Math Is Fun Forum

Happy new year (january, 2, 18:20)!
The prime are really disorsered. As pi man said "Brilliant minds have spent countless hours on this ..." I either don't think some pattern ever exists.
I may be wrong, but changing the base may help in some cases, but it's a special case of the number theory with congurents. I think the prime numbers should have some fractal properties, in some system, not the usual, but based on another mathematical rule. For example, there's a theorem (which I rediscovered before knowing it's been already discovered), saying that every integer can be represented in an unique way as a sum of non-succesive numbers of Fibonacci. I think this, because of some requrrent definitions and properties of the prime numbers, such as the Erastrotenes sieve.
And another - I don't think that many of the results will be computer-generated. For a theorem to be proved, it isn't sufficient to be true for numbers up to a million, nor up to 10^million. You need a proof.
Nowadays, there are some very interesting results about prime numbers, involving contemporary mathematics, such as integrals, fields, modular functions. Every "spheres" of maths are connected. I like the analytical number theory, but i don't understand not a bit of it.
And there are some general unsolved hypotesis, which, when proved, will have general consequenses to all fields in mathematics.
Some of the most popular are the Riemann's hypothesis and ABC conjecture.
I think we haven't mathematically "grown" enough to understand all the proprties of the prime numbers. But I think that some day we will. And I hope to be soon.

Yep.
If the test consisted 1 question with 28000 answers and the student didn't knew anything

But not the craziest.

Couldn't you give some information about this inequality.
I have't heard it before.

I really like this

These formulas are based on modular forms. They are the best known series for computing pi.

It's too hard to be simplified. But it can be proved:

mh.
And what does this DRASTIC?

Exactly. In general.

The L function is the result.
In the above plot the ponts represent the information given by Ricky in his post. So the L functtion is the answer.
The S function was defined by me to help myself. It gives "the number of leafs of depth k in the characteristic tree of the problem".
I'm not sure you'll undersand this, because i can't explain it. I've made to pictures for me, but I'll post them.
The E function is a mathematical function:
http://mathworld.wolfram.com/En-Function.html

Hi Aspen.
I don't think the place of this topic is in the "help me" section.
Could someone mode it to the guestbook, please?