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The IPv4 address range isn't that big.
A class A network (/8) has about 16 million hosts, and in theory there is 256 of them. As a result, the internet has about 4,294,966,784 hosts. Of course, this is an approximation.
Many address ranges are actually reserved (e.g. 127.0.0.0/8, 10.0.0.0/8), a...