I shall add how useless and flawed is the use of serial numbers for protecting a software.
You purchase some software and this software is locked, you need some serial number (a key) to unlock the software so it can proceed with the installation.
The key is has several letters/numbers and some are very long, so it create a great numbers of combinations that makes impossible to discover it trying all the possible combinations.
An analogy is your house's door, it has a keylock where you put your key and so you can enter your home. Your neighbour has also a door and a key, but his key only open his door and not yours and your key only open you door and not the neighbours.
So everybody has his property protected, but this analogy is flawed, software keys do not work in the same way!
Software key must have other requirment that makes the keys of practical no use.
The company that sells the software doesn't sell one software, it sells hundreds or thousands of copies of the same software.
The softwares are sold in CDs, also in DVD today, so the company needs to make a big number of CDs to be sold. The only way of making a large number of CDs is by means of a pressing machine, you cannot burn one by one thousands with a CD burned.
For making a pressed CD you need a matrix (a master CD) and the pressing machine will done thousands of exact copies of the matrix, so one sold CD is exactly the same as other sold CD.
You cannot make the key unique to a particular CD, making each CD with an unique key it will mean that one CD will not be equal to other CD and this will kill the pressing machine.
This can be done only burning one by one with a CD burner attached to a software generator and this is only possible for very small companies that sell very few CDs per month.
The result is that  all the thousands CDs pressed with the same matrix are exactly the same and all can be unlocked by the same key, you can only change the CD and its key when the matrix  end its life and you need to create a new matrix for another thousnads and thousands of CDs.
The analogy of your house door is destroyed, now you have a new and real analogy. Your door and yours neighbour door has exactly the same keylock, with your key you enter your home, your neighbour home, the police station and the jail, your neighbour does exactly the same.
You only cannot enter a house in another city if the keylocks used in this city were made by another matrix and it must have been different to the used in your city.

As all the softwares are the same and can be unlocked by the same key, a "public key", it doesn't give the feeling of protection, so it was created a particular key.
With each CD sold is attached a particular key somewhere, in the CD cover, in the manual or in some paper. Now you have your particulart key for your home and your neighbour has a particular key for his house.
But all is a great farse and joke, you can open your neighbour's door with your key and your neighbour enter your house using his own key!!!!
It were burned 10,000 CDs you have 10,000 particular keys and each one of this 10,000 particular key is able to unlock any of the 10,000 CDs, a big joke.
The only use of this particular key is for upgrades with a discount, the company will not give two upgrades for the same key, at leats this thing they can track.
Also you can have bad luck with the upgrade, you want to make the upgrade and you discover that you cannot do it because someone did it before you, in some way he discovered your key.
This is the only reason why you must never give your serial number to anyone.

Stupidity also evolves!