[Solved]: How to show that f(x) is primitive recursive?

Problem Detail: 

Let

$$f(x)=\begin{cases} x \quad \text{if Goldbach's conjecture is true }\\ 0 \quad \text{otherwise}\end{cases}$$

Show that f(x) is primitive recursive.

I know a primitive recursive function is obtained by composition or recursion, but I don't know what should I do about this problem.

Asked By : Gigili

Answered By : Dave Clarke

Goldbach's conjecture is either true or false. Do a case analysis on the two possibilities. In one case, $f(x)=x$, which is primitive recursive. In the other case, $f(x)=0$, which is also primitive recursive. Therefore $f$ is primitive recursive.

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Question Source : http://cs.stackexchange.com/questions/6122