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  2. Generation of primes - Wikipedia

    en.wikipedia.org/wiki/Generation_of_primes

    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.

  3. Sieve of Eratosthenes - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Eratosthenes

    A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.

  4. APL syntax and symbols - Wikipedia

    en.wikipedia.org/wiki/APL_syntax_and_symbols

    Quad WA or ⎕WA, another dynamic system variable, shows how much Work Area remains unused or 41,226 megabytes or about 41 gigabytes of unused additional total free work area available for the APL workspace and program to process using. If this number gets low or approaches zero - the computer may need more random-access memory (RAM), hard disk ...

  5. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.

  6. Sieve of Atkin - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Atkin

    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 ...

  7. Formula for primes - Wikipedia

    en.wikipedia.org/wiki/Formula_for_primes

    Rowland (2008) proved that this sequence contains only ones and prime numbers. However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper ...

  8. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.

  9. Prime95 - Wikipedia

    en.wikipedia.org/wiki/Prime95

    Prime95 tests numbers for primality using the Fermat primality test (referred to internally as PRP, or "probable prime"). For much of its history, it used the Lucas–Lehmer primality test , but the availability of Lucas–Lehmer assignments was deprecated in April 2021 [ 7 ] to increase search throughput.