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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. [2]
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 ...
Joseph Bertrand. 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.
Bertrand's box paradox – Mathematical paradox; Bertrand's postulate – Existence of a prime number between any number and its double; Bertrand's theorem – Physics theorem; Bertrand's ballot theorem – Theorem that gives the probability that an election winner will lead the loser throughout the count; Bertrand–Edgeworth model ...
Cayley's theorem; Clique problem (to do) Compactness theorem (very compact proof) Erdős–Ko–Rado theorem; Euler's formula; Euler's four-square identity; Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first ...
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 ...