Two Compact Incremental Prime Sieves

Trading Time for Space in Prime Number Sieves

A prime number sieve is an algorithm that nds the primes up to a bound n. We present four new prime number sieves. Each of these sieves gives new space complexity bounds for certain ranges of running times. In particular, we give a linear time sieve that uses only O(p n=(log log n) 2) bits of space, an O l (n= log log n) time sieve that uses O(n=((log n) l log log n)) bits of space, where l > 1...

Improved incremental prime number sieves

An algorithm due to Bengalloun that continuously enumerates the primes is adapted to give the rst prime number sieve that is simultaneously sublinear, additive, and smoothly incremental: { it employs only (n= log log n) additions of numbers of size O(n) to enumerate the primes up to n, equalling the performance of the fastest known algorithms for xed n; { the transition from n to n + 1 takes on...

Two Fast Parallel Prime Number Sieves

Progress in heteroatom - containing aluminophosphate molecular sieves

Over the past 30 years, heteroatom-containing aluminophosphate molecular sieves as a prime class of heterogeneous single-site solid catalysts have been quickly developed since the first discovery of aluminophosphate molecular sieves in 1982, and a large variety of such materials with 48 unique zeotype structures have been prepared. This work mainly presents the progress in the development of he...

Quantum Unique Ergodicity for Locally Symmetric Spaces Ii

We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients Γ\G/K, where G ' PGLd(R), K is a maximal compact subgroup of G and Γ < G is a lattice associated to a division algebra over Q of prime degree d. The primary novelty of the present paper is a new method of proving positive entropy of quantum limits, which avoids s...