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2. Table of prime factors - Wikipedia

   en.wikipedia.org/wiki/Table_of_prime_factors

   An even number has the prime factor 2. The first: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 (sequence A005843 in the OEIS). An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. A square has even multiplicity for all prime ...

3. List of prime numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_prime_numbers

   This is a list of articles about 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.

4. Prime number - Wikipedia

   en.wikipedia.org/wiki/Prime_number

   A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...

5. Integer factorization - Wikipedia

   en.wikipedia.org/wiki/Integer_factorization

   Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is called a composite number, or it is not, in which case it is called a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way.

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. Prime-counting function - Wikipedia

   en.wikipedia.org/wiki/Prime-counting_function

   All instances of log (x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln (x) or loge(x). In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. [1][2] It is denoted by π(x) (unrelated to the number π). The ...

8. Sieve of Eratosthenes - Wikipedia

   en.wikipedia.org/wiki/Sieve_of_Eratosthenes

   In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that ...

9. Prime gap - Wikipedia

   en.wikipedia.org/wiki/Prime_gap

   A prime gap is the difference between two successive prime numbers. The n -th prime gap, denoted gn or g (pn) is the difference between the (n + 1)-st and the n -th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence (gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered.