Search results
Results from the WOW.Com Content Network
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 .
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]
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid in his work Elements . There are several proofs of the theorem.
Pages in category "Theorems about prime numbers" The following 31 pages are in this category, out of 31 total. ... Prime number theorem; Proth's theorem; R.
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 .
The distribution of primes in the large, such as the question how many primes are smaller than a given, large threshold, is described by the prime number theorem, but no efficient formula for the -th prime is known.
In mathematics, Euclid numbers are integers of the form E n = p n # + 1, where p n # is the nth primorial, i.e. the product of the first n prime numbers. They are named after the ancient Greek mathematician Euclid , in connection with Euclid's theorem that there are infinitely many prime numbers.
The multiplicative property of the norm implies that a prime number p is either a Gaussian prime or the norm of a Gaussian prime. Fermat's theorem asserts that the first case occurs when p = 4 k + 3 , {\displaystyle p=4k+3,} and that the second case occurs when p = 4 k + 1 {\displaystyle p=4k+1} and p = 2. {\displaystyle p=2.}