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Random numbers according to a rule / function

Hi buddies ,

               I want to write a module / program that generates random
numbers according to some rule (or function).

Say , "A number that is divisible by 13 & 19" or "A prime number whose sum
of digits is exactly 10" , etc.

Let me call this module as RandomRule[ f ].   Everytime I evaluate this
function , I must get a number 'x' such that f [x] is True.

For different invokes , RandomRule[ f ] must give different values.  There
are no restrictions on the function ' f ' .

For simplicity, let ' x '  be an integer.

            This is what I tried :

"A number that is divisible by 13 and 19"

     I put the command

              (Mod [ # , 14 ] == 0  &&  Mod[ # , 19 ] ==0  )&

 in a Do loop until the above statement returns True. And returned the value
of Random[Integer,{100,1000}]
that made this statement True.

 My problem is , how can I generalize this to include ANY function ' f ' ?

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