How to calculate minimum zener current if it is not explicitly specified in the datasheet?
The minimum current for reasonable regulation is Izk, but this parameter is not always shown in the datasheet. It is the current in the zener at the corner where it is just starting to break over.

For the 1N4740A from Fairchild, that is listed as 250  microamps.

There is an excellent reference on zener diodes available. (Search for Izk).

Edit: Updated part number for correct suffix. Made note on what Vz to use.

When calculating the maximum resistance, I use the maximum zener voltage (although it is unlikely to be this high at Izk).

HTH