- **Miscellaneous Math**
(*https://www.mersenneforum.org/forumdisplay.php?f=56*)

- - **Bob, I'm calling you out!**
(*https://www.mersenneforum.org/showthread.php?t=3221*)

Bob, I'm calling you out!Bob (you know who you are),
I posted this on the other forum you frequent, but in case you don't catch it, her it is again. I challenge you to find one inconsistency or one ill-defined phrase in my post EFFICIENCY: PRIME TEST vs PRIME GENERATOR or my CLARIFICATION post. In case you don't like the WAY I defined my generator, I'll even redefine it here for you: Let p(n) be the nth prime Let p(n)# be p(n)*p(n-1)*p(n-2)*...*5*3*2 Let abs() be absolute value Let +/- be "plus or minus", though the theory works with just minus Let q(x1,x2,x3,...xn):positive integers --> positive integers given by q(x1,x2,x3,...xn)= abs( A +/- B) where A and B are given by: p(n)# divides A*B p(n+r) doesn't divide A*B for all r in the positive integers gcd(A,B)=1 each xi is the positive integer exponent on each p(i) Then if q(x1,x2,x3,...xn) < [p(n+1)]^2, then q(x1,x2,x3,...xn)is prime. This is because contradiction of the distributive principle shows that q(x1,x2,x3,...xn) will not have any of p(1), p(2),... p(n) as factors, and the square root of q(x1,x2,x3,...xn) is less than p(n+1). Now, is that well-defined enough? As I said before, to get all primes < [p(n+1)]^2, it's important to use ALL POSSIBLE disjoint partitions of {p(1),....,p(n)} into the two sets to be put into A and B. This will produce primes without testing any composites, because the elimination of those composites is intrinsic to the definition of A and B, the gcd(A,B)=1, and the "less than" test. This indicates that this algorithm may still be in the running as the most efficient way to find primes, given that it doesn't waste time testing a large number of BIG composites. Prove me wrong, if you dare! |

I have a question: How can you prove primality of p(n+1)?
And how can you prove that p(n+r) doesn't divide A*B for all r in the positive integers (as it seems to be implicit in your demonstration)? Luigi :help: |

[QUOTE=synergy]Bob (you know who you are),[/QUOTE]
This isn't fourth grade. This is not an appropriate approach for asking a famous mathematican, even a crotchety famous mathematician, to review your work. I haven't followed closely, but if I recall correctly, Bob's comments on your work have fallen into two categories. One category was that you haven't yet learned the fundamentals of measuring complexity. The other is that you seem to be unaware of related published work. I don't see any indication that you have addressed either of these issues. Famous people are inundated with nonsense from cranks. If you want a slice of their time, you need to clearly distinguish yourself from those cranks. "Calling him out" isn't a very effective strategy for improving your positioning. |

[QUOTE=wblipp]This isn't fourth grade. This is not an appropriate approach for asking a famous mathematican, even a crotchety famous mathematician, to review your work.
I haven't followed closely, but if I recall correctly, Bob's comments on your work have fallen into two categories. One category was that you haven't yet learned the fundamentals of measuring complexity. The other is that you seem to be unaware of related published work. I don't see any indication that you have addressed either of these issues. Famous people are inundated with nonsense from cranks. If you want a slice of their time, you need to clearly distinguish yourself from those cranks. "Calling him out" isn't a very effective strategy for improving your positioning.[/QUOTE] None of my business, but the famous mathematician could perhaps explain what is wrong with the other person's reasoning [U]concretely....[/U] Like: You said this, but this is wrong because of ....whatever. Instead, he is talking in a condescending tone of voice about go and read this, and you are too ignorant, etc. Just like he would say: I know you will walk into my trap. :razz: I know what is wrong, but I am not going to tell you, because I want to teach you a lesson! And the lesson is that you are not allowed to have ideas, unless you have studied as much as I did and followed all my instructions.... I am sure BOB is a very knowledgable and smart man, but he thinks we are dumb students and he is the teacher. This is wrong. This here is a platform where people with the same interest get together. Everybody is on a different level, and we teach each other or learn from each other. BOB would be right if he would reprimand a student for not studying, because he is wasting the time and money of the university, but he can't do the same to people who come here with original or not so original ideas. There is a nice way of telling someone why is he wrong. Nobody likes to be treated like dirt. Just my 2 cents. |

Okay, maybe it was a little over the top, but it was meant a little humorously, and like amateur said (thank you), he makes unsupported claims that my posts are "rediculous" and "not well defined". I just want him to support his claims, or quit making them. I'm here both to learn and to share, and I can see a place for positive criticism in that, but not outright aggression. If he supports his claims, then I will see them as being positive criticism, and thank him for his comments. Maybe I don't (yet) have a ph.d., but there is a certain amount of respect that should go both ways, and I feel it hasn't been.
ET, Second question first. You create A and B that way. Take an example. Starting with {2,3,5,7,11} you put some in A, some in B. So A might be 2^a*5^b*7^c, and B would have to be 3^d*11^e in order to use all of them from the set. So A*B has all of the above primes as factors, and no others i.e. no prime p(n+r) divides A*B. First question: Let's look at this inductively. Using {2,3} i.e. abs(2^a +/- 3^b) you can get all primes from 5 to 25. Then you use the primes you just found, {2,3,5,7,11,13,17,19} and 23, but we won't use 23, I'll explain in a minute why. Put some of the set in A, ALL OF THE REST in B, and apply the absolute value thingie. Now, here is where the 23 comes in. EVERY output less than 23^2=529 will be prime. These will all be between 23 and 529. Next step? Use the primes you just found, except 523, to find all primes between 523 and 523^2=273529. Granted, we're getting a huge number of variables, but it's exciting that the range grows so fast, and no composites need checking. Don't know if it is efficient, but smart algorithms could be created to pick partitions between A and B that are most likely to give small enough outputs to be within the target range without too much trouble. Even if it isn't efficient, it should be worth something as a theoretical understanding of one more facet of the distribution of the primes. Aaron |

:surrender
I just read a posting by Bob on another website, wherein he explains why my theory is "rediculous". Basically, the number of computations, even if we can ensure optimal partitioning, are truly astronomical. So it isn't efficient. But it's still interesting! Thank you for your positive criticism. I truly apologize for getting "huffy". I didn't - couldn't know why you were so against me, until you said. Now I know you really did have a reason. I also apologize if I offended anyone else. Aaron |

[QUOTE=synergy]
ET, Second question first. You create A and B that way. Take an example. Starting with {2,3,5,7,11} you put some in A, some in B. So A might be 2^a*5^b*7^c, and B would have to be 3^d*11^e in order to use all of them from the set. So A*B has all of the above primes as factors, and no others i.e. no prime p(n+r) divides A*B. First question: Let's look at this inductively. Using {2,3} i.e. abs(2^a +/- 3^b) you can get all primes from 5 to 25. Then you use the primes you just found, {2,3,5,7,11,13,17,19} and 23, but we won't use 23, I'll explain in a minute why. Put some of the set in A, ALL OF THE REST in B, and apply the absolute value thingie. Now, here is where the 23 comes in. EVERY output less than 23^2=529 will be prime. These will all be between 23 and 529. Next step? Use the primes you just found, except 523, to find all primes between 523 and 523^2=273529. Granted, we're getting a huge number of variables, but it's exciting that the range grows so fast, and no composites need checking. Don't know if it is efficient, but smart algorithms could be created to pick partitions between A and B that are most likely to give small enough outputs to be within the target range without too much trouble. Even if it isn't efficient, it should be worth something as a theoretical understanding of one more facet of the distribution of the primes. Aaron[/QUOTE] I see. It seems you are working on two different fields of factoring: congruences modulo a prime numbers product and trial factoring up to the square root of a number. A hint: take a look at the Fermat's little theorem and check out results to avoid Carmichael numbers. You will have a good challenge to check the efficience of your idea. Luigi |

[QUOTE=amateur]None of my business, but the famous mathematician could perhaps explain what is wrong with the other person's reasoning [U]concretely....[/U]
Like: You said this, but this is wrong because of ....whatever. Instead, he is talking in a condescending tone of voice about go and read this, and you are too ignorant, etc. Just like he would say: I know you will walk into my trap. :razz: I know what is wrong, but I am not going to tell you, because I want to teach you a lesson! And the lesson is that you are not allowed to have ideas, unless you have studied as much as I did and followed all my instructions.... I am sure BOB is a very knowledgable and smart man, but he thinks we are dumb students and he is the teacher. This is wrong. This here is a platform where people with the same interest get together. Everybody is on a different level, and we teach each other or learn from each other. BOB would be right if he would reprimand a student for not studying, because he is wasting the time and money of the university, but he can't do the same to people who come here with original or not so original ideas. There is a nice way of telling someone why is he wrong. Nobody likes to be treated like dirt. Just my 2 cents.[/QUOTE] Are you and synergy this arrogant with all of your teachers? I told synergy in the very beginning that his/her scheme was unworkable because it required too much computation. I would call that a concrete response. I suggested to you and synergy that you spend some time learning the basics of this subject. This suggestion was ignored. I suggested to synergy that he/she count the number of required operations. This suggestion was ignored. It is possible to cure ignorance by studying. It is impossible to cure willful and arrogant ignorance. You and synergy better learn this, or you will have a very hard time in school. Synergy suggested, in a sci.math post that (2^x 3^y - 5^w 7^z) was prime if it was less than 121 because it is not divisible by 2,3,5,7. I asked synergy to demonstrate how to determine x,y,w,z so that N = (2^x 3^y - 5^w 7^z) for a given N < 121. This request was ignored. I asked synergy if he could demonstrate that every prime p < 121 was in fact in the range of this exponential expression. This too was ignored. Synergy proposed that if p = A - B or A + B, where A and B were taken as the product of primes less than some bound, and if p were bounded, then p was prime. I agreed with this. But I pointed out that this was handwaving, not an algorithm, because it failed to specify a method for constructing A and B. Indeed, synergy even failed to show that every p HAD such a representation. Now, in later posts, synergy suggests finding A & B by searching all the possible subsets. I suspected this is what he had in mind originally. If synergy had bothered to do even the minimal amount of background research, he would have discovered what I told him in the first place: It requires too much arithmetic. Yet, synergy continued to cling to his idea that because his "method" did not involve checking composites, that it would be faster than existing methods. I also suggested that synergy look at the SIZE of A and B and estimate the amount of arithmetic needed to calculate them. This too was ignored. Let S(n) = {p < n | p prime} and let S = S1 + S2. To prove p prime, we must find A = product(p in S1) and B = product(p in S2) such that p = A+B, or p = A-B and p < square of the largest element of S. This does indeed give a method for proving p prime. However, we have not proved that every prime p has such a representation. Furthermore there are 2^n such subsets to be examined. And the arithmetic to compute A and B is extensive. We have #S(n) ~ n/log n by the PNT. max(A, B) is approximately exp(n). Thus, the arithmetic to find a represention in the desired form is O(2^(n/log n) exp(n)). This is DOUBLY exponential in the size of the problem. You and synergy are typical of cranks. You refuse to take suggestions, you refuse to learn the background information needed to discuss the subject, and you are not even aware of the *extent* of how much you don't know. I hope you don't have this attitude with your other teachers. I quote from above: "BOB would be right if he would reprimand a student for not studying" This is exactly what you and synergy HAVE done. You refused to do your studying. I even told you what should be studied. :furious: You can't discuss a subject until you know the basics. |

Thank you Bob for your reply.
There are a few misunderstandings I would like to clear up. I have no teachers, it has been a few decades since I finished school, and I have no formal education in mathematics. Just plain high school math and what I have picked up here and there, because I am interested in this subject. I guess, this would be enough for someone to stop taking me seriously, and calling me a crank /English Slang Dictionary: "a mentally deranged person"/ :smile: Well, my mental derangement (insanity) has been good enough for obtaining Mensa membership. It is no big deal, but they are not famous for having mentally handicapped members.... :wink: Yes, I do lack the necessary knowledge. I wish I had it, because then I wouldn't have to ask for help, I could work out things for myself. Math is my hobby. I like trying to find solutions for difficult problems, and I refuse to feel bad about it. :wink: Also, I don't mind making a fool of myself, because that is part of the process. I have a few ideas that might be new and interesting, and if so, I would like to share it with other people. That's why I am looking for someone who could tell me if the ideas I have are new or old, and in case they are useful, how could they be improved? I don't intend to continue studying at my age, but I don't think that I should be silenced just because I am not an expert. I had this idea on how to make a filter for primes. It is similar to Eratosthenes' Sieve, but different.... I haven't seen it anywhere, and it is slow, but I think it has potential. It could be streamlined to make it more efficient. Even so, it should be of interest for someone who is into this subject. Because I am a layperson, it has been written and explained in plain English, but so far everybody was able to understand the method. I know that you are a very busy person, but it would be an honour if you would agree to take a look at it. Maybe when you see my idea you will change your mind about me. It is not earthshattering, not perfect, not even fast enough to revolutionize the search for primes, but I hope you will see the uniqueness of it. I have posted it on my webpage. If you agree I will send you the URL. amateur p.s. sorry for my mistakes, English is my second language. |

As far as synergy's idea is concerned, my knowledge is limited to make an opinion. I just pointed out that someone who is trying to come up with original ideas should not be called a crank, and an idea that doesn't work because it has a flaw is not a gibberish, but an idea that has a flaw :wink:
Edison: "If I find 10,000 ways something won't work, I haven't failed. I am not discouraged, because every wrong attempt discarded is often a step forward...." |

[QUOTE=amateur]Thank you Bob for your reply.
There are a few misunderstandings I would like to clear up. I have no teachers, it has been a few decades since I finished school, and I have no formal education in mathematics. Just plain high school math and what I have picked up here and there, because I am interested in this subject. I guess, this would be enough for someone to stop taking me seriously, and calling me a crank /English Slang Dictionary: "a mentally deranged person"/ :smile: (1) A crank need not be mentally deranged. They merely insist on clinging to a misguided viewpoint despite evidence to the contrary. They refuse to learn. (2) What makes you a crank is your pursuit of this subject combined with an unwillingness to STUDY THE BASICS. (3) Synergy (not you!) replied with rather juvenile taunts (i.e. "calling you out") Well, my mental derangement (insanity) has been good enough for obtaining Mensa membership. (4) Whoopee. Membership in Mensa does not qualify you to do mathematics. Yes, I do lack the necessary knowledge. (5) Then ACQUIRE it. Elementary number theory should not be difficult, because after all you are a Mensa member. :devil: I wish I had it, because then I wouldn't have to ask for help, I could work out things for myself. (6) But when an expert tells you something, you rejected it, fully aware that you lacked basic knowledge. This is what makes you a crank. Maybe you should try brain surgery? I'm sure you know as much about that as you do about number theory. No? Why not? Math is my hobby. I like trying to find solutions for difficult problems, and I refuse to feel bad about it. :wink: Also, I don't mind making a fool of myself, because that is part of the process. (7) Failure to solve a problem does not make one a fool. Not listening to experts when you know you lack skills does. I don't intend to continue studying at my age, but I don't think that I should be silenced just because I am not an expert. (8) You should not be silenced. However, you should think very carefully before posting about a technical subject in a public forum especially when YOU DON'T KNOW THE SUBJECT. I had this idea on how to make a filter for primes. It is similar to Eratosthenes' Sieve, but different.... I haven't seen it anywhere, and it is slow, but I think it has potential. It could be streamlined to make it more efficient. (9) There you go again. You say "I think it has potential". But you are NOT QUALIFIED to make that judgment. And the fact that you have not seen it anywhere does not mean anything, since you have seen so little. Even so, it should be of interest for someone who is into this subject. I know that you are a very busy person, but it would be an honour if you would agree to take a look at it. Maybe when you see my idea you will change your mind about me. It is not earthshattering, not perfect, not even fast enough to revolutionize the search for primes, but I hope you will see the uniqueness of it. (10) "uniqueness". More unqualified hyperbolee. You would be much better off if you READ ABOUT THIS SUBJECT. Until you do, I simply can't be bothered looking at your work. It isn't worth my time. [/QUOTE] see above. |

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