Can Diophantine Equations Determine When an Equation is Prime?

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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