The numbers for the national lottery are generated by a crude but colourful machine there are of course much better ways to generate them than this.

How efficient are are generators ?, how can they be tested ?.

(My guess at the number of shuffles required to return the playing cards to their original state was 52! [8.0658 * 10^67] is this correct ?)

I agree. For a 52 card deck, there are 52!(factorial) possible combinations.

Here's a sort of proof. For a 4 card deck (cards A, B, C & D) thare are 24 possible combinations.

4!=4x3x2x1=24

Here are the possible combinations.

ABCD ABDC ACBD ACDB ADCB ADBC

BABC BACB BCAB BCBA BDAC BDCA

CABD CADB CBAD CBDA CDAB CDBA

DABC DACB DBCA DBAC DCAB DCBA

It's not quite legit to say that the cards in a 52 card deck will return to their original state in 52! shuffles. Each shuffle is independent (or should be!) of the previous shuffle. All we can say is that for each shuffle, there is a 1 in 52! chance that the cards will be in a particular order, so it could happen on the next shuffle, or the cards and/or the shuffler may disintegrate before it happens.

Actually, the crude machines with the ping-pong balls (I'm assuming that's what they use in the UK) are really quite random. Because everyone can see what's going on, they are very difficult to bias (cheat). On the other hand it is very easy to bias what's going on inside a piece of electronic equipment.