An overestimate of the number of Goldbach couples
Given an even number N > 2, we'll call Goldbach pairs for N the pairs of prime numbers the sum…
Multa non quia difficilia sunt non audemus sed quia non audemus sunt difficilia
Category: Sieve theory
Selberg’s sieve: generalization and conclusion of the proof
This article concludes the "technical" part of the proof of Selberg's sieve and lays the foundation for the applications that…
Selberg’s sieve: study of the error term
We have seen that, thanks to Selberg's sieve, an estimate of a sieve function can be calculated; this estimate is…
Selberg’s sieve: study of the parameters λ
As we have seen, some parameters λd appear in the Selberg's sieve formula, which are used both in the estimation…
Selberg’s sieve: statement and beginning of the proof
In this article we'll begin to get to the heart of sieve theory, analyzing in detail the so-called "Selberg's sieve".…
Why don’t algorithmic approaches work well in sieve theory? (part II)
In the previous article we calculated the sieve function of Erathostenes' sieve starting from the algorithm, obtaining a formula with…
Why don’t algorithmic approaches work well in sieve theory? (part I)
In the previous article we examined in detail the sieve of Eratosthenes, both at an algorithmic level and as a…
The sieve of Erathostenes and the formal definition of sieve
In this article we'll explain what a sieve is, based on the most famous example, the sieve of Eratosthenes. It…
Chen’s Theorem: statement and introduction to the proof
Chen's Theorem is one of the closest theorems most similar to Goldbach's Conjecture known so far. It is the work…
Bidimensional sieve of Eratosthenes
This page allows viewing a “bidimensional” version of the sieve of Eratosthenes applied to a given number. Differently from its…
Molte cose non è perché sono difficili che non osiamo farle,
ma è perché non osiamo farle che sono difficili
Many times, it is not because things are difficult that we do not dare,
but it is because we do not dare that things are difficult
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