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The sieve of Eratosthenes can be expressed in pseudocode, as follows: [8] [9] algorithm Sieve of Eratosthenes is input: an integer n > 1. output: all prime numbers from 2 through n. let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true.
Compared with the CLOCK eviction algorithm, retained objects in SIEVE stay in the old position. Therefore, new objects are always at the head, and the old objects are always at the tail. As the hand moves toward the head, new objects are quickly evicted (quick demotion), which is the key to the high efficiency in the SIEVE eviction algorithm.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
The oldest known method for generating a list of primes is called the sieve of Eratosthenes. [127] The animation shows an optimized variant of this method. [128] Another more asymptotically efficient sieving method for the same problem is the sieve of Atkin. [129] In advanced mathematics, sieve theory applies similar methods to other problems ...
The Legendre sieve has a problem with fractional parts of terms accumulating into a large error, which means the sieve only gives very weak bounds in most cases. For this reason it is almost never used in practice, having been superseded by other techniques such as the Brun sieve and Selberg sieve. However, since these more powerful sieves are ...
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Modern sieves include the Brun sieve, the Selberg sieve, the Turán sieve, the large sieve, the larger sieve and the Goldston–Pintz–Yıldırım sieve. One of the original purposes of sieve theory was to try to prove conjectures in number theory such as the twin prime conjecture. While the original broad aims of sieve theory still are ...
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