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  2. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    Short video visualizing the Prime Number Theorem. Prime formulas and Prime number theorem at MathWorld. How Many Primes Are There? Archived 2012-10-15 at the Wayback Machine and The Gaps between Primes by Chris Caldwell, University of Tennessee at Martin. Tables of prime-counting functions by Tomás Oliveira e Silva; Eberl, Manuel and Paulson ...

  3. Euclid's lemma - Wikipedia

    en.wikipedia.org/wiki/Euclid's_lemma

    Theorem — If is a prime number that divides the product and does not divide , then it divides . Euclid's lemma can be generalized as follows from prime numbers to any integers. Theorem — If an integer n divides the product ab of two integers, and is coprime with a , then n divides b .

  4. Formula for primes - Wikipedia

    en.wikipedia.org/wiki/Formula_for_primes

    Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]

  5. Euclid's theorem - Wikipedia

    en.wikipedia.org/wiki/Euclid's_theorem

    Since no prime number divides 1, p cannot be in the list. This means that at least one more prime number exists beyond those in the list. This proves that for every finite list of prime numbers there is a prime number not in the list. [4] In the original work, Euclid denoted the arbitrary finite set of prime numbers as A, B, Γ.

  6. Category:Theorems about prime numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_about...

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  7. 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.

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