I was learning about this 3 years ago. i expected to at least understand the question in a exact way. However, i tried simple questions, like equations instead of symbols. Then i found examples of execution time and complexity structures. 
My first question was: How you get 
$$sin(\Gamma^{2}(n))$$
In first step it's not a decision problem, rather a power question. ¿How fast can i get the image? i asked myself. and here is where NP gets in. The decision problem with exponential complexity needs to be reduced to polynomial time by a deterministic algorithm. so then, it's just equal to reduce polynomial to logarithm time. So i wondered, how is it possible?
In my Bachelor's Thesis i found that complex analysis can answer this question where the float-output equation can't handle the calculus of image. Looks like you reduce space complexity to find the output using complex numbers in the case of:
$$
[
f(z_{o}) = \int_U f(z) \frac{1}{z - z_o} \,\mathrm{d} z
]\
$$
Where H(z) is in [1]
In a traditional case, find primes is slow, instead, using cauchy's integral is possible to find them faster with some effort.
Bibliography:
[1] Connes, A. (2019). Around Wilson's theorem. Journal of Number Theory, 194, 1-7.

I was learning about this 3 years ago. i expected to at least understand the question in a exact way. However, i tried simple questions, like equations instead of symbols. Then i found examples of execution time and complexity structures. 

My first question was: How you get 
$$sin(\Gamma^{2}(n))$$

In first step it's not a decision problem, rather a power question. ¿How fast can i get the image? i asked myself. and here is where NP gets in. The decision problem with exponential complexity needs to be reduced to polynomial time by a deterministic algorithm. so then, it's just equal to reduce polynomial to logarithm time. So i wondered, how is it possible?

In my Bachelor's Thesis i found that complex analysis can answer this question where the float-output equation can't handle the calculus of image. Looks like you reduce space complexity to find the output using complex numbers in the case of:

$$
\[
f(z_{o}) = \int_U  f(z) \frac{1}{z - z_o} \,\mathrm{d} z
]\
$$
Where H(z) is in [1]

In a traditional case, find primes is slow, instead, using cauchy's integral is possible to find them faster with some effort.

Bibliography:

[1] Connes, A. (2019). Around Wilson's theorem. Journal of Number Theory, 194, 1-7.

The P=NP problem could be solved, some theory about