Can Diophantine Equations Determine When an Equation is Prime?

  • Context: Undergrad 
  • Thread starter Thread starter ~Death~
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Discussion Overview

The discussion revolves around the potential for Diophantine equations to determine when an equation is prime. Participants explore the feasibility of writing an article on this topic, considering both personal experiences and the mathematical implications of Diophantine equations in relation to prime numbers.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses a desire to write an article based on their programming work with Diophantine equations and their potential link to prime numbers.
  • Another participant advises caution regarding the correctness of results before submitting any work for publication.
  • A different participant mentions that while there are sets of Diophantine equations that could define prime numbers, no known solutions have been found for these sets.
  • The original poster reflects on their academic progress and seeks additional ideas for writing topics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the viability of using Diophantine equations to determine prime numbers, and the discussion includes both encouragement and skepticism regarding the topic.

Contextual Notes

There are limitations regarding the current understanding of Diophantine equations and their relationship to prime numbers, as well as the personal experience level of the original poster.

~Death~
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I've always wanted to write an article for an undergrad math journal- i had a friend who did it

and I am kind of jealous lol

ive programmed in python a simple program that finds and counts the solutions to a diophantine equation

and I'm wondering if I found the set of solutions that determines when an equation

f(x,y) is prime

would that be enough to write something?

Or would i just get laughed at ?
 
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I would be very careful that the result is correct before sending it in.
 
ok thanks

itd definitely take me awhile and id make sure it was correct

maybe if anyone has other ideas on what i could try and write on

i mean i only just finished 2nd year so maybe I am getting a bit ahead of myself
 
There are a number of sets of diophantine equations where all solutions define prime numbers and all prime numbers have corresponding solutions, but afaik no one has found a solution for even one of these sets. good luck
 

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