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Originally Posted by You Need a Thneed
10^36 is so ridiculously many addresses, If every internet device that has been or ever will be invented was randomly assigned a random IP address out of the entire list of possibilities - The chances are still virtually zero that any two devices would ever be assigned the same address.
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IPv6 addresses are assigned to organizations in much larger blocks as compared to IPv4 address assignments—the recommended allocation is a /48 block which contains 2^80 addresses, being 2^48 or about 2.8×10^14 times larger than the entire IPv4 address space of 2^32 addresses
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So when you request an IP address for your company, you'll be handed a block of addresses larger in size that the entirety of the existing internet.
BUT WAIT THERE'S MORE:
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customers can create 65536 /64 networks from their assigned /48 block, each having 2^64 addresses. In contrast, the entire IPv4 address space has only 2^32 (about 4.3×10^9) addresses
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So from your assigned block of IPv6 address space, you can then go on to create over 65,000 unique networks, each of which can be 4 billions times larger than all of the IPv4 internet.
