“Since each prime number can only be divided by 1 and itself, the set of all prime numbers is one example of a primitive set.”
Erdős guessed that no primitive set beats the primes on his sum, which comes out to about 1.64. Mathematicians spent decades getting close bounds and never closing the gap. A 26-year-old at Oxford closed it while officially working on other problems. Math is still the one place where a grad student with no budget beats everyone with a grant.