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In mathematics, Bertrand's postulate (now a theorem) states that, for each , there is a prime such that < <.First conjectured in 1845 by Joseph Bertrand, [1] it was first proven by Chebyshev, and a shorter but also advanced proof was given by Ramanujan.
In number theory, Bertrand's postulate is the theorem that for any integer >, there exists at least one prime number with n < p < 2 n − 2. {\displaystyle n<p<2n-2.} A less restrictive formulation is: for every n > 1 {\displaystyle n>1} , there is always at least one prime p {\displaystyle p} such that
Pages in category "Theorems about prime numbers" ... Bertrand's postulate; Proof of Bertrand's postulate; Bonse's inequality; Brun–Titchmarsh theorem; Brun's ...
Bertrand's postulate and a proof; ... Articles devoted to theorems of which a (sketch of a) proof is given. Banach fixed-point theorem; Banach–Tarski paradox ...
Proof of Bertrand's postulate; Fermat's theorem on sums of two squares; Two proofs of the Law of quadratic reciprocity; Proof of Wedderburn's little theorem asserting that every finite division ring is a field; Four proofs of the Basel problem; Proof that e is irrational (also showing the irrationality of certain related numbers) Hilbert's ...
In November of the same year, Larsen published a paper titled "Bertrand's Postulate for Carmichael Numbers" [9] on the open access repository arXiv that made a more consolidated proof of Maynard and Tao's postulate but involving Carmichael numbers into the twin primes conjecture and attempting to shorten the distance between the numbers per ...
In classical mechanics, Bertrand's theorem states that among central-force potentials with bound orbits, there are only two types of central-force (radial) scalar potentials with the property that all bound orbits are also closed orbits.
Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of Bertrand's postulate; Proof that the sum of the reciprocals of the primes diverges; Cramér's conjecture; Riemann hypothesis. Critical line theorem; Hilbert–Pólya conjecture