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  2. RSA numbers - Wikipedia

    en.wikipedia.org/wiki/RSA_numbers

    RSA-120 1993-06-09 ppmpqs ... and 14.2 hours to find the factors using the square root) ... (this pair has a yield of relations approximately 13.5 times that of a ...

  3. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    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, 3, 5, and so on, up to the square root of n. For larger numbers, especially when using a computer, various more sophisticated factorization algorithms are more efficient.

  4. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.

  5. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.

  6. Symbols of grouping - Wikipedia

    en.wikipedia.org/wiki/Symbols_of_grouping

    For example √ p+q is the square root of the sum. The bar is also a symbol of grouping in repeated decimal digits. The bar is also a symbol of grouping in repeated decimal digits. A decimal point followed by one or more digits with a bar over them, for example 0. 123 , represents the repeating decimal 0.123123123... .

  7. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

  8. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k). m is smoother than n if the largest prime factor of m is below the largest of n.

  9. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    Yves Gallot's proth.exe has been used to find factors of large Fermat numbers. Édouard Lucas, improving Euler's above-mentioned result, proved in 1878 that every factor of the Fermat number , with n at least 2, is of the form + + (see Proth number), where k is a positive integer. By itself, this makes it easy to prove the primality of the ...