Trurl

Well if you know methods to find semiPrimes please share. I will show you a use to find the Prime number that multiplying by a known Prime number would aid in finding the product of the semiPrime. I need to find all Prime numbers where the smaller Prime factor is between 1.0 * 10^90 and 1.0 * 10^130 So I would multiply every odd number by the arbitrary Prime 5. Find new semi semiPrimes and divide those original Prime number values into: Clear[x, y, g, pnp] pnp = 2211282552952966643528108525502623092761208950247001539441374831\ 912882294140\ 2001986512729726569746599085900330031400051170742204560859276357953\ 757185954\ 2988389587092292384910067030341246205457845664136645406842143612930\ 176940208\ 46391065875914794251435144458199;

Well there is a difference between not making sense and saying it is not useful. One of the reason to use this method is having no knowledge of a factor being Prime or semiPrime. You say you’d never use it on a composite, but what if the composite was 32 digits and ended in 99? (I’m still working to make better examples. I know this one needs clarification.) You say it is redundant and makes the given number larger. I argue that as little as 3 times the size may increase it but yields a number easier to factor; sometimes. But what if I didn’t have a sieve and I wanted to find Primes between two larger numbers. Finding a Prime I didn’t know would be hard. So I would take every odd number between those numbers and multiply by 5. (It’s not division and it is only multiplying one time each number.) Would factoring these new numbers and proving they are semiPrime be harder then recursive division of these same numbers? That is the question. I know there are other more advanced algorithms, but now I am concentrated on this one. It may or not be useful. But I simply test would be to take your entire table you are sieving and multiply each number in question by 3 and sieve again. It produces slightly larger numbers you would factor in the future of the sieve anyway. By this I mean you will sieve these large numbers later as the sieve progresses anyway. Why not skip the smaller numbers? But does a standard sieve make it possible to eliminate Prime values without a continuous sieve? By this I mean starting at a given values not a continuous line from start to zero. Can your sieve start at numbers in the millions without a known starting point? I could be wrong of course but the forum is to test ideas. But as you guys pointed out a semiPrime test would give my test reason. But as I have stated in the past factoring semiPrimes is the key to finding a pattern in Primes.

What I said makes perfect sense: Prime times composite equal composite. Prime time semiPrime equals composite. Prime times Prime equals semiPrime. And if you can factor that semiPrime within reasonable, you have just solved the pattern of Prime numbers. The purpose of the multiplication is to increase the number of factors and know what the Prime factors of the newly created semiPrime. That is all. It is less than 1 minute observation. I don’t know that you are trying to understand what I am saying or just trying to destroy my idea. Which is ok because I welcome the challenge, but the above is what I claimed from the 1st post.

You are correct. But I am did not lie. I said unknown number if Prime, times known Prime would create 2 more factors because the number is now a semiPrime. Which doesn’t prove it is useful. But I will leave you with this thought. Do you agree or disagree that the ability to factor semiPrimes or even identifying them would result in the solution of all Primes numbers? That is why I take unknown Prime times Prime to form semiPrimes as a Primality test. That is why I mention this method that seems redundant and foolish but contains a hidden problem. I am not trained in number theory. It would take me days just to learn the notation to some of these sieves. It could be my redundant multiplication makes the numbers larger. But what if I state the redundancy of this method is useful if you can find within doubt that a semiPrime is formed; By multiplying the unknown number by a known Prime.

You are correct a composite number made lager isn’t always necessary. But if that number is so large that you can’t factor it, multiplying it by a Prime number may change the perspective and create more factors. But I am concerned with Prime numbers. A Prime times a Prime is a semiPrime. If I suspect that a number is Prime and it is so large I can’t factor it maybe I can determine if its product is a semiPrime. Yes it can lead to larger numbers but it may be the only information you can get about the number. My method is not rocket science. It is a simple observation. I was not high when I thought of it. I may have increased the magnitude of the number (relatively small) but I have also increased the number of factors. But the method would prove more useful if there was a reliable method to factor semiPrimes. And my question to you is why sieve Primes and not keep track of the semiPrimes at the same time? But I welcome your challenge. It is only an idea until someone tests it.

It will take me some time to write this up but I will test one of your numbers with the calculator on my phone. Say we don’t know if 4829995653 is Prime, semiPrime, or composite. Then we multiply it by a known Prime. I usually start with 5. 5* 4829995653 =24149978265 This product is now either semiPrime or composite. But trial and error we find 24149978265 / 3 =8,049,992,755 So the product was semiPrime it is composite, so unknown number times known Prime is composite so the unknown number is composite. ——— Very simple. May or not prove useful. But if you are dealing with a sieve, the sieve is practically doing the same simple process. But the only difference is this is jumping to steps that would occur in the future of the sieve. This is just a tool. It doesn’t always simplify the process. Like you said Prime times Prime gives a semiPrime that isn’t always verified easily. And if the unknown number is already a semiPrime the product still could be difficult to factor. I don’t know how useful it is, but what if you were completely your sieve in both the present and future numbers.

WIREDThe Kryptos Key Is Going Up for SaleJim Sanborn is auctioning off the elusive solution to K4, the outdoor sculpture that sits at CIA headquarters. But isn’t the value decreased every time someone new learns the secret? Besides isn’t it cheating and defying the original purpose?

No I am just biased because it is my method. But as KJW said even Fermat’s prime test has liars. Prime *Prime *Prime should always equal a composite but even * 5 can be hard to find factors. I know it sounds stupid in application: multiple by five and see what you get. I don’t always approach math scientifically. Sometimes intuitively. The Prime by prime equals semiPrime I don’t think is a complex thought. That is to be not tried before. It is just a fast observation. I will have to research these algorithms. I have never used them. I have tried to avoid Primes. I tried to study circuits and amateur radio. Something more tangible. But here I am again attempting to do data science. But you are right that I don’t always use the scientific method. To me finding Primes in a series is misleading. Greater minds than us have tried and failed. My odometer hit 116811 then 116816 then 116818. Suppose I was looking to find 2 pairs of matching numbers. These would be easy to see but difficult if I tried to find an equation that described when this occurs in sequence from zero to 116828. I mention this because I think prime numbers share the same elusive behavior. Mathematicians look at them and see patterns that aren’t there or see chaos.

Remember I am not factoring but testing for primality. So again I multiply 156,423,343 by 5 and get 782,116,715 which according to my rules is semiPrime. So 156,423,343 is Prime. I didn’t cheat and thought you may have given me a counter example. But if were to try and factor I would start on the right side of the digits. For 782,116,715 I would start on the right with what factors would go into 15. (3 & 5 ) 7-3 =4 __—////// But I’m not sure dividing right to left will factor, but as far as I know the number is prime. If the given number was semiPrime to start multiplying it by 5 should produce a composite number. I would have to write it up. I don’t have time tonight. I have made posts about prime testing and factoring semiPrimes. However those problems are not the path I was steering towards on this thread.

Well they are in no order. I multiplied by 5 and could factor the result easily (not at all). So far a second test I tied implying 9,991,991 by 23 and again tried to factor the product with no success. I repeated the multiplication of 9,991,991 by 7 and could not factor it either. I chose the Prime multiple randomly. I was on my phone so I wanted to keep it small. My logic is this: Number in question if it is Prime multiplied by known Prime results in Prime times Prime Or semi Prime (which I won’t be able to factor) And this means both numbers that were multiplied are Prime —-—————————————————————— But if the number in question is not a Prime number the multiplication with the known Prime will result in a composite number that should be easier to factor (and it helps simplify the knowledge gained by the sieve) ______-_ So basically it is just multiplying by a Prime and factoring the product to work around division of N by every smaller number. I don’t know how useful it is or that it works all the time. Or why Guass didn’t mention it because he didn’t have a computer and was doing arithmetic by hand. But as Ghideon mentioned that semiPrimes are even more difficult to factor. But there is no factoring of semiPrimes (other than difficult in that the formed semiPrimes have no other factors) . If this work and proves useful (which it hasn’t yet), this “math hack” could speed up many of number crunching. To me the main weakness is the difficulty of factoring the semiPrime like Ghideon said, but the sieve information should help. And the factoring that results in a composite number should be relatively easy.

Well I’m not saying a semi prime is easier to factor. I’m saying the number in question is not Prime, multiplying it by a known Prime will not result in a semi prime and thus easier to factor. If both numbers are Prime there will be a difficult semiPrime to factor. You could check by trying the process again with a different Prime number multiple. I test it with 9,991,991 It is difficult to factor. I multiplied by 5, 23, and 7 First look I’d say it was Prime because it ends in 5 and the 49,959,955 is difficult to factor. 9,991,991*36=359,711,676 not prime. That is just a random Prime number. That shows nothing. Just an illustration of 9,991,991 wasn’t Prime it might be easier to factor the product of a prime and non Prime. I need some time to look at this further. But a shoutout to @studiot can you see what I was attempting to do?

No I mean multiplication. If the number in question is Prime then multiplying it by a known Prime would create a semi prime. If the number in question isn’t Prime a semi prime wouldn’t be produced. I’m saying the non semi prime should be easier to factor then testing if the original number was Prime. A semi prime may be more difficult to factor, but if you multiply the test prime by a number that isn’t Prime the factorization should be trival. (maybe) So if 12 was tested to be Prime, we multiply it by 5 a known Prime number. 60 Sixty on the sieve is not Prime. 2*2*3*5 Not a semi prime thus not prime. Obviously we need bigger numbers. But I think it may be useful if applied to the sieve. If not no big deal just another abstract thought.

But what if the ability to do anything is contradicted by what anything is defined by? But if the gods don’t want to or can’t prove to us they exist where does that put us. Explain to me where that puts science and humanity. I know how you guys feel about Elon Musk but he is living the dream. Have many kids to stop population decline, going to Mars… If there is no personal God, Elon should be our model. And science only makes sense to us. I mean it is something we do but does it make sense outside of humanity? And when humanity is gone what becomes of science?

Well my figuring is to take 5 or any other and multiply it by the number in question of being prime. So if you were determining if 11 was Prime you’d multiply it by a known Prime say 5. You get 55 which is not Prime but a semi prime. But is it as difficult as determining Prime to prove semi prime? With lager numbers it may work easily for some numbers but harder to prove it semi prime? But any factor that isn’t Prime would break down into smaller Prime factors. I just brought this up because I agree with you the 6x+-1 is to heavily computational without a Prime number test. You said that all Primes can be expressed by 6x+-1 but computing in series some pairs are false positives. Without a test for Primes doesn’t this throw a monkey wrench into the series? My question is: is it easier to prove a number is semi prime than prime? Just for the fact it is no longer prime? And non prime factors are easier to factor.

But I think our view of omnipotent is limited. We know science and I often think about physics in church. But I don’t think our science is enough to decried omnipotence. Like when we get to heaven is there a lot of singing? But math and science can be just as much used as a form of worship. Increasing the human understanding, curing a disease (as mentioned) or enjoying what there is to learn. If the gods cannot remind us they are there what are we doing? I don’t mean just where we came from but what are these strange things like science are we doing? If someone finds a pattern in Primes, Guass is not going to say I was so close. Einstein didn’t live long enough to complete unification. Science is fun but I would argue that science is augmented by a personal God not rendered useless.

Here I am questioning the value of evidence. And even when science is right it makes no difference if we do nothing about it. I compared it to the gods who can present no evidence to man to prove they exist. And when you use science what are the guidelines for applying it? I am not blaming science. To me that is the same as blaming religion. People are the reason it is wrong. I don’t know what science covers that; maybe psychology? But I don’t think man has the ability to ever solve these problems. That is were a personal God comes in.

I was looking at the 6x-+1 thread and I agree with Studiot that he still needs a test for Primes to simplify the computation. I was unaware of the 6x+-1 and I don’t want to hijack his thread. But to test for Primility could you multiply the number in question by any known Prime number and see if the product is only divisible by those numbers? I mean you already know the Prime factor you used. If in doubt test with another known Prime. If 6x+1 describes all Prime numbers, it is not a sieve you need but a test for Prime numbers to complete the computation problem. I know it sounds too simplistic. But has anyone heard of it before? If I am wrong just ignore. I just didn’t want to distract from the other thread.

It’s the objective facts that have no effect on the decision. I saw a video on “verbal judo.” It is said that in a tense situation logical arguments do not win. I don’t think logic works in politics either. Again I used vaccines as an example. I am not a doctor. I’m just saying science is just facts to you use it. Unless you are inventing new technology or creating new guidelines than there is no value to evidence. Just as the gods determining what sign to show you. We know that some say climate change is natural. I believe it is very real. But what if I have irrefutable evidence? Do. I just say: I told you so as the planet explodes? Science is good. But I don’t think humans are Vulcan. They don’t always think logically. And not every problem is logical. If we had “pure logical” decisions do you think the world would be better? And what is the science to the application to science? Evidence is just evidence till applied.

That just means it is a blessing to find a wife. I don’t know I’m not married. But others describe it as one of the best part of their life. I haven’t said vaccines don’t work. I’m saying the scientists don’t always agree. And I’m saying that even if the science is 100% correct if the implication is bad the true science doesn’t matter.

I was referring to the current state of the CDC. You have a guy that doesn’t believe in vaccines in charge of the agency. So if vaccines weren’t bad his actions will make vaccines a bad thing. Which is ironic cause he said they were bad and now they are. So he is telling the truth now.

I’m just saying the physicist and believer are viewing the same world with different results. For people who are married they would see finding his wife guided by God. Religion is like computer security in that you must be able to authenticate and trust. It may be hard to deny the effectiveness of vaccines, but you have to trust those who distribute them. So we thought we could trust them and they break the system and ironically vaccines are bad for you. (That is because they made it bad.) I believe in science but it is limited. In a previous thread in religion I said something similar and someone replied that that wasn’t science’s purpose but philosophy’s. But to relate back to what sign would make you remember the gods? As far as seeing God in every day life, you don’t see it because you are untrained. It is like learning math. You learn math and start seeing patterns everywhere. A camouflage pattern never repeats. This is important because my knowledge of patterns doesn’t apply. My science is useful but my patterns don’t apply everywhere.

In your own comments the function MCheck and PCheck say Prime. But aren’t you missing a bunch of numbers. Do you do this to find a pattern in Primes or create the largest Prime from the pattern? After the sieve eliminates number you say only Primes will remain. What proves the left over numbers are Prime? MCheck and PCheck?

What is the class definition for MCheck? How do you test 6x-1 to be prime then 6x+1 to be Prime? Are you saying 5 6*5-1 =29 6*5+1 =31 But the problem is knowing 29 and 31 are prime. Is that what your program does: identify Primes by sieving 29 and 31? I’m just trying to see if I can understand this correctly.

Well I wasn’t in total disagreement. But you have to take into account that some see God in every day life. They are experiencing God in reality in every day life. But I argue the same for science. Yes it evolves as society changes. I respect you don’t believe. I wasn’t always a believer. I was just trying to show the converse. If you are not familiar with religions, religions just look like a reason to wage war or starve people. But aside from miracles and signs, the tangible part of religion that should be observable and tangible is how people live their lives. Martial arts is very religious and spiritual. But has tangible concepts like fighting battles. But fighting is only one part. Improving one’s self mentally and physically is the true goal. So just because you believe religion comes from projections of the mind how can you be absolutely sure? I like science but today there are conflicting view such as is there climate change or not? Are vaccines good or bad? Sounds like science is being as misused as religion.

No. I am saying I don’t know why we suffer. Even Jesus suffered when he was crucified. I don’t think there is any human explanation for this. But isn’t everything we experience and learn based on an intellectual construct influenced by a collective human experiences? History is written but how often is history inaccurate? Also we don’t live very long. Einstein’s equations live on but his mind didn’t. I mean he published works but how his mind worked and brilliant ideas he had he didn’t publish is lost. I guess we could forget the gods but that is true of any of our information. But to me it sounds that you are saying religion is imagined and science is real. I’m not really trying to change your mind I am just debating you. I’m not going to debate which one is correct. But even if religion was “imaginary” it still would be as real as science because religion is influencing people and they use it in their decision making.