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

[quddusaliquddus]

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?

 

[Adam]

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.

 

[selfAdjoint]

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.

 

[quddusaliquddus]

I don't mean code.
Thanks guys.