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  2. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined. Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1.

  3. Formula for primes - Wikipedia

    en.wikipedia.org/wiki/Formula_for_primes

    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 it was conjectured to contain all odd primes, even though it is rather inefficient.

  4. 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.

  5. Prime number - Wikipedia

    en.wikipedia.org/wiki/Prime_number

    The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of 5 ...

  6. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...

  7. Fundamental theorem of arithmetic - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, = =). This theorem is one of the main reasons why 1 is not considered a prime number : if 1 were prime, then factorization into primes would not be unique; for example, 2 = 2 ⋅ 1 = 2 ⋅ 1 ⋅ 1 ...

  8. 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.

  9. Table of Gaussian integer factorizations - Wikipedia

    en.wikipedia.org/wiki/Table_of_Gaussian_Integer...

    A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite.The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime.