As an attempt - it's a simple definition, easy to check for small numbers, but leads to some difficult questions - are there infinitely many of them? (found yes

As an attempt - it's a simple definition, easy to check for small numbers, but leads to some difficult questions - are there infinitely many of them? (found yes by Erdos) How dense are they in the number line? Are there any odd ones > 5? "Numbers that can only be produces as the sum of 459 primes" is not as easy to find examples of, so less aesthetically pleasing to mathematicians.