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# Bertrand's postulate

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**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* − 2.

This statement was first made in 1845 by Joseph Bertrand. Bertrand verified his statement for all numbers in the interval [2, 3 × 10^{6}].

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 primes. In 1932, Paul Erdős published a simpler proof using the Chebyshev function θ(*x*).