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  2. 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.

  3. Perfect number - Wikipedia

    en.wikipedia.org/wiki/Perfect_number

    Perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.

  4. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    A k-cycle is a cycle that can be partitioned into k contiguous subsequences, each consisting of an increasing sequence of odd numbers, followed by a decreasing sequence of even numbers. For instance, if the cycle consists of a single increasing sequence of odd numbers followed by a decreasing sequence of even numbers, it is called a 1-cycle.

  5. Magic number (programming) - Wikipedia

    en.wikipedia.org/wiki/Magic_number_(programming)

    the use of 2 to check whether a number is even or odd, as in isEven = (x % 2 == 0), where % is the modulo operator the use of simple arithmetic constants, e.g., in expressions such as circumference = 2 * Math.PI * radius , [1] or for calculating the discriminant of a quadratic equation as d = b^2 − 4*a*c

  6. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares : That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N . Each odd number has such a representation. Indeed, if is a factorization of N, then.

  7. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_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 .

  8. Goldbach's conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_conjecture

    Thus if n is a large even integer and m is a number between 3 and ⁠ n / 2 ⁠, then one might expect the probability of m and n − m simultaneously being prime to be ⁠ 1 / ln m ln(n − m) ⁠. If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly

  9. Sieve of Sundaram - Wikipedia

    en.wikipedia.org/wiki/Sieve_of_Sundaram

    The remaining numbers are doubled and incremented by one, giving a list of the odd prime numbers (i.e., all primes except 2) below 2n + 2. The sieve of Sundaram sieves out the composite numbers just as the sieve of Eratosthenes does, but even numbers are not considered; the work of "crossing out" the multiples of 2 is done by the final double ...