A prime sieve is an algorithm that finds the primes up to a bound n. We say that a prime sieve is incremental, if it can quickly determine if n+1 is prime after having found all primes up to n. We say a sieve is compact if it uses roughly √ n space or less. In this paper we present two new results: • We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log logn) ti...

In the past decade or so, the most elementary of the sieve methods of analytic number theory has been adapted to a geometric setting. In this geometric setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over Z. We will present the method and some of the results that have been proved using it. For instance, the prob...

Introduced by Xenakis 50 years ago, sieves have proved to be a relevant and robust device for music composition. Examples of complex and symmetric sieves usage in original works are presented along with a few possible applications not explored before. The dichotomy between predetermined abstract structures such as sieves and their actualization through random procedures is discussed and it is a...

Carbon Molecular Sieves (CMS) are unique materials which are widely used in processes based on pressure swing adsorption (PSA) for nitrogen generation by oxygen removal from air [1, 2, 3] and for the enrichment of methane from biogas or landfill gas [4]. Steadily improved CMS were launched in the last years to cover these applications. The recent materials are characterized by higher sorption c...

Preface These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January–June 2002. The notes were taken by Boris Moroz, and it is a pleasure to thank him for writing them up in the current form. In addition, thanks are due to the institute for its hospitality and fi...

We are motivated by a tantalizing open question in exact algorithms: can we detect whether an n-vertex directed graph G has a Hamiltonian cycle in time significantly less than 2? We present new randomized algorithms that improve upon several previous works: a. We show that for any constant 0 < λ < 1 and prime p we can count the Hamiltonian cycles modulo p n 3p ⌋ in expected time less than c for...