What is Bertrand's postulate?
{{nosources|date=August 2023}} '''Bertrand's postulate''' states that if ''n'' > 3 is an [[integer]], then there always exists at least one [[prime number]] ''p'' with ''n'' < ''p'' < 2''n''&nbsp;−&nbsp;2. This statement was first made in 1845 by [[Joseph Louis François Bertrand|Joseph Bertrand]]. Bertrand verified his statement for all numbers in the interval [2, 3 × 10<sup>6</sup>]. His statement was completely proven by [[Pafnuty Chebyshev]] in 1850. For this reason, the postulate is also called the '''Bertrand-Chebyshev theorem''' or '''Chebyshev's theorem'''. [[Srinivasa Ramanujan]] gave a simpler proof. Ramanujan later used that proof when he discovered [[Ramanujan prime]]s. In 1932, [[Paul Erdős]] published a simpler proof using the [[Chebyshev function]] θ(''x''). == Other websites == * [http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper24/page1.htm Ramanujan's simpler proof] {{Math-stub}} [[Category:Number theory]]