Let L={1^n|n is prime}

Using the Myhill-Nerode theorem show L is non-regular.

I have already got this explanation from my lecture but I don't understand. Here's the explanation given in lecture:

Assume without loss of generality that i < j

Pick an arbitrary prime p > i, where p > 2

Since p > 2 and (j-i) > 0, we know that: p + 0 (j-i) is prime and p + p (j-i) is NOT prime

Let 1<=k <= p:

p + (k-1)(j-i) is prime

p + k (j-i) is NOT prime

We show that:

1^i . 1^([p+(k-1)(j-i)]-i) L

1^j . 1^([p+(k-1)(j-i)]-i) L