Bertrand's postulate (statement and examples)

Postulate. For every integer $n>1$, there exists a prime $p$ such that $n<p<2n$.

Verify for $n=10$: primes in $]10,20[$: $11,13,17,19$. At least one exists.

Verify for $n=100$: primes in $]100,200[$: $101,103,107,109,113,\ldots$

Conclusion. Bertrand's postulate (Chebyshev's theorem) holds; it is a nontrivial result usually proved by elementary estimates on binomial coefficients.