plaidCTF 2014 - rsa (for450)

For PlaidCTF2014, Eindbazen and fail0verflow joined forces as 0xffa, the Final Fail Alliance.
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Forensics (450 pts)
Our archaeologists recovered a dusty and corrupted old hard drive used by
The Plague in his trips into the past. It contains a private key, but this
has long since been lost to bitrot. Can you recover the full key from the
little information we have recovered?

You can download the recovered information here.