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Sieve of Sundaram: algorithm steps for primes below 202 (unoptimized). The sieve starts with a list of the integers from 1 to n.From this list, all numbers of the form i + j + 2ij are removed, where i and j are positive integers such that 1 ≤ i ≤ j and i + j + 2ij ≤ n.
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. for i = 2, 3, 4, ..., not exceeding √ n do if A[i] is true for j = i 2, i 2 +i, i 2 +2i, i 2 +3i, ..., not exceeding n do set A[j] := false return ...
In spite of Gilbreath's concern in the original article, by this time the code had become almost universal for testing, and one of the articles remarked that "The Sieve of Eratosthenes is a mandatory benchmark". [13] It was included in the Byte UNIX Benchmark Suite introduced in August 1984. [16]
Chen's theorem, which shows that there are infinitely many primes p such that p + 2 is either a prime or a semiprime (the product of two primes); a closely related theorem of Chen Jingrun asserts that every sufficiently large even number is the sum of a prime and another number which is either a prime or a semiprime.
The following is pseudocode which combines Atkin's algorithms 3.1, 3.2, and 3.3 [1] by using a combined set s of all the numbers modulo 60 excluding those which are multiples of the prime numbers 2, 3, and 5, as per the algorithms, for a straightforward version of the algorithm that supports optional bit-packing of the wheel; although not specifically mentioned in the referenced paper, this ...
Another common optimization is therefore to mark only prime^2, prime^2 + 2 * prime, prime^2 + 4 * prime, ... for any prime > 2. Taking this one step further is to exclude all even numbers from the array of booleans in the first place: algorithm Sieve of Eratosthenes is input: an integer n > 1. output: all prime numbers from 2 through n.
Leo can manipulate text or code in any human or computer programming language (e.g., Python, C, C++, Java), as Leo is a language-independent or "adaptable LPE" (literate programming environment). [1] Syntax highlighting is provided for many different programming languages. [2] Leo is written in Python and can be extended with plugins written in ...
To support specified character encoding, the editor must be able to load, save, view and edit text in the specific encoding and not destroy any characters. For UTF-8 and UTF-16, this requires internal 16-bit character support. Partial support is indicated if: 1) the editor can only convert the character encoding to internal (8-bit) format for ...