20160323, 17:06  #23  
Sep 2009
3×659 Posts 
Quote:
Pick any n such that f(n)=p where p is prime. Then f(n+p), f(n+2p), etc will all be divisible by p since each power of x will be the same mod p as it is for f(n). So most values of n will generate a composite (unless it's a constant polynomial which can only generate 1 prime). Chris 

20160324, 19:01  #24  
Banned
"Luigi"
Aug 2002
Team Italia
3×1,597 Posts 
Quote:


20160326, 01:16  #25 
"Matthew Anderson"
Dec 2010
Oregon, USA
1001111100_{2} Posts 
Hi Math People
Attached are slides for my writeup for n^2 + n + 41. I have removed all reference to the word bifurcation. That was incorrect. The points in the graph of divisors lie on parabolas. Regards Matt 
20160419, 08:35  #26 
Mar 2016
2^{3}·37 Posts 
A peaceful day for all members
there are some "new" results for the polynomial f(n)=n^2+n+41 for n<=2^35 http://www.devalco.de/basic_polynomi...a=1&b=1&c=41#7 For people who are not familiar with quadratic prime generators: It is possible to make a sieving construction for quadratic irreducible polynomials like f(n)=n² +1. The Sieve of Eratosthenes is a more specific variation of this construction. Normally the primes with p=f(n) or pf(n) appear double periodically on the polynomial. If you divide the appearing primes you can be sure that there only rest a prime or the number one. Would nice to have a little feedback. The topic is quite interesting for people who look for some prime generators. An overview is in the web under http://devalco.de/#106 Have a lot of fun with the primes Bernhard 
20160430, 07:47  #27 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{2}×3×53 Posts 
Hi Math People,
Thank you for considering my little project. As I have state before the word "bifurcation" was incorrectly used by me to describe a graph. New words are graph of discrete divisors. For what it is worth. Also, Bernhard, your work on seiving and quadratic functions is very interesting. Regards, Matthew 
20170425, 12:42  #28 
"Matthew Anderson"
Dec 2010
Oregon, USA
1001111100_{2} Posts 
primes of the form n^2+n+41
Hi all,
I continue to doodle with h(n). I define h(n) as n^2 + n + 41. We assume n is a positive integer. So far we know that no primes less than 40 ever divide h(n). Also, there are no positive integers n that make 59 divide h(n). We prove these two facts by exhaustive search in a residue table. Some of my progress is shown at this webpage  https://sites.google.com/site/primeproducingpolynomial/ We know that if n is congruent to x mod y and (x,y) is on the curve p(r,c) = (c*x – r*y)2 – r*(c*x – r*y) – x + 41*r^2 = 0 and 0<r<c, c>1 and gcd(r,c) = 1 and all four of r,c,x, and y are integers, then h(n) is a composite number. further, all n such that h(n) is a composite number are probably on p(r,c)=0. Each such pair (r,c) yields integer points on a parabola. Possible next steps  We want to show that h(n) is prime an infinite number of times. p(r,c) is 0 for an infinite number of values x and y. Given that x and y are counting numbers and restrict x and y to be not a solution of p(r,c) = 0, can we infer that there are still an infinite set of pairs (x,y) such that n = x mod y will give us a prime value for h(n)? This seems to be a hard question. Regards, Matt 
20171016, 00:47  #29 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{2}×3×53 Posts 
Hi all,
There are two webpages that I have made regarding Prime Producing Polynomial. The webpages are  sites.google.com/site/mattc1anderson/primeproducingpolynomial sites.google.com/site/primeproducingpolynomial Regards, Matt 
20201103, 22:58  #30 
"Matthew Anderson"
Dec 2010
Oregon, USA
27C_{16} Posts 
Hi again all,
I added a counter example to a conjecture of mine that i about 2 years old. Regarding our Prime Producing Polynomial Project for the enhancement of mathematical trivia database Specifically, counterexample to conjecture about x2_plus_x_plus_41.pdf Cheers, Matt Last fiddled with by MattcAnderson on 20201103 at 22:59 
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