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  2. Sieve of Eratosthenes - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Eratosthenes

    Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square). In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit.

  3. 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.

  4. 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 ...

  5. Primality test - Wikipedia

    en.wikipedia.org/wiki/Primality_test

    A primality test is an algorithm for determining whether an input number is prime.Among other fields of mathematics, it is used for cryptography.Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not.

  6. Meissel–Lehmer algorithm - Wikipedia

    en.wikipedia.org/wiki/Meissel–Lehmer_algorithm

    Meissel already found that for k ≥ 3, P k (x, a) = 0 if a = π(x 1/3).He used the resulting equation for calculations of π(x) for big values of x. [1]Meissel calculated π(x) for values of x up to 10 9, but he narrowly missed the correct result for the biggest value of x.

  7. Sieve of Pritchard - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Pritchard

    A prime number is a natural number that has no natural number divisors other than the number 1 and itself.. To find all the prime numbers less than or equal to a given integer N, a sieve algorithm examines a set of candidates in the range 2, 3, …, N, and eliminates those that are not prime, leaving the primes at the end.

  8. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    Another example is the distribution of the last digit of prime numbers. Except for 2 and 5, all prime numbers end in 1, 3, 7, or 9. Dirichlet's theorem states that asymptotically, 25% of all primes end in each of these four digits.

  9. Shor's algorithm - Wikipedia

    en.wikipedia.org/wiki/Shor's_algorithm

    Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor . [ 1 ] [ 2 ] It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum ...