100,000,000,000
The first digit would have to be 1, the remaining digits, zero.
1023456789
10234567
10234567
0123456789
Since there are only five different digits, a 6-digit number can only be generated if a digit can be repeated. If digits can be repeated, the smallest 6-digit number is 111111.
The smallest 4-digit number without any repeated digits is 1023, as it starts with the smallest possible digit (1) followed by the next smallest digits (0, 2, 3). The largest 4-digit number without any repeated digits is 9876, which uses the largest digits available in descending order.
102
103
999,999,999,999
You didn't mention whether we're allowed to repeat (re-use) a digit.Here are the smallest 5 primes using only those digits:With repeated digit: 223, 233, 277With no repeated digit: 257, 283
1000000000 or, if negative numbers are permitted, then -9999999999