20151013, 16:08  #23  
Aug 2002
Buenos Aires, Argentina
5×269 Posts 
Quote:
This was intended for the OP, not for you. Quote:
Last fiddled with by alpertron on 20151013 at 16:20 

20151013, 16:29  #24  
Nov 2003
2^{2}×5×373 Posts 
Quote:
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:
not to create possible confusion among newbies. This requires that we pose our questions with care. Quote:
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. 

20151013, 16:48  #25 
Aug 2002
Buenos Aires, Argentina
10101000001_{2} Posts 
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.
Last fiddled with by alpertron on 20151013 at 16:48 
20151013, 17:01  #26  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Your English is very very good for a nonnative speaker. Certainly much better than my French! Quote:
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 IS pedantic. 

20151013, 17:25  #27 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2×7×677 Posts 
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.

20151013, 19:49  #28  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,347 Posts 
Quote:
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 is composite (because 338193759479 divides it). So, therefore if you wanted 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. Last fiddled with by Batalov on 20151013 at 19:51 

20151014, 12:58  #29  
Nov 2003
2^{2}·5·373 Posts 
Quote:
It would be nice if the OP replied to some of the posts.... Last fiddled with by R.D. Silverman on 20151014 at 12:59 

20151014, 13:20  #30 
Aug 2002
Buenos Aires, Argentina
5·269 Posts 
At this point he should feel like a sheep surrounded by wolves. I do not think he wants to continue discussing here.

20151014, 13:20  #31 
Romulan Interpreter
Jun 2011
Thailand
3^{3}·347 Posts 
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...

20151014, 13:58  #32  
May 2004
New York City
2^{3}×23^{2} Posts 
Quote:
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. 

20151014, 14:19  #33  
"Robert Gerbicz"
Oct 2005
Hungary
2·727 Posts 
Quote:
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. 

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