Finding latest successful logins and failed attempts to a CentOS server

In Linux, the last command shows successful login attempts and displays session information (pts, source, date and length).

The lastb command records all bad login attempts. Both share the same man page, but the difference is that last reads the binary /var/log/wtmp file, and lastb reads the /var/log/btmp file by default.

The range of these files depends on your log rotation schedule, but it should span a few weeks. Most distributions will rotate /var/log/wtmp monthly, so you can read a previous record, usually listed as /var/log/wtmp.1 by specifying the file with the -f parameter... last -f /var/log/wtmp.1

The question is here offtopic, but a very short answer: maybe you should just check /var/log/secure (e.g. grep for "failed").