you can use Guid's instead of random int , they are going to always be unique
There is no way to guarentee an int is unique unless you check every one that already exists, and even then - like the comments say , you are guarenteed duplicates when you pass 1000 ids
EDIT:
I mention that I think Guid's are best here because of the question , first indexing the table is not going to take long at all - it is assumed that there are going to be less then 1000 students because of the size of int, 128 bits is fine in a table with less then 1000 rows.
Guid's are a good thing to learn - even though they are not always the most effecient way
Creating a unique Guid in c# has a benifit that you can keep using and displaying that id - like in the question , without another trip to Db to figure out which unique id was assigned to the student