Let say I need a 3 digit number, so it would be something like:
>>> random(3)
563
or
>>> random(5)
26748
>> random(2)
56
>
Does 0 count as a possible first digit? If so, then you need random.randint(0,10**n-1). If not, random.randint(10**(n-1),10**n-1). And if zero is never allowed, then you'll have to explicitly reject numbers with a zero in them, or draw n random.randint(1,9) numbers.
Aside: it is interesting that randint(a,b) uses somewhat non-pythonic "indexing" to get a random number a <= n <= b. One might have expected it to work like range, and produce a random number a <= n < b. (Note the closed upper interval.)
Given the responses in the comments about randrange, note that these can be replaced with the cleaner random.randrange(0,10**n), random.randrange(10**(n-1),10**n) and random.randrange(1,10).