4 ms·

https://en.wikipedia.org/wiki/Happy_number https://en.wikipedia.org/wiki/Happy_number

• gweinberg 9y ago
  Happy numbers led me to Fortunate numbers, which are Fortunate not because they are well off but because the guy studying them was named Fortune. https://en.wikipedia.org/wiki/Fortunate_number https://en.wikipedia.org/wiki/Fortunate_number Fortune conjectured that all Fortunate numbers are prime. I know jack about number theory but isn't that obvious from the density of primes? If there were a composite Fortunate number Fn it couldn't have any factors less than the nth prime number, which means it would have to be greater than the nth prime number squared.
  • cperciva 9y ago
    Not at all obvious. It is a very open question whether prime gaps are bounded by ~(log N)^2... AFAIK, even assuming the GRH, the best upper bound is roughly N^(1/2).
    • jwilk 9y ago
      Indeed: https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_conjecture https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_conjecture
      • cperciva 9y ago
        Yeah, that's the conjecture I was thinking of.