ln(x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

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 number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

Prime number theory may refer to: Prime number Prime number theorem Number theory Fundamental theorem of arithmetic, which explains prime factorization...

of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta...

that there is always a prime number between k and 2k, so in particular pn+1 < 2pn, which means gn < pn. The prime number theorem, proven in 1896, says...

Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first...

Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture...

which rounds down to the nearest integer. By Wilson's theorem, n + 1 {\displaystyle n+1} is prime if and only if n ! ≡ n ( mod n + 1 ) {\displaystyle n...

loge(x). In number theory, Bertrand's postulate is the theorem that for any integer n > 3 {\displaystyle n>3} , there exists at least one prime number p {\displaystyle...

_{x\rightarrow \infty }{\frac {\pi (x)}{x/\log x}}=1.} This statement is the prime number theorem. An equivalent statement is lim x → ∞ π ( x ) li ⁡ ( x ) = 1 {\displaystyle...

ln(x) or loge(x). In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens...

function as the primes become too large. The prime number theorem in analytic number theory provides a formalisation of the notion that prime numbers appear...

analytic number theory, the Siegel–Walfisz theorem was obtained by Arnold Walfisz as an application of a theorem by Carl Ludwig Siegel to primes in arithmetic...

In mathematics, the prime ideal theorem may be the Boolean prime ideal theorem the Landau prime ideal theorem on number fields This disambiguation page...

divisors Prime number, prime power Bonse's inequality Prime factor Table of prime factors Formula for primes Factorization RSA number Fundamental theorem of...

number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime number...

In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with the...

A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or...

ln ⁡ ( n + 1 ) {\displaystyle H_{n^{2}}-H_{n}\sim \ln(n+1)} The prime number theorem provides the following asymptotic equivalence: n π ( n ) ∼ ln ⁡ n...

number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem,...

them to a variety of different mathematical fields. The classical prime number theorem serves as a prototypical example, and the emphasis is on abstract...

says that primes 3 mod 4 are more common than primes 1 mod 4 in some sense. (For related results, see Prime number theorem § Prime number race.) In 1923...

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime...

physics and has number theoretic significance. In particular, according to the prime number theorem, it is a very good approximation to the prime-counting function...

The Erdős–Delange theorem is a theorem in number theory concerning the distribution of prime numbers. It is named after Paul Erdős and Hubert Delange....

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...