Well, factor is clearly the wrong technical term here, you probably meant the last digit? Like the last digit (remainder of modulo 10 division: p%10 in C-notation) of a prime number (p>5) in base 10 can be {1,3,7,9}.

And yes, in base 6 that becomes 1 and 5, as p%6 = 1 or 5, equivalent to p=6k±1. Interesting observation, thanks :)