Theorem

Bertrand's Postulate

Number Theory

For every integer n greater than 1, there is always at least one prime number p with n less than p less than 2n. Conjectured by Joseph Bertrand and proved by Pafnuty Chebyshev, it gives a simple bound on the gaps between primes.

Facts

Statement

A less restrictive formulation is: for every n > 1, there is always at least one prime p such that n < p < 2n. 1

Proof Year

1852 1

Classification

Statement Form

Existence Theorem 1

Statement Form

Inequality 1

Connections

Source Bertrand's Postulate (Wikipedia)

Sources

1. Bertrand's Postulate (Wikipedia)

Wikimedia Foundation

Lead section
Chebyshev proved it in 1852 and so it is also called the Bertrand-Chebyshev theorem or Chebyshev's theorem.
History section
Chebyshev proved it in 1852 and so it is also called the Bertrand-Chebyshev theorem or Chebyshev's theorem.
Proved By: Pafnuty Chebyshev, Lead
Chebyshev proved it in 1852 and so it is also called the Bertrand-Chebyshev theorem or Chebyshev's theorem.

Switch Atlas

The Inner World

The Civil World

The Natural World

Bertrand's Postulate

Has Statement Form

In Branch

Proved By