/usr/lib/linux/3.13.0-166-generic/compiler is in linux-buildinfo-3.13.0-166-generic 3.13.0-166.216.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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GCC: (Ubuntu 4.8.4-2ubuntu1~14.04.4) 4.8.4