/usr/share/doc/libssl-doc/demos/privkey.pem is in libssl-doc 1.0.1f-1ubuntu2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 | -----BEGIN RSA PRIVATE KEY-----
MIIBPAIBAAJBAN+FmbxmHVOp/RxtpMGz0DvQEBz1sDktHp19hIoMSu0YZift5MAu
4xAEJYvWVCshDiyOTWsUBXwZkrkt87FyctkCAwEAAQJAG/vxBGpQb6IPo1iC0RF/
F430BnwoBPCGLbeCOXpSgx5X+19vuTSdEqMgeNB6+aNb+XY/7mvVfCjyD6WZ0oxs
JQIhAPO+uL9cP40lFs62pdL3QSWsh3VNDByvOtr9LpeaxBm/AiEA6sKVfXsDQ5hd
SHt9U61r2r8Lcxmzi9Kw6JNqjMmzqWcCIQCKoRy+aZ8Tjdas9yDVHh+FZ90bEBkl
b1xQFNOdEj8aTQIhAOJWrO6INYNsWTPS6+hLYZtLamyUsQj0H+B8kNQge/mtAiEA
nBfvUl243qbqN8gF7Az1u33uc9FsPVvQPiBzLxZ4ixw=
-----END RSA PRIVATE KEY-----
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