It is unworthy of excellent men to lose hours like slaves in the labor of calculation.    Gottfried Wilhelm Leibniz

 
I have often told students that becoming good at math is a lot like becoming good at a sport or at playing an instrument – practice is extremely important. Hours and hours of practice.

However, there is a [...]

Are there an infinite number of prime numbers? Or maybe there is a largest prime number, and every number after that is composite. To get a little insight into this, we might start listing the prime numbers, beginning 2, 3, 5, 7, 11, …, to see if any pattern emerges. About all that is [...]