Who got the bitcoins when nobody was mining it in the very begin?
If nobody mined it what used to happen to them?
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In the beginning, the Standard Client mined blocks by default. The difficulty was low enough that a single computer could reasonably create blocks just with its CPU. The Standard Client stopped CPU mining by default when GPU mining became prevalent.
Early blocks were most likely mined by Satoshi and other first adopters. One can see that the Genesis Block was created on January 3rd, while the next block was mined on January 9th, showing that most likely the blocks would not be mined unless there was someone on the network - Satoshi was probably running a node from the start, second person joined the network a week later.
Bitcoins are only generated when a block is mined. If a block is not mined, no new coins are generated. The system does not generate new coins every 10 minutes, but every block, which is designed to be mineable on average in 10 minutes.
If blocks would stop being generated for some time, creation of new coins will be halted until a new block appears. Worst case scenario if a lot of computing power drops from the network, the system will be slowed down until the Difficulty is readjusted. This happens every 2 weeks worth of blocks.
On TestNet, if a block is not generated in 15 minutes, Difficulty is dropped to 1 automatically to make it a more efficient testing environment. MainNet does not do this.