## Bertrand's postulateAlso known as Betrand's conjecture, if n
is an integer greater than 3, then there is at least one prime
number between n and 2n-2. This postulate (which should
now be called a theorem) is named after the French mathematician Joseph
Bertrand (1822–1900) who, in 1845, showed it was true for values of
n up to 3,000,000. The Russian Pafnuty Chebyshev (1821–1894)
gave the first complete proof in 1850, so that it is sometimes called Chebyshev's
theorem (although another theorem also goes by this name). In 1932
Paul Erdös gave a more elegant proof,
using the binomial coefficients,
which is the one that appears in most modern textbooks. Bertrand's postulate
implies that the n-th prime p_{n} is
at most 2^{n}. ## Related category• PRIME NUMBERS | |||||

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