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Metal laboratory sieves An ami shakushi, a Japanese ladle or scoop that may be used to remove small drops of batter during the frying of tempura ancient sieve. A sieve, fine mesh strainer, or sift, is a tool used for separating wanted elements from unwanted material or for controlling the particle size distribution of a sample, using a screen such as a woven mesh or net or perforated sheet ...
In mathematics the Function Field Sieve is one of the most efficient algorithms to solve the Discrete Logarithm Problem (DLP) in a finite field. It has heuristic subexponential complexity. Leonard Adleman developed it in 1994 [ 1 ] and then elaborated it together with M. D. Huang in 1999. [ 2 ]
The techniques of sieve theory can be quite powerful, but they seem to be limited by an obstacle known as the parity problem, which roughly speaking asserts that sieve theory methods have extreme difficulty distinguishing between numbers with an odd number of prime factors and numbers with an even number of prime factors. This parity problem is ...
The quadratic sieve attempts to find pairs of integers x and y(x) (where y(x) is a function of x) satisfying a much weaker condition than x 2 ≡ y 2 (mod n). It selects a set of primes called the factor base, and attempts to find x such that the least absolute remainder of y(x) = x 2 mod n factorizes completely over the factor base.
The Goldston–Pintz–Yıldırım sieve (also called GPY sieve or GPY method) is a sieve method and variant of the Selberg sieve with generalized, multidimensional sieve weights. The sieve led to a series of important breakthroughs in analytic number theory. It is named after the mathematicians Dan Goldston, János Pintz and Cem Yıldırım. [1]
A molecular sieve is a material with pores (voids or holes), having uniform size comparable to that of individual molecules, linking the interior of the solid to its exterior. These materials embody the molecular sieve effect , the preferential sieving of molecules larger than the pores.
The general number field sieve, on the other hand, manages to search for smooth numbers that are subexponential in the size of n. Since these numbers are smaller, they are more likely to be smooth than the numbers inspected in previous algorithms. This is the key to the efficiency of the number field sieve.
The Jurkat–Richert theorem is a mathematical theorem in sieve theory. It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture . [ 1 ] : 272 It was proved in 1965 by Wolfgang B. Jurkat and Hans-Egon Richert .