Great to see this! I'm not convinced of the problem with my prior, though... The judgements for the different instances of Q(n) may be logically independent, but they won't be probabilistically independent. In fact, the logical information that Q(x) is true of exactly 90% of numbers under a given limit number L will eliminate all theories where that isn't true. I find it likely that this will push the probability of Q(L+1) up significantly.

For example, the theory that Q holds for every number not divisible by 10 becomes much more probable.