mersenneforum.org  

Go Back   mersenneforum.org > Math Stuff > Computer Science & Computational Number Theory

Reply
 
Thread Tools
Old 2017-05-13, 11:22   #1
bhelmes
 
bhelmes's Avatar
 
Mar 2016

4508 Posts
Default the multiplicativ structur of the discriminant for quadratic polynomials

A peaceful day for all,

there is a nice table for the discriminant of special quadratic polynomials and their resulting pattern:

http://devalco.de/periodic_system_of...riminants.html

It is a preview and i think their should be some more information added.

Nevertheless for those mathematicans having fun with primes
i try to build up a periodical system which seems to have some relationship with the periodical system of chemical elements.

I have calculated the polynomial f(n)=n²+bn+c in some limits for b and c,
chosen only the polynomials which construct some infinite series of prime numbers, and tried to get a relationship for those discriminants which
consists of two primes and the discriminants with one prime.

Mathematical feedback and suggestion for improvements
are welcome

Greetings from the primes
Bernhard
bhelmes is offline   Reply With Quote
Old 2017-05-13, 11:48   #2
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

Quote:
Originally Posted by bhelmes View Post
A peaceful day for all,

there is a nice table for the discriminant of special quadratic polynomials and their resulting pattern:

http://devalco.de/periodic_system_of...riminants.html

It is a preview and i think their should be some more information added.

Nevertheless for those mathematicans having fun with primes
i try to build up a periodical system which seems to have some relationship with the periodical system of chemical elements.

I have calculated the polynomial f(n)=n²+bn+c in some limits for b and c,
chosen only the polynomials which construct some infinite series of prime numbers, and tried to get a relationship for those discriminants which
consists of two primes and the discriminants with one prime.

Mathematical feedback and suggestion for improvements
are welcome

Greetings from the primes
Bernhard
if you say discriminant = b^2-4c for the first one you get 16-4*(-11) = 16+44=60 not 15. the only reason you can reduce the discriminant to b^2-4c is because a=1 ( aka your polynomials are all monic). in fact any time b is 4 you seem to be reducing it by a factor of 4. edit: and some of these could be changed to other polynomials to compress the n values for the primes for example n²+4n-11 is only odd when n is even in which case you get 4y^2+8y-11. this polynomial will create the same primes as the previous but with fewer values needing to be tested overall ( on average half as many).

Last fiddled with by science_man_88 on 2017-05-13 at 12:17
science_man_88 is offline   Reply With Quote
Old 2017-05-24, 15:43   #3
bhelmes
 
bhelmes's Avatar
 
Mar 2016

23×37 Posts
Default

A peaceful evening for all,

there is a collection of monic quadratic irreducible polynomials f(n)=n^2+bn+c where the discriminant is b^2-4c.

I choose the polynomials with discriminant=p1*p2, where p1 and p2 are primes and add the polynomials with discriminant p1 and p2 :

http://devalco.de/triple_system.php

It seems to be that the three polynomials with discr. = p1*p2, p1 and p2
"contains" all primes.

If someone has a good mathematical proof, it would be nice to get a description.

Have a lot of fun with primes
Bernhard
bhelmes is offline   Reply With Quote
Old 2017-05-27, 01:33   #4
MattcAnderson
 
MattcAnderson's Avatar
 
"Matthew Anderson"
Dec 2010
Oregon, USA

2·11·29 Posts
Default

Hi Bernhard and everybody,

I appreciate the work you did on your webpage Bernhard. I was able to scroll down and choose a polynomial and then see the sequence when the input is an integer.

Keep up the good work.

Regards,
Matt
MattcAnderson is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
QS polynomials Till Factoring 5 2018-02-12 16:30
Polynomial Discriminant is n^k for an n-1 degree polynomial carpetpool Miscellaneous Math 14 2017-02-18 19:46
SNFS polynomials. chris2be8 FactorDB 1 2012-03-10 16:49
SNFS polynomials for k*b^n+-1 mdettweiler Factoring 15 2010-01-14 21:13
Polynomials and Probability Orgasmic Troll Puzzles 4 2003-09-16 16:23

All times are UTC. The time now is 23:53.

Wed Jan 20 23:53:53 UTC 2021 up 48 days, 20:05, 0 users, load averages: 1.22, 1.56, 1.60

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.