## 18. The integral mean value and the absolute error function R

In this post we'll apply the mean value Theorem for integrals in order to transform what we know about the…

## Origins of the two Goldbach’s conjectures

Background Europe, 18th century. While the Western powers were all a flourishing of industries, cultural exchanges and scientific discoveries, the…

## 17. The functions W and V

The general idea of the Prime Number Theorem proof consists in starting from the proof of Chebyshev's Theorem (strong version),…

## 16. The prime number Theorem: history and statement

Looking at a prime numbers table, it's very simple to notice how their distribution seems to escape any regularity; instead…

## 15. Chebyshev’s Theorem: strong version

In this post we'll revisit Chebyshev's Theorem, according to which the function π(x), that counts the number of prime numbers…

## 13. The factorial function and the Lambda* function

Almost certainly you already know the factorial function, indicated by x!, which is read as "x factorial" and for an…

## 12. From integer numbers to real numbers – second part

In this post we'll see a technique that will let us overestimate or underestimate a value assumed by a function…

## Study of existence of complementary space pairs based on dashed line of second order

Prerequisites: Dashed line theory definitions and symbols Our proof strategies Proof strategy based on dashes Characterization of spaces The purpose…