[timinman]

Nice game. Something weird can happen in the brain when we have to choose a binary answer under pressure. Maybe the fact that we are answering positively for prime (which is not the default) adds to that. For me it helped to rename 'yes' to 'prime' and 'no' to 'divisible'.

[cyborgx7]

Same here. What happened to me is, instead of asking myself "Is this a prime number?" I kept starting to ask myself "Can this number be expressed as a multiplication of two other numbers?" for which the answers are obviously reversed.

[davidamarquis]

Finding divisors is often hard when your number is large. It turns out the condition that a number n can be expressed as a multiple of two other numbers is equivalent to there being a number z less than n except for 1 and n-1 so that (z^2 mod n) == 1.

This condition is the basis of the Miller-Rabin primality test. Sadly its a bit hard for humans to implement this algorithm for mentally proving primality.

[mmahemoff]

Yes, I found the UX aspect here interesting as it twisted my brain a bit too. A current example of this is the Brexit referendum, where the question was initially posed as a Yes or No, but required revision to a "Remain" or "Leave", which is much easier for casual observers to grok and lets people get behind their favourite actual position instead of embracing an arbitrary Boolean value (as happened with the Scottish referendum's Yes and No camps).

Also, Prime itself is a tricky term for a Yes-No question as it's really a negative concept - the absence of something. So asking if X is prime is requiring double-negative logic in the same way as an app setting like "Disable X feature [On / Off]".