Zener Diode Minimum Input Voltage
You want to avoid operating at Izk. That is the point where breakdown begins and there is noticeable change. A good place to operate at is the Izt (zener test current) which is usually provided in the datasheet. 

Anyways...

This problem is going to depend on what you current limiting resistor is. If we assume you are operating at Izk (no load) then you first need to figure out what value resistor you are going to be using. If we assume 0.25W resistor, then

$$ P_{resistor} &gt; R_{max}*I_{zk}^{2} $$
$$ R_{max}  &lt; 77.16k $$

In this case, it doesn't matter a whole lot because the resistance is just high. But its a good check to do !

Now that we have that, we can just plug in the values 

$$ I_{zk} = \frac {V_{in} - V_{z} } {R}$$

If you plug in a high value of R ( R closer to R_max, you'll find that Vin tends to be quite high and if you use a low value R, then Vin tends to be close to Vz. 

However this will probably only apply to the no load configuration. As soon as you throw a load on, there will be less current going into the zener. This is also why I suggested you avoid working at Izk, because if you are at boundary between reverse bias and breakdown ( a zener is only useful when its in breakdown), and you throw a load, you can put your zener  back into reverse bias region.