We introduce a variant of the large sieve and give an example of its use in a sieving problem. Take the interval [N ] = {1, . . . , N} and, for each odd prime p 6 √ N , remove or “sieve out” by all n whose reduction n(mod p) lies in some interval Ip ⊆ Z/pZ of length (p−1)/2. Let A be the set that remains: then |A| ≪ N log N , a bound which improves slightly on the bound of |A| ≪ N logN which re...

The ability of aphids to detect and find sieve tubes suggests that aphids receive cues for sieve-tube recognition by taking samples. Specific natural conditions such as pH value, sugar species and concentration, viscosity, and oxygen pressure may enable sieve-tube detection. We tested the preference of Megoura viciae and Myzus persicae for potential plant-borne orientation parameters in artific...

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...

A prime number sieve is an algorithm for finding all prime numbers in the range [2,n]. For large n, however, the actual run time of existing algorithms on a single processor computer is prohibitive. Fortunately, the classic Sieve of Eratosthenes and its extensions are suitable for massively parallel architectures or networks of workstations. Two mappings of the third extension sieve are present...