Predicates and quantifiers exercises

Primitive Recursive(p.r) Functions is said to be a primitive recursive function if it is obtained from initial functions by finite number of applications of compostion or primitive recursion

1. Let f(x) be the number of primes x. Show f(x) is p.r. 2. Let P(x; t) be a computable predicate, Show f(x; y) be the maximum value of t y such that P(x; t) = 1. If no such t y exists with P(x; t) = 1, then f(x; y) = 0. Show f(x; y) is p.r