Prime times Prime

Unable to paint today due to a sinus infection, I have been analyzing prime number patterns. As others before me have already done, I am trying to discern a pattern in the ending digits, which are always 1,3, 7 and 9 (excluding the two 2 "weird" primes of 2 and 5). I realized something fun - not Earth shattering - probably realized before by countless others but still fun for me. All primes multiplied by themselves obviously result in a non-prime number; but what is interesting is that the resulting number always end with either 1 or 9!