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 Classification
Statement Form Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Bertrand's Postulate (Wikipedia)
Wikimedia Foundationlead section, restated formulation
A less restrictive formulation is: for every n > 1, there is always at least one prime p such that n < p < 2n.
History section
Chebyshev proved it in 1852 and so it is also called the Bertrand-Chebyshev theorem or Chebyshev's theorem.
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