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.
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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 Bertrand's Postulate
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Source MacTutor History of Mathematics, University of St Andrews: Joseph Louis François Bertrand
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Source Bertrand's Postulate (Wikipedia)
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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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