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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.
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 ...
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.
This sample program implements the Sieve of Eratosthenes to find all the prime numbers that are less than 100. NIL is the ALGOL 68 analogue of the null pointer in other languages. The notation x OF y accesses a member x of a STRUCT y .
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.
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
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 ...
1000 rem sieve of eratosthenes 1010 rem modified from quick basic math project demo 1020 rem 2010 rem l is the limit of the sieve 2020 rem we will find all prime numbers up to l 2030 let l = 1000 2040 rem n is the sieve itself 2050 dim n (1000) 2060 rem fill the sieve with all numbers up to l 2070 for i = 1 to l 2080 let n (i) = i 2090 next i ...