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  2. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.

  3. Pocklington primality test - Wikipedia

    en.wikipedia.org/wiki/Pocklington_primality_test

    Theorem: Factor N − 1 as N − 1 = AB, where A and B are relatively prime, >, the prime factorization of A is known, but the factorization of B is not necessarily known. If for each prime factor p of A there exists an integer a p {\displaystyle a_{p}} so that

  4. List of number fields with class number one - Wikipedia

    en.wikipedia.org/wiki/List_of_number_fields_with...

    Also in 2009, Morisawa showed that the class numbers of the layers of the cyclotomic Z 3-extension of Q have no prime factor less than 10 4. [11] Coates has raised the question of whether, for all primes p , every layer of the cyclotomic Z p -extension of Q has class number 1.

  5. Sieve of Eratosthenes - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Eratosthenes

    The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. [1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [ 2 ]

  6. Fundamental theorem of arithmetic - Wikipedia

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

    In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. [3] [4] [5] For example,

  7. Smith number - Wikipedia

    en.wikipedia.org/wiki/Smith_number

    In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed.

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