What are the advantages and disadvantages of using sequentially generated numbers or randomly generated numbers for primary database keys?
Was the intent of your question to distinguish the pros and cons of sequential versus random numbers? Sequential numbers never repeat, and you won't run into trouble until the next number is larger than the column can hold, which is usually not a problem unless you define the column as
tinyint or something. Random numbers might repeat since they are only really pseudo-random, but I wouldn't worry about it, because, again, you're probably not going to have a table large enough for this to occur. Random numbers also have the advantage that you won't be tempted to try SELECT MAX(ID) in order to get back the key of the latest inserted record -- but that's a different discussion.
It's more likely that you're interested in the advantages and disadvantages of a surrogate key as compared to a natural or "real" primary key.
As you may be able to tell from the above, the advantages of one are the disadvantages of the other.
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