Question

Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely many primes of the form n2 + 1?

Answer 1

I wish I had an answer for you! Unfortunately, this one has stumped even professional mathematicians for over a century. It was first presented by mathematician Edmund Landau in 1912, and it’s gone unproven ever since. I can’t give you a solution, but I can definitely say you should submit your findings to a mathematical journal if you ever find one!