Unsolved Mystery of Prime Numbers: Why Is It So Hard?

AI Thread Summary
Prime numbers continue to pose a significant mathematical challenge, particularly in finding a definitive pattern or analytical expression for the distribution of primes. While it is relatively straightforward to write code that identifies prime numbers and calculates P(n), the function representing the count of primes less than or equal to n, the core issue remains the absence of a closed-form solution for P(n). Current approaches yield statistical approximations but fail to provide an exact formula, highlighting the complexity and ongoing mystery surrounding prime numbers.
quddusaliquddus
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Hi,
Let's talk about Prime Numbers. Still an unsolved mystery, I don't understand why it's still unsolved. Has anyone discovered why its hard to find a pattern? Or is this a silly question?
 
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What do you mean, hard to find a pattern? I can write a few lines of code to find all the primes. The divisions can take ages for the larger primes, but the pattern of code is very simple.
 
You can define a function of numbers P(n), which is the number of primes less than or equal to n. So P(3) is 2, because there are two primes (2 and 3) less than or equal to 3. P(10) is 4. And with a programmed filter you can evaluate P(n) for any given n.

The problem, however is to find an analytical expression for P(n). And that is the one that is unsolved. They have good statistical approximations, but no closed form solution.
 
I don't mean code.
Thanks guys.
 

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