# Ramanujan's Proof of Bertrand's Postulate

@article{Meher2013RamanujansPO,
title={Ramanujan's Proof of Bertrand's Postulate},
author={Jaban Meher and M. Ram Murty},
journal={The American Mathematical Monthly},
year={2013},
volume={120},
pages={650 - 653}
}
• Published 1 August 2013
• Mathematics
• The American Mathematical Monthly
Abstract We present Ramanujan's proof of Bertrand's postulate and in the process, eliminate his use of Stirling's formula. The revised proof is elegant and elementary so as to be accessible to a wider audience.
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## References

SHOWING 1-5 OF 5 REFERENCES
A proof of Bertrand's postulate
• Mathematics
J. Formaliz. Reason.
• 2012
We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev concerning the distribution of prime numbers, subsuming, as a corollary, Bertrand's postulate.
Allahabad 211 019, India jaban@hri.res.in Department of Mathematics, Queen's University
• Allahabad 211 019, India jaban@hri.res.in Department of Mathematics, Queen's University
• 2013
Proofs from the Book, fourth edition
• Proofs from the Book, fourth edition
• 2009
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• This content downloaded from 61.95.189.187 on Wed, 7 Aug 2013 12:45:04 PM All use subject to JSTOR Terms and Conditions