# Pi chains.

The prime counting function, denoted by $$\pi(x)$$ counts the number of primes less or equal to $$x$$.

Consider the process of continually finding the value of $$\pi(x)$$ of $$x$$ until it equals zero.

For example,for $$x=1000$$ we have $\pi(1000) = 168 \rightarrow 39 \rightarrow 12 \rightarrow 5 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 0$

$\pi(20) = 8 \rightarrow 4 \rightarrow 2 \rightarrow 1 \rightarrow 0$

From the above we can say that $$1000$$ has a pi chain of length 8 and $$20$$ has a pi chain of length 5.

How many integers have a pi chain of length 9?

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