Our proof strategies: an overview
Prerequisite: Goldbach’s conjecture As already indicated, our ultimate goal is to use dashed line theory to prove Goldbach’s conjecture. Dashed…
Multa non quia difficilia sunt non audemus sed quia non audemus sunt difficilia
Tag: prime number
Factorizer
This page allows performing the decomposition of a number into its prime factors, and computing the value of some arithmetic…
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…
The factorial function and the Λ* function
Almost certainly you already know the factorial function, indicated by x!, which is read as "x factorial" and for an…
Chebyshev’s Theorem (weak version)
With this post we begin an analytical study of the function pi(x), that returns the number of primes less than…
The product of the first prime numbers: an underestimation
We saw that the product of the first prime numbers can be overestimated by a function of exponential kind with…
The least common multiple of the first positive integers
We know that a way to compute the least common multiple between two or more integer numbers is based on…
1. From prime numbers to dashed lines
A dashed line can be represented as a table having a fixed number of rows, and, potentially, infinite columns, numbered…
The product of the first prime numbers: an overestimation
A way to start investigating the sequence of prime numbers is to consider, starting from the beginning, portions of increasing…
The definition of prime number
We'll start our study of prime numbers explaining the definition of prime number. It's commonly known that a prime number…
Some important results
The statement phrased by Christian Goldbach is a "conjecture", so, as a matter of principle, it is a hypothesis. This…