how to do math under sleep deprivation or how to find an address in a city you do not know with time being a factor. I think this is psychology’s best application. But I am not the best at doing karate forms. I try to get a visual picture and “rotate” left, right, turn, kick but I am wondering how the others go through the routine. I was wondering if there are any techniques for kinesthetic intelligence or is it my learning approach?