how so ?

The number between them have a high number of small factors including 2 and 3.

  2 * 3 = 6: 5 and 7 are prime.
  2 * 3 * 2 = 12: 11 and 13 are prime
  2 * 3 * 3 = 18: 17 and 19 are prime
  2 * 3 * 5 = 30: 11 and 13 are prime
  2 * 3 * 7 = 42: 41 and 43 are prime.
  However, 2 * 3 * 101 = 606 but 605 is not prime.
  But, 
  2 * 3 * 5 * 5 = 150 and 149 and 151 are prime.
  2 * 3 * 2 * 3 * 5 = 180 and  179 and 181 are prime.

I don't see where the insight is. twin primes must be of the form (6k-1, 6k+1). So of course there will be a 2,3 at least.

Smaller numbers have multiples that are more densely distributed among the integers.

The point is twin primes (6k-1, 6k+1) are more likely for a large k when k is a composite number than a prime AND the more factors of k the higher chance for twin primes.

EX: K = (6 * 2 * 3 * 5 * 7 * 11 * 13 ) gives a twin prime.