Goldbach's conjecture
Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. However, if "L""n" denotes the "n"-th lucky number, and "p""n" the "n"-th prime, then "L""n" &gt; "p""n" for all sufficiently large "n".