Look at these numbers. Do you notice any patterns?

 

4

6

12

18

30

42

60

72

102

108

138

150

180

192

198

228

240

270

282

312

348

420

 

Well, except for the 4, all of these numbers are evenly divisible by 6.

However, that is not the only thing that distinguishes this set. Every one of these numbers also comes between two prime numbers. As a matter of fact, except for 2 and 4, in every instance of prime numbers separated by one number *, that number is always evenly divisible by 6.

* at least, in every instance of prime numbers under 11,000 – that is how far I checked.