Imaginary prime number divisor

  • Thread starter Thread starter thedragonbook
  • Start date Start date
  • Tags Tags
    Imaginary Prime
AI Thread Summary
The discussion revolves around the hypothetical implications of an imaginary number that could divide a prime number, distinct from the mathematical concept of the imaginary unit "i." Participants question whether this concept must be limited to imaginary numbers or if it can include any complex numbers, referencing the factorization of integers using Gaussian integers. The conversation touches on how Gaussian integers can reveal interesting number theoretic properties, such as expressing certain primes as sums of two squares. Ultimately, the discussion concludes that if the concept is purely imaginative, it lacks mathematical validity. The thread is locked due to the nature of the topic being deemed non-mathematical.
thedragonbook
Messages
24
Reaction score
0
What would be the implications of assuming the existence of an imaginary number that can divide a prime number and is related to the number it is dividing? By imaginary I mean a number that is just in our imagination and not the imaginary number "i".
 
Last edited:
Mathematics news on Phys.org
The question is a little weird. Does it have to be an imaginary number or can it be any complex number? For example 2 = (1+i)(1-i).The Gaussian integers which are all numbers of the form a+bi for a and by integers form a ring which can be used to deduce some interesting number theoretic facts, for example every prime equivalent to 1 mod 4 can be expressed as the sum of two squares

http://en.wikipedia.org/wiki/Gaussian_integer
 
I don't mean the imaginary number "i". I meant to say some thing that is just an idea - an imagination.
 
thedragonbook said:
I don't mean the imaginary number "i". I meant to say some thing that is just an idea - an imagination.

Well, then it's not math. Locked.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

B Why are imaginary numbers called "imaginary"? If they really exist
Replies
8
Views
2K
B How does the Riemann Hypothesis/Riemann Zeta function even work?
Replies
17
Views
919
B What is the Difference between imaginary part and imaginary number?
Replies
2
Views
2K
B Imaginary Pythagorus
Replies
12
Views
228
B Are All Imaginable Integer Series Necessarily Infinite?
Replies
17
Views
2K
A Is it required to use the Reimann function to solve the problem?
Replies
8
Views
1K
A Proving Goldbach's conjecture by induction (or why it doesn't seem to work)
Replies
10
Views
2K
MHB Solution to the Riemann Hypothesis in plain English
Replies
5
Views
3K
I Simplest self-contained numeral system for complex numbers?
Replies
8
Views
2K
MHB -c5.LCM and Prime Factorization of A,B,C
Replies
3
Views
987

Hot Threads

Recent Insights

Back
Top