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If Bitcoin addresses can be generated offline, then the Bitcoin network doesn't check for duplicate addresses while generating a new one. Can't I just make a script and generate milions of Bitcoin addresses and then make a profit when someone will have one of those addresses and sends bitcoins there?

How does the Bitcoin network prevent this?

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While this is theoretically possible, it is practically impossible.

Keys are 256 bit in length and are hashed in a 160 bit address.(2^160th power) Divide it by the world population and you have about 215,000,000,000,000,000,000,000,000,000,000,000,000 addresses per capita.(2.15 x 10^38

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Probability prevents this from happening as the bitcoin address space is 2^160 or

1,461,501,600,000,000,000,000,000,000,000,000,000,000,000,000,000 (apx)

here is a picture to put it into perspective. Ok so now you are thinking well it is quick to generate them so I will just make more. Looking at this thread How to pre-generate 100M bitcoin addresses? you can generate 770k addresses in 15 minutes so lets do the math. that is

54,168,210,000,000,000,000,000,000,000,000,000,000 (apx)

years to generate all the bitcoin addresses. get cracking.

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