Official 'exchange of inanities' thread [Was: mm127 is prime, cuz I say so]
...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? Try it with how meny primes you like... and with how meny 2^....1 you like... it always works 
[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? Try it with how meny primes you like... and with how meny 2^....1 you like... it always works[/QUOTE] That is false. For n=4, all are composite. Also for n=11, all are composite. :razz: 
[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? [/QUOTE] I see a sequence of numbers. I see no mathematical argument at all that suggests every number in the sequence is prime. You have a strange notion about what constitutes a proof. [QUOTE] Try it with how meny primes you like... and with how meny 2^....1 you like... it always works[/QUOTE] "It always works". Is this your proof? A simple assertion? I suggest that you think about what you wrote. For example, please prove to us that 2^(2^1271)  1 is prime. 
[QUOTE=kalikidoom;412554]<blah>... it always works[/QUOTE]For various values of "works".

[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? Try it with how meny primes you like... and with how meny 2^....1 you like... it always works[/QUOTE] 1) n must be prime for 2^n1 to be prime 2) by that same logic m=2^n1 must be prime for 2^m1= 2^(2^n1)1 to have a chance at being prime. 3) as LaurV pointed out not all n that are prime will allow 2^n1 to be prime. 
[QUOTE=LaurV;412564]That is false. For n=4, all are composite. Also for n=11, all are composite. :razz:[/QUOTE]
I expect that the OP intended for n = 2. However, I'd still like an answer to my question as to why the OP thinks that presenting a sequence of numbers is in any way a "proof". There were no mathematical statements asserting that some (set of) condition(s) is true, nor were there any logical statements. It was just a list of numbers. How can this be a proof? 
Well, the original poster said:
[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)... I mean... isn't that at least a proof that there's an infinate amout of them?[/QUOTE] He didn't say that he has a proof. 
[QUOTE=alpertron;412571]Well, the original poster said:
He didn't say that he has a proof.[/QUOTE] He suggested that a sequence of numbers [b]constituted[/b] a proof. It is hard to correct someone's misconceptions without knowing how and why they believe what they believe. A simple statement that what was posted is not a proof says very little./// We need to know why the OP thought that simply presenting a sequence of numbers [I]might[/i] be a proof. 
[QUOTE=R.D. Silverman;412573]He suggested that a sequence of numbers [b]constituted[/b] a proof.
It is hard to correct someone's misconceptions without knowing how and why they believe what they believe. A simple statement that what was posted is not a proof says very little./// We need to know why the OP thought that simply presenting a sequence of numbers [I]might[/i] be a proof.[/QUOTE] one thought I had is that they might think that because you can infinitely add to the representation that it represents and infinite amount of numbers and might intersect the primes infinitely often. 
[QUOTE=science_man_88;412574]one thought I had is that they might think that because you can infinitely add to the representation that it represents and infinite amount of numbers and might intersect the primes infinitely often.[/QUOTE]
Gibberish from someone who hasn't yet passed first year algebra. 
[QUOTE=R.D. Silverman;412575]Gibberish from someone who hasn't yet passed first year algebra.[/QUOTE]
I didn't say it was mathematically sound, I was trying to think like the OP might be thinking. Yet assumes I plan on going back to school again. 
[QUOTE=science_man_88;412576]I didn't say it was mathematically sound, I was trying to think like the OP might be thinking. Yet assumes I plan on going back to school again.[/QUOTE]
Keep out of the discussion until you know what you are talking about. Your comments do not add anything and will only confuse the naiive reader. 
[QUOTE=R.D. Silverman;412577]Keep out of the discussion until you know what you are talking about.
Your comments do not add anything and will only confuse the naiive reader.[/QUOTE]So judgemental. This is the Internet. You have no more say than anyone else. 
I think that's why lots of computational power is used to trial factoring the Mersenne number 2[SUP]2^1271[/SUP]1. Unfortunately there are many people who believe (I do not why) that this particular number is prime.

[QUOTE=retina;412578]So judgemental. This is the Internet. You have no more say than anyone else.[/QUOTE]
An idiotic notion. It implies that you believe that prose from someone who can't write a cogent English sentence and whose knowledge of mathematics is nonsense has the same value as that of an expert. 
[QUOTE=R.D. Silverman;412580]An idiotic notion. It implies that you believe that prose from someone who can't write a cogent English sentence
and whose knowledge of mathematics is nonsense has the same value as that of an expert.[/QUOTE]No. It implies that you don't have any control over people like that and what they write. Trying to censor posters is not the right solution IMO. Better to educate readers and teach them that not everything they read is accurate or true. Encouraging critical thinking is far more valuable than promoting a nanny forum where everything is supposedly controlled. 
[QUOTE=retina;412581]No. It implies that you don't have any control over people like that and what they write. Trying to censor posters is not the right solution IMO. Better to educate readers and teach them that not everything they read is accurate or true. Encouraging critical thinking is far more valuable than a promoting a nanny forum where everything is supposedly controlled.[/QUOTE]
I am not promoting a nanny forum. But new participants (and non native English speakers) whose math backgound is naiive may not be able to discern that SM88 spews nothing but nonsense. And such a person will not have knowledge of SM88's long history of doing so. And SM88's posts in this thread certainly distracts from the goal of trying to lead the OP to some understanding of what constitutes a proof. Indeed, his posts throughout the forum greatly contribute toward doing nothing but increasing the noise. 
[QUOTE=alpertron;412579]I think that's why lots of computational power is used to trial factoring the Mersenne number 2[SUP]2^1271[/SUP]1. Unfortunately there are many people who believe (I do not why) that this particular number is prime.[/QUOTE]
Because it's pretty? Proof by esthetics. :smile: 
This is for the original poster (other people please do not spoil):
Start with the number 41, which is prime. Add the number 2 and you get 43, which is prime. Then add 4 and you get 47 which is prime again. Then add 6 and you get 53 which is prime again. Do this procedure say 30 times and you will always get primes. Now turn off the calculator. Does it mean that this always generates primes? If not, why not? 
[QUOTE=alpertron;412579]I think that's why lots of computational power is used to trial factoring the Mersenne number 2[SUP]2^1271[/SUP]1. Unfortunately there are many people who believe (I do not why) that this particular number is prime.[/QUOTE]
Fortunately, for people who have more than two working brain cells, mathematics is not done by "belief". 
[QUOTE=alpertron;412586]This is for the original poster:
Start with the number 41, which is prime. Add the number 2 and you get 43, which is prime. Then add 4 and you get 47 which is prime again. Then add 6 and you get 53 which is prime again. Do this procedure say 30 times and you will always get primes. [/QUOTE] This does not adequately describe the procedure. You have added 2, then 4, then 6. "Do this 30 times" can be taken to mean, "add 2 then 4 then 6" 30 times. The meaning of the word "this" in your last sentence is not well defined. Math is a language in which it is possible to say [i]exactly[/i] what is meant. [QUOTE] Does it mean that this always generates primes? If not, why not?[/QUOTE] Sigh. You are completely missing the point. I am [b]not[/b] asking the OP to supply missing reasoning. I am asking him/her to explain why merely posting a sequence of numbers without [b]any[/b] given reasoning might constitute a proof. My merely stating that what was presented isn't a proof does not teach anything. Indeed, it would constitute "proof by assertion". I am trying to address the more basic question: "what is a proof?". To do so, we must find out why the OP thought that what was presented is a proof. It isn't that the "reasoning" is wrong. The problem (I am getting repetitive) is that there was no reasoning supplied! 
[QUOTE=R.D. Silverman;412589]This does not adequately describe the procedure. You have added 2, then 4, then 6.
"Do this 30 times" can be taken to mean, "add 2 then 4 then 6" 30 times. The meaning of the word "this" in your last sentence is not well defined. Math is a language in which it is possible to say [i]exactly[/i] what is meant. Sigh. You are completely missing the point. I am [b]not[/b] asking the OP to supply missing reasoning. I am asking him/her to explain why merely posting a sequence of numbers without [b]any[/b] given reasoning might constitute a proof. My merely stating that what was presented isn't a proof does not teach anything. Indeed, it would constitute "proof by assertion". I am trying to address the more basic question: "what is a proof?". To do so, we must find out why the OP thought that what was presented is a proof. It isn't that the "reasoning" is wrong. The problem (I am getting repetitive) is that there was no reasoning supplied![/QUOTE] See: [url]http://www.themathlab.com/geometry/funnyproofs.htm[/url] The given list is incomplete, of course. 
[QUOTE=R.D. Silverman;412589]This does not adequately describe the procedure. You have added 2, then 4, then 6.
"Do this 30 times" can be taken to mean, "add 2 then 4 then 6" 30 times. The meaning of the word "this" in your last sentence is not well defined. [/QUOTE] So if you see in a passtime magazine the sentence fill in the blanks: 2, 4, 6, xx, xx, xx you would not write 8, 10, 12? Come on Bob. This was intended for the OP, not for you. [QUOTE]Sigh. You are completely missing the point. I am [b]not[/b] asking the OP to supply missing reasoning. I am asking him/her to explain why merely posting a sequence of numbers without [b]any[/b] given reasoning might constitute a proof.[/QUOTE] With the sequence of 30 prime numbers, I asked the OP if all the terms in the infinite sequence are prime or not without calculator. Only reasoning. I have to repeat that the OP [u]believes[/u] that the original sequence produces always prime numbers, but he is asking a proof from other people. That's why I presented this simple exercise. 
[QUOTE=alpertron;412592]So if you see in a passtime magazine the sentence fill in the blanks: 2, 4, 6, xx, xx, xx you would not write 8, 10, 12?
[/QUOTE] But this is NOT what you wrote. You gave a procedure, "add 2, then 4, then 6.... Repeat 30 times." Nowhere in your specification of the procedure was there an indication that the addends were supposed to KEEP increasing. I am beginning to think that you have trouble writing clear, unambiguous English. [QUOTE] Come on Bob. This was intended for the OP, not for you. [/QUOTE] This is a forum one of whose purposes is the discussion of mathematics. We have an obligation not to create possible confusion among newbies. This requires that we pose our questions with care. [QUOTE] With the sequence of 30 prime numbers, I asked the OP if all the terms in the infinite sequence are prime or not without calculator. Only reasoning.[/QUOTE] Now I know that you can't write English. "prime or not without calculator" is not a grammatically correct phrase. It is nonsense. What you mean is "prime or not without doing any calculation". or, "without using a calculator" And you are missing the verb "determine", as in "determine whether all the terms........." Learn to proofread what you write! BTW, the discriminant is 163. 
It is clear that I cannot write in perfect English, since this a second language and almost nobody speaks this language near me. But I think that most nonpedantic people can understand what I write. Thanks for the corrections.

[QUOTE=alpertron;412595]It is clear that I cannot write in perfect English, since this a second language and almost nobody speaks this language near me.
[/QUOTE] Please accept my very sincere apology. I was not aware that you were not a native English speaker. mea culpa. Your English is very very good for a nonnative speaker. Certainly much better than my French! [QUOTE] But I think that most nonpedantic people can understand what I write. Thanks for the corrections.[/QUOTE] This is the wrong attitude. My writing teachers made it very clear that when one writes, it is NOT the obligation of the reader to discern what we mean. It is the writer's job to be clear. Furthermore, the nature of mathematics is that it [b]IS[/b] pedantic. 
[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? Try it with how meny primes you like... and with how meny 2^....1 you like... it always works[/QUOTE] Instead of trying it with n = 2, which leads to 3, 7, 127, try it with n = 5, or n = 11, or n = 13, 17, etc. 
[QUOTE=kalikidoom;412554]...(2^(2^(2^n1)1)1)...
I mean... isn't that at least a proof that there's an infinate amout of them? Try it with how meny primes you like... and with how meny 2^....1 you like... it always works[/QUOTE] This is not a good sentence or an argument. First you need to make it understandable. Compare: 1. "It always works for me to go outside without a jacket when I see sun in the window." Nothing to argue about here. "It always works (for you)." Fine! And no one can say  "wait, what if there is rain later in the day?" You've already answered  "It always works (for you)", whatever it means. Maybe the rain works for you; who are we to judge?.. 2. "If I see sun in the window, then there will be no rain today (and therefore I go out without the jacket)." The latter is in fact an argument  it has a premise and it has a conclusion. It is not a true argument, though, because everyone can point out a lot of cases, when you see the sun in the window and there will be rain one hour later. Now, compare: (1) what you wrote is some (charitably speaking) ..."opinion". It is your opinion and it doesn't matter that a) it doesn't mean anything to others, b) it cannot be verified (there is no "if", there is no "then"...) Nothing to discuss there. (2) We can assume that what you actually wanted to write was "If n is prime, then 2^n1 is (always) prime". That is in fact an argument  it has a premise and it has a conclusion. It is not a true argument, because n=11 is prime, but 2^n1 is not prime. (3) We can only guess that furthermore you wanted to write this: "If n is prime and 2^n1 is prime, then 2^(2^n1)1 is (always) prime". Which however is also false: n=13 is prime and 2^n1=8191 is prime, but 2^(2^n1)1 [B]is composite[/B] (because 338193759479 divides it). So, therefore if you [I]wanted[/I] to say "(2)" or "(3)" then what you wanted to say was false; and you cannot use it to build into any theories. (In logic, there is a rule: "from false, anything follows". In other words, when you have a false statement it is as good as no statement at all.) If you wanted to say "(1)", then it simply is meaningless and cannot be meaningfully discussed. 
[QUOTE=Batalov;412608]This is not a good sentence or an argument.
First you need to make it understandable. Compare: 1. "It always works for me to go outside without a jacket when I see sun in the window." Nothing to argue about here. "It always works (for you)." Fine! And no one can say  "wait, what if there is rain later in the day?" You've already answered  "It always works (for you)", whatever it means. Maybe the rain works for you; who are we to judge?.. [/QUOTE] Except that he did not say that it always works for him. He did say "it always works" PERIOD. It would be nice if the OP replied to some of the posts.... 
At this point he should feel like a sheep surrounded by wolves. I do not think he wants to continue discussing here.

[QUOTE=R.D. Silverman;412638]It would be nice if the OP replied to some of the posts....[/QUOTE]
I think he will not. This is deliberately a "stone in the lake thrown" to see how and if the clever people here manage to take it out. As a "proof" (hehe, I like your list!) I will bring the fact that the typos are deliberate, "infinate", "amout", "meny" (repeated). These all are well underlined, and there is no way you miss them; for a nonnative speaker, I immediately go to the dictionary if I don't know the spelling. I am sure I do plenty of grammar mistakes, but I try not to do typing mistakes. Sometimes one typo is cleverer than me and it escapes uncorrected, but never so many in a row, unless they are deliberate. I assume the guy is a frequent on the forum, possibly native speaker, trying to hide himself when throwing stones in the lake... 
[QUOTE=alpertron;412640]At this point he should feel like a sheep surrounded by wolves. I do not think he wants to continue discussing here.[/QUOTE]
Regarding your example, expanding the polynomial x^2 + x + 41. Is there any way to PROOVE this is prime for all integers x between 0 and 39 inclusive, without actually testing or enumerating the range? In other words, is this interesting fact unique or the first of a sequence of such polynomials with all values prime within a significant range? That would be a nice puzzle to ask in this thread. 
[QUOTE=davar55;412647]Regarding your example, expanding the polynomial x^2 + x + 41.
Is there any way to PROOVE this is prime for all integers x between 0 and 39 inclusive, without actually testing or enumerating the range? [/QUOTE] Good question, it was an olympiad problem in 1987, see: [url]http://www.artofproblemsolving.com/wiki/index.php/1987_IMO_Problems/Problem_6[/url] So if we know that the above f(x)=x^2+x+41 is prime for f(0),f(1),f(2),f(3) then we know that it is also prime for f(4),..,f(39). As I can remember there is a proof that there is only a finitely many such n value for that we can apply the statement, and we know all of them. 
See: [url]http://mathworld.wolfram.com/LuckyNumberofEuler.html[/url]

Vaguely related?
[YOUTUBE]3K12i0jclM[/YOUTUBE] (Even if it isn't related, it sure is presented in an entertaining way.) 
You can read more about that on [url]http://mathworld.wolfram.com/PrimeGeneratingPolynomial.html[/url] . But understanding it requires knowledge about Number Theory.
It is interesting to notice that this polynomial generates a lot more primes than random polynomials. This is because the values given by the Euler polynomial are never divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 37. In the case p=2 this is easy to see because f(x) = x^2+x+41 is always odd, so f(x) is never multiple of 2. For the other cases you can use the quadratic formula: x = (1+/ sqrt(14*41)) / 2 (mod p) The argument of the square root is the discriminant: 14*41 = 163 (RDS mentioned this a few posts back). This discriminant must be a square mod p, otherwise we cannot extract the square root mod p and f(x) will not be multiple of p. By using the Jacobi symbol we can check this quickly and find that 163 is not a quadratic residue mod 3, 5, 7, 11, 13, 17, 19, 23, 29 or 37. Since most composite numbers are divisible by small primes and f(x) is never divisible by the numbers shown above, we can conclude that the density of primes is greater for this polynomial. This can be checked experimentally. In general, for most irreducible quadratic polynomial f(x) it can be shown that about half of the primes up to some bound cannot be divisors of f(x), so the density of primes is much greater than for linear polynomials. This is the explanation for the Ulam spiral. Euler polynomial is better yet in terms of density of primes, because of the set of primes not dividing the polynomial shown above. 
You can see on [url]http://www.alpertron.com.ar/ULAM.HTM[/url], the Ulam spiral with the polynomials that generate the diagonals and the prime numbers less than 100 that cannot divide these polynomials. You will notice that when these prime numbers are small, the diagonals have greater density of prime numbers (there are more green dots) on the spiral.

[QUOTE=R. Gerbicz;412652]Good question, it was an olympiad problem in 1987, see: [url]http://www.artofproblemsolving.com/wiki/index.php/1987_IMO_Problems/Problem_6[/url]
So if we know that the above f(x)=x^2+x+41 is prime for f(0),f(1),f(2),f(3) then we know that it is also prime for f(4),..,f(39). As I can remember there is a proof that there is only a finitely many such n value for that we can apply the statement, and we know all of them.[/QUOTE] Let the discriminant of such a polynomial be D. To have a long sequence of consecutive primes Q(sqrt(D)) must have class number 1 (i.e. the imaginary quadratic field must be a UFD). There are only finitely many such. 
[QUOTE=R.D. Silverman;412689]There are only finitely many such.[/QUOTE]
Would that not be better written as "There are only so many finitely defined"? 
[QUOTE=chalsall;412691]Would that not be better written as "There are only so many finitely defined"?[/QUOTE]
negative, misplaced modifier 
[QUOTE=R.D. Silverman;412707]negative, misplaced modifier[/QUOTE]
Please further define. 
[QUOTE=R.D. Silverman;412707]negative, misplaced modifier[/QUOTE]
Still awaiting.... 
[QUOTE=R.D. Silverman;412707]negative, misplaced modifier[/QUOTE]
Mr. Silverman. As you seem to take great joy in challenging others, might you please answer questions presented to you? 
[QUOTE=chalsall;412722]Mr. Silverman. <snip>[/QUOTE]
Chris, that is your fault, you don't know how to make Mr. Silverman reply to your posts. You should say (in reply to the post with discriminant): "Mr. Silverman, I bet you didn't know that, you just read it in the R. Gerbicz's link in post #34" I bet he would reply to that immediately. :razz: 
Donnie comes to mind...
[QUOTE] I know that you know.
And I know that you know that I know that you know.  WTF are you talkin' 'bout?[/QUOTE][YOUTUBE]dbE2VU4SM[/YOUTUBE] 
[QUOTE=chalsall;412711]Still awaiting....[/QUOTE]
An intelligent person might realize that I am not continuously online. I do sleep. The meaning of 'misplaced modifier' should be clear in any language. It certainly applies in French (my second language) as well as English. An adjective or adverb is not placed in the correct position within the sentence. 
[QUOTE=LaurV;412724]I bet he would reply to that immediately. :razz:[/QUOTE]
Thanks for the suggestion. :smile: I very much appreciate Mr. Silverman's input. It might be nice if he learnt how to play well with others. To each their own, of course. (My girlfriend bought me a shirt that reads "Warning: Doesn't play well with others." I regularly wear it.) 
[QUOTE=chalsall;412780]Thanks for the suggestion. :smile:
I very much appreciate Mr. Silverman's input. It might be nice if he learnt how to play well with others. To each their own, of course. (My girlfriend bought me a shirt that reads "Warning: Doesn't play well with others." I regularly wear it.)[/QUOTE] At least you play well with her. I'm sure you both appreciate it. :smile: 
[QUOTE=R.D. Silverman;412741]An adjective or adverb is not placed in the correct position within the sentence.[/QUOTE]
Really? 
[QUOTE=chalsall;412783]Really?[/QUOTE]
:smile: :davar55: 
Hint: compare [SPOILER]"finitely many" and "many finitely"[/SPOILER]

[QUOTE=davar55;412782]At least you play well with her. I'm sure you both appreciate it.[/QUOTE]
Yeah. It's cool. She also bought me a shirt which says "There's no place like 127.0.0.1". Almost nobody gets the joke. 
Ha! That is brilliant!
Note to self: I must order a shirt to say the first text on front and the second one on back. Or viceversa. Or better order two shirts? 
[QUOTE=chalsall;412793]Yeah. It's cool. She also bought me a shirt which says "There's no place like 127.0.0.1".
Almost nobody gets the joke.[/QUOTE] [QUOTE=LaurV;412827]Ha! That is brilliant! Note to self: I must order a shirt to say the first text on front and the second one on back. Or viceversa. Or better order two shirts?[/QUOTE] Were I to get such a shirt, I would be sure it's the updated (and much simpler) version: "There's no place like ::1." 
What about
[QUOTE]There are only 10 kind of people. those who understand binary and those who don't[/QUOTE] 
I know it's 3.14159... in the sky, but how about a bunch of
cool specific # jokes? 
[QUOTE=Dubslow;412836]Were I to get such a shirt, I would be sure it's the updated (and much simpler) version: "There's no place like ::1."[/QUOTE]
[URL]https://www.zerodayclothing.com/products/noplacelike/noplacelike.php[/URL] 
[QUOTE=davar55;412851]I know it's 3.14159... in the sky, but how about a bunch of
cool specific # jokes?[/QUOTE]I'm not sure about my favourite number but am certain about my least favourite: 288 [spoiler]It's just two gross.[/spoiler] 
[QUOTE=davar55;412851]I know it's 3.14159... in the sky, but how about a bunch of
cool specific # jokes?[/QUOTE] What's the last number in Pi? i. (If pie, then "e.") 
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