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REM Eratosthenes Sieve Prime Number Program in BASIC 1 SIZE = 8190 2 DIM FLAGS (8191) 3 PRINT "Only 1 iteration" 5 COUNT = 0 6 FOR I = 0 TO SIZE 7 FLAGS (I) = 1 8 NEXT I 9 FOR I = 0 TO SIZE 10 IF FLAGS (I) = 0 THEN 18 11 PRIME = I + I + 3 12 K = I + PRIME 13 IF K > SIZE THEN 17 14 FLAGS (K) = 0 15 K = K + PRIME 16 GOTO 13 17 COUNT = COUNT + 1 ...
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.
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.
Sieve method, or the method of sieves, can mean: in mathematics and computer science, the sieve of Eratosthenes, a simple method for finding prime numbers in number theory, any of a variety of methods studied in sieve theory; in combinatorics, the set of methods dealt with in sieve theory or more specifically, the inclusion–exclusion principle
The sieve methods discussed in this article are not closely related to the integer factorization sieve methods such as the quadratic sieve and the general number field sieve. Those factorization methods use the idea of the sieve of Eratosthenes to determine efficiently which members of a list of numbers can be completely factored into small primes.
In this example the fact that the Legendre identity is derived from the Sieve of Eratosthenes is clear: the first term is the number of integers below X, the second term removes the multiples of all primes, the third term adds back the multiples of two primes (which were miscounted by being "crossed out twice") but also adds back the multiples ...
Just use three colours, one for the number used is the current step of the sieve, one for non-primes and then one for primes. And highlight clearly you start fron n 2 when using n in the sieve by making the number flash or something. C e n t y 22:02, 28 September 2007 (UTC) Oppose per centy.
Sieve is a C++ compiler that will take a section of serial code, which is annotated with sieve markers, and parallelize it automatically. The programmer wraps code they wish to parallelise inside a lexical scope, which is tagged as 'sieve'. Inside this scope, referred to commonly as a 'sieve block', certain rules apply :