= Solution
Multiplying the reciprocal <improper prior> by the <likelihood function> gives
$$
p(N\mid y)=\frac{N^{-2}}{S_y},\qquad N\geq y,
\qquad S_y=\sum_{k=y}^{\infty}k^{-2}<\infty.
$$
Thus this <discrete uniform endpoint posterior> is proper. Its exact cumulative probability is $S_y^{-1}\sum_{k=y}^n k^{-2}$. Integral approximation gives $S_y\approx\int_y^\infty t^{-2}\,dt=1/y$ and $\sum_{k=y}^n k^{-2}\approx\int_y^n t^{-2}\,dt=1/y-1/n$, so
$$
\boxed{\Pr(N\leq n\mid y)\approx1-\frac yn,\qquad
\operatorname{median}(N\mid y)\approx2y=200.}
$$
These approximations are useful when $y$ is moderately large and are not exact discrete identities. For example the exact untruncated median at $y=100$ is $199$. Although its <quantiles> are finite, its <posterior mean> is infinite, since its expectation numerator is the divergent sum $\sum_{N=y}^\infty1/N$.
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