When math textbooks need an example of a right triangle, they frequently use a triangle with sides of length 3, 4, and 5, since the numbers work out so nicely: \(3^{2}+4^{2}=5^{2}\) by the Pythagorean theorem. If that gets tiresome, 12, 5, 13 might be used: \(5^{2}+12^{2}=13^{2}\). Clearly, multiplies of these numbers work also, e.g. \(6^{2}+8^{2}=10^{2}\).
Such [...]

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 [...]