Bertrand's postulate

Bertrand's postulate states that if n > 3 is an integer, then there always exists at least one prime number p with n < p < 2n − 2. 

This statement was first made in 1845 by Joseph Bertrand. Bertrand verified his statement for all numbers in the interval [2, 3 × 106].

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).

 References 

 Other websites 
 Ramanujan's simpler proof

Category:Number theory