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Bertrand was a professor at the École Polytechnique and the Collège de France. He was a member of the Paris Academy of Sciences and was its permanent secretary for twenty-six years.
He conjectured, in 1845, that there is at least one prime between n and 2n-2 for every n > 3. Chebyshev proved this conjecture in 1850.
Bertrand translated into French Carl Friedrich Gauss's work on the theory of errors and the method of least squares.