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.[1] Bertrand verified his statement for all numbers in the interval [2, 3 × 106].
His statement was completely proven by Pafnuty Chebyshev in 1850.[2] 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).[3]
Bertrand's Postulate Media
References
- ↑ Journal de l'ecole imperiale politechnique (in fr) (1845).
- ↑ Chebyshev, Pafnuty. Mémoire sur les nombres premiers. Journal de Mathématiques Pures et Appliquées.
- ↑ Erdos, Paul. Beweis eines Satzes von Tschebyschef. Acta Scientarium Mathematicarum (1932).