Ah of course and that makes far more sense.

Adding this prime to the end of a number guarantees a composite.

I wonder if that is a property the belongs to primes, or if there are non-trivial composite examples (any number ending in 2 has this property).

You can rephrase that conjecture to say... given any sequence of digits not ending in 2 (or 0), is there a prime number that ends in that sequence. That's an interesting conjecture!

yes I like that phrasing.

Similarly we can say there is a class of primes that have this property, what other classes of numbers also have this property?

Acchhh!!! Brain fart!!!