Bertrand's postulate

Ramanujan Primes and Bertrand's Postulate

Ramanujan's Proof of Bertrand's Postulate

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.

A proof of Bertrand's postulate

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. Even if Chebyshev’s result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions ψ and θ still play a central role in the modern development...

Arithmetic in Metamath, Case Study: Bertrand's Postulate

Unlike some other formal systems, the proof system Metamath has no built-in concept of “decimal number” in the sense that arbitrary digit strings are not recognized by the system without prior definition. We present a system of theorems and definitions and an algorithm to apply these as basic operations to perform arithmetic calculations with a number of steps proportional to an arbitrary-preci...

A generalization of Bertrand's test

One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the Bertrand's test. If this test fails, we can use a generalization of Bertrand's test and such tests can be continued innitely. For simplicity, we call ratio test,...