Celebrating Uncle Paul’s 103rd Birthday
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We know that the sequence of prime numbers $2, 3, 5, 7, \ldots$ is infinite and the size of its gaps between two prime numbers is not bounded. In fact we can give a sequence of $k$-consecutive composite numbers, $N+2, N+3, N+4, \ldots, N+(k+1)$ where $\displaystyle{N = \prod_{p\leq k+2} p}$. Bertrand conjectured that the gap to the next prime cannot be larger than the number we start our search at. I this talk I paid homage to Paul Erdős (whom I refer to as “Uncle Paul”) by discussing his elegant proof of Bertrand’s conjecture.