My mental health was poor today, and I spent my study time watching math videos. This included one on open problems that are relatively simple to state but have proven difficult to solve. It was quite interesting, but had several errors (some of which I noticed and some of which I found pointed out in the comments). Therefore I won’t link it here.
My favorite open problem is the first one that caught my imagination: the conjecture that there are infinitely many perfect numbers. This turns out to be closely related to the conjecture that there are infinitely many Mersenne primes, a type of prime number that is one less than a power of two. So a conjecture about summing factors is related to the existence of a type of prime numbers. Cool huh?
probably cool
Trust me, I’m a professional.