20131105, 06:25  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
5·233 Posts 
prime producing polynomial x^2 + x + 41
Hello Internet Mathematical Community,
I want to mention a little webpage that I recently got off my chest. https://sites.google.com/site/mattc1...ingpolynomial Surely these few lines do not do it justice. (RDS please hold your silence) Regards, Matt A. 
20131105, 13:11  #2  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·3·311 Posts 
Quote:
The polynomial you cite has been well studied. What do you hope to add or contribute? If you are really interested in the mathematics that is associated with this polynomial, then you need to study why the fact that Q(sqrt(163)) has class number 1 is fundamental to the study of this polynomial. Indeed. Do you even know where the number 163 comes from in this context?? Do you know what a class number is? Before you try to discuss this polynomial you need to learn some of the math behind it. If you can't be bothered to do that then please stop the discussion. I would start by reading the Hardy & Wright chapter on quadratic fields. You then need to study binary quadratic forms, composition of forms, class numbers and genera. Harvey Cohn wrote an excellent book: "Advanced Number Theory" [Dover!] discussing all of these things. I can recommend other books on algebraic number theory as well if you like. 

20131105, 15:49  #3  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,901 Posts 
Quote:
Matt, just because you don't understand a word of what RDS is saying doesn't give you right to shut him up. Indeed, these few lines don't do the subject any justice. Why don't you first read mathworld, wikipedia, OEIS, etc? What are you planning to add to what is already known, and how? 

20131106, 01:48  #4 
"Matthew Anderson"
Dec 2010
Oregon, USA
5·233 Posts 
Hi,
I have noticed some properties of the polynomial expression x^2 + x + 41, which I will call h(x). For example, this expression is never divisible by a positive integer less than 40. Here is why. Using an even and odd argument, we can show that h(x) is never divisible by 2. If the input, x, is even, then h is odd. Similarly, if the input, x, is odd, then h is again odd. And odd numbers are not divisble by two. Also, an argument with divisibility by three can be made. No matter if x is 0,1,or 2 mod 3 the output is never 0 mod 3. And so on with the primes up to 40. If h(x) is not divisible by any primes below 40, then it is not divisible by any counding number less than 40. Please let me know if you understand so far. Regards, Matt Also, the power point document linked above is again linked here  https://docs.google.com/viewer?a=v&p...I4ODU1NWQ5ZDk1 For what its worth, M.C.A. 
20131106, 03:43  #5 
Aug 2006
3·1,993 Posts 
This is easy to see. If it were in a math paper this wouldn't even get a proof, just a line "By modular considerations, we can see ...".
Last fiddled with by CRGreathouse on 20131106 at 03:45 
20131106, 13:26  #6  
"Bob Silverman"
Nov 2003
North of Boston
1110100101000_{2} Posts 
Quote:
The coefficients are positive and f(x) := x^2 + x + 41 is trivially greater than 43 for x > 1. Further for ANY polynomial g(x), if a  g(x) then a  g(x + k*a) for all k \in Z. 

20131106, 18:14  #7 
"Matthew Anderson"
Dec 2010
Oregon, USA
5·233 Posts 
Thank you for the constructive feedback.
And also, I have read the three references suggested in the thread. So much for this dead project. Regards, Matt 
20131107, 12:18  #8  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×3×311 Posts 
Quote:
H. Cohn's entire book. And yes. I know the likelihood that you will take my advice. People in this thread seem to view the actual LEARNING of mathematics as a chore to be avoided. 

20131107, 18:30  #9 
"Forget I exist"
Jul 2009
Dumbassville
2×5×839 Posts 
miscellaneous math is a subforum, but if you teach my pharmaceutical calculations teacher ( or professor) how to do 60/40 in their head so they can teach me I'll be fine with that. I tend to shortcut to get the answer quicker for some of what we are doing.
Last fiddled with by science_man_88 on 20131107 at 18:34 
20131108, 09:05  #10 
"Nathan"
Jul 2008
Maryland, USA
45B_{16} Posts 
Able me no parse to text this. In other words, say what?!

20131108, 11:39  #11 
"Forget I exist"
Jul 2009
Dumbassville
20306_{8} Posts 

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