The more factors an (even) number n has, the more likely it is that n+-1 is prime because those numbers cannot have any of the factors of n as factors. At the same time it is impossible that n+-2 or 4 are prime and unlikely that n+-3 is prime because 3 is likely to be a factor of n. And if additionally 5 is a factor, the primeless gap is even wider. So the primes stand out.