The Pythagoreans of ancient Greece were fascinated by whole numbers. One particular interest involved what we now call amicable numbers. Amicable numbers come in pairs in which each number is the sum ...

We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime ...

As a high school student in the mid-1990s, Pace Nielsen encountered a mathematical question that he’s still struggling with to this day. But he doesn’t feel bad: The problem that captivated him, ...

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question ...