8. (10 points) There is a five-digit number, when it is divided by $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13$ these 12 natural numbers, the remainders are all different. This five-digit number is $\qquad$
【Solution】Solution: According to the problem, we have:
This five-digit number, when divided by 1, leaves a remainder of 0, and when divided by 2, leaves a remainder of 1. Then, it is found that when divided by $3,4,5,6,7,8,9$, 10, 11, the remainders are $2,3,4,5,6,7,8,9,10$ respectively, which meets the conditions.

It is observed that the remainders are all one less, so the only way to find the number that meets the conditions is to find the least common multiple of $1,2,3,4,5,6,7,8,9,10,11$ and subtract 1.

The least common multiple is: $1 \times 2 \times 3 \times 2 \times 5 \times 7 \times 2 \times 3 \times 11=27720$.
It also needs to satisfy that when divided by 13, the remainder is 11 or 12.
The number that meets the conditions is $27720 k-1$, try to enumerate $k=1,2,3$, to meet the condition of being a five-digit number.
After enumeration, it is $27720 \times 3-1=83159$.
Therefore, the answer is: 83159