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This Chrome (series 48 ) is not current; also i386 is for 32-bit systems.

The Chromium which comes with Mint17.3 usVersion 50.0.2661.102 Built on Ubuntu 14.04, running on LinuxMint 17.3 (64-bit)...

Knoppix 7.6.1 and Knoppix 7.7 both work with either 32-bit or 64-bit kernels.
The knoppix cheat code at boot gives you 32-bit; the cheatcode knoppix64 gives you 64-bit.
With 7.7, Knoppix...

I'm using 64-bit Mint 17.3 Xfce as I write this. Just earlier I installed what appears to be an amd64 version of Chromium which seems to be
in working order, although I've not connected to Google...

Here's a conjecture you might want to consider:

FWIW, Chromium is supported by Linux Mint and Knoppix.
Chromium is supposed to be an open source equivalent of Chrome.

Chrome 64-bit builds will...