What is the ratio of number of prime to number of natural numbers $\Bbb{P}$ is the count of prime numbers in $\Bbb{Z}$
And so, $\Bbb{Z}-\Bbb{P}=NP$ is the count of non-prime numbers in $\Bbb{Z}$
what is the answer of this equation: $\Bbb{P} / NP$
I thought that question and I made that proof, if I'm mistake please correct me.
$E=$Even, $O=$Odd
$1, 2, 3, 4, \cdots \Bbb{Z}$
$O, E, O, E, \cdots$  
Clearly there is $\Bbb{Z}/2$ count of Even, and $\Bbb{Z}/2$ count of Odd numbers exist.
If any number in $\Bbb{Z}$ can write as $M \times N$ it is non-prime number, otherwise it's prime number $M \times N$ can be one of that $4$ combinations:
$E \times E = E$
$E \times O = E$
$O \times E = E$
$O \times O = O$  
So, $M \times N$ is $\frac{3}{4}$ in ratio of Even numbers, and $\frac{1}{4}$ ratio of Odd.
Even Numbers: $\frac{3}{4}$ * NP
Odd Numbers:  $\frac{1}{4}$ * NP  
Even Numbers: $0 * P$
Odd Numbers : $P$  
There is equal counts of even and odd numbers, so;
$\frac{3}{4} * NP + 0 = 1/4 * NP + P$
$\frac{1}{4} * NP = P$
$NP = 2 * P$  
If this equation is true, then non-prime numbers are only double-times of prime numbers. Please check my proof.
 A: "$P$ is the number of prime numbers in $Z$" makes no sense until you develop a theory of infinite numbers. Such a theory was developed by Cantor in the late 19th century. When you learn it, you will find that the number of integers, the number of even integers, the number of odd integers, the number of primes, and the number of non-primes are all the same; they are all what is called $\aleph_0$, which we read as "aleph-zero" or "aleph-nought". 
A: I don't exactly follow your logic, and your conclusion is incorrect, but you may be interested to know that this is a historic problem which spurred a lot of developments in analytic number theory up through the nineteenth century, and is intimately related with such famous problems as the Riemann Hypothesis.
Unfortunately, a simple counting argument like yours won't be powerful enough to do the job. You should have a look at the Prime Number Theorem, which is essentially an answer to the question that you posed. It states that the number of primes below $x$, which we write $\pi(x)$, has a growth rate on par with the function $x/\ln x$.
A: Wow, that was some of the most over garbled and over explained thinking I've seen, no wonder you got lost. I'm thinking this was put here as a troll!
You eventually determined that prime numbers are always an odd number.
"1/2" at the most "1/3" at what point is it "1/4" at what point is it "1/5". 
You didn't flesh out how often an odd number is a prime number. This is the only critical part of determining the "Diminishing" ratio and you simply skipped it.
Please think beyond what you think you've learnt and actually process what you're doing.
You can't rely on pre-formulated deductions and then go around asking other people for the answer with out understanding where it came from.
Knowledge is empty without comprehension. And it's obvious you're not comprehending what it is you're asking for.
Cheers.
PS. In determining this ratio, you also determine why bigger machines are less efficient and why quad core processors work better on 4 separated streams as opposed to one task or why 4 wheels of a car can't hold 4 times the weight 1 wheel can.
A: I think the most usual way of thinking about this is to find
$$
\lim_{n\to\infty} \frac{\text{number of positive prime numbers}\le n}{\text{number of positive integers}\le n}.
$$
The limit is $0$.
This depends on listing the numbers in their usual order.  Suppose one writes them in this different order:
$$
\text{1st prime number}, \text{first non-prime number}, \text{second prime number}, \text{second non-prime number}, \text{third prime number}, \text{third non-prime number}, \ldots.
$$
Then the limit would be $1/2$.
Later note:  See this article:
"An Elementary Proof that Primes are Scarce", by E. L. Spitznagel Jr., American Mathematical Monthly, volume 77, number 4, April 1970, pages 396--397. jstor.org/stable/2316153 
