This probably isn't good enough, but given the two properties we can establish what the function is for all p, so given enough patience we can determine g(955) explicitly.

However, note from property 1 that g is bijective: g has an inverse. (Because if for some that would imply that is false.) And note also from 1 that . Thus from 2 we have that

So .

(Actually the only p for which g(p) = p is p = 0, so really we have that .)

-Dan