It does give you a good intuition as to why twin primes aka N, N+2 are so common.
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.Smaller numbers have multiples that are more densely distributed among the integers.
EX: K = (6 * 2 * 3 * 5 * 7 * 11 * 13 ) gives a twin prime.