0
   

Ellipses and hyperbolas of decompositions of even numbers into pairs of prime numbers.

 
 
Reply Fri 21 Apr, 2023 02:13 pm
This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.
Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.

1. The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n

2. The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n

where p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),
k and t are indices of prime numbers,
2n is a given even number,
k, t, n ∈ N.

If we construct ellipses and hyperbolas based on the above, we get the following:

1. There are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.

2. There is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.

Will there be any new thoughts, ideas about this?
Here is an article on the subject Edit [Moderator]: Link removed
  • Topic Stats
  • Top Replies
  • Link to this Topic
Type: Discussion • Score: 0 • Views: 327 • Replies: 0
No top replies

 
 

Related Topics

Countdown (or Up) Your Music Mof--kas! - Question by tsarstepan
Seven Million Posts Approaching - Discussion by Sturgis
Help with this number riddle - Question by dontspotmepls
Writing with numbers question - Question by jessoftherose
Palindrome time - Discussion by TomTomBinks
Meaning of these numbers - Question by andyr25
infinity1<>infinity2? - Question by hamilton
numerology - Question by dyslexia
 
  1. Forums
  2. » Ellipses and hyperbolas of decompositions of even numbers into pairs of prime numbers.
Copyright © 2024 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.03 seconds on 05/30/2024 at 07:29:00