Earlier quoted context omitted.
49 looks prime to me. Another commentator says it doesn't count because it's a square number, but square numbers don't really have a particular "look" to me in the same way that 2-digit numbers ending in 5 or with digits summing to a multiple of 3 do.
Based on my failure at this game, anything times 19 looks prime to me.
The "looks prime" rule assumes you check for multiples of 3, so that removes one.
All the rest end in an even digit or 5.