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On my laptop, in Chrome, when I Google "What is my IP?", I get an IPv6 returned as my public IP address. On the same laptop, in Firefox, I Google the same thing, and get an IPv4 returned as my public IP address.

How is this possible? How can my computer have two different public IP addresses?

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    Google "happy eyeballs" for an explanation of how browsers decide whether to choose IPv4 or IPv6. – sburlappp Oct 16 '14 at 23:51
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Your computer could have a million public IP addresses if configured as such. There's no 1:1 ratio required between computers and IP addresses.

I think you've answered your own question, though, even if you don't know it. Your computer (and the network you're on) has both IPv4 and IPv6 support. Chrome seems to be preferring IPv6 and firefox, IPv4.

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How can my computer have two different public IP addresses?

Your ISP has assigned you a IPv4 address and a IPv6 address.

How is this possible?

Your operating system and hardware supports both IPv4 and IPv6

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