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...

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...

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...

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...

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....

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

In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula...

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...

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

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

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...

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...

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...

_{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...

analytic number theory. The following are examples of problems in analytic number theory: the prime number theorem, the Goldbach conjecture, the twin prime conjecture...

In chapter 3, the Prime Number Theorem (PNT) is introduced. The function which mathematicians use to describe the number of primes in N numbers, π(N)...

that F4 is the last Fermat prime. The prime number theorem implies that a random integer in a suitable interval around N is prime with probability 1 / ln...

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...

various contexts. The prime number theorem is a key result in this subject. The Mathematics Subject Classification for multiplicative number theory is 11Nxx...

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

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

In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite...

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...

of prime k-tuples less than a given magnitude by generalizing the prime number theorem. It was first proposed by G. H. Hardy and John Edensor Littlewood...

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