How many IPv6 IP addresses are there?

IPv6 uses a 128-bit address which allows for 2128 , or approximately 3.4 x 1038 addresses. 3.4 x 1038 is equal to 340 undecillion IP addresses. 
Therefore, there are 340,000,000,000,000,000,000,000,000,000,000,000,000 IPv6 addresses.

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