The Social Security Administration advises:

Which Social Security numbers are invalid? An invalid or impossible SSN is one that we never assigned. We have never assigned an SSN with the first three digits of:

000;

666; or

900 series

Additionally, prior to June 25, 2011, we never assigned an SSN with the first three digits of:

000;

666;

Above 772 in the 700 series;

800 series; or

900 series

We have never assigned an SSN with the second two digits of 00 or the last four digits of 0000.

More information is available here.