The sieve is a morphological scale-space operator that filters an input signal by removing intensity extrema at a specific scale. In images, this processing can be carried out along a path -the 1D sieveor over a connected graph -the 2D sieve. The 2D version of the sieve generally performs better; it is however much more complex to implement. In this paper we present the 1.5D sieve, a Hamiltonia...

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 this paper, I explain the Quadratic Sieve, its Multiple Polynomial variation, the Number Field Sieve, and give some worked examples of the afore-mentioned algorithms. Using my own Maple implementation of the Quadratic Sieve, I explore the effect of altering one of the parameters of the Quadratic Sieve algorithm, with respect to both time and success rate.