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
StatementA less restrictive formulation is: for every n > 1, there is always at least one prime p such that n < p < 2n. 1 Proof Method Classification
Statement Form Statement Form Connections
Has Statement Form
In Branch
Principal Result Of
Source MacTutor History of Mathematics, University of St Andrews: Joseph Louis François Bertrand
Proved By
Source Bertrand's Postulate (Wikipedia)
Sources
1. Bertrand's Postulate (Wikipedia)
Wikimedia FoundationLead 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.
View the Source 2. ProofWiki: Bertrand-Chebyshev Theorem
ProofWikiProof sectionQuote, Proof section
Aiming for a contradiction, suppose there is no prime number $p$ with $n < p \le 2 n$.
MacTutor History of Mathematics, University of St Andrews: Joseph Louis François Bertrand
MacTutor History of Mathematics, University of St AndrewsPrincipal Result Of: Joseph Bertrand, Biography textQuote, Principal Result Of: Joseph Bertrand, Biography text
G N Matvievskaja, Bertrand's postulate in Euler's notes ( Russian ) , Istor.-Mat.
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