Should I worry about imap connections from an unknown IP?

I'm the only person with access to my server. I don't do any reselling. In my logwatch last night I had this entry:

--------------------- Connections (secure-log) Begin ------------------------

Connections:
Service imap:
69.56.245.114: 2 Time(s)
127.0.0.1: 176 Time(s)


I have no idea who's IP the 69.56.245.114 is. It's a webhost in texas (theplanet.com) which is far away from me.

 

Do invalid logins show up there also? For some reason I was thinking that if they show up in that log in means they were successful connections.

I do have a good password and I'm very careful with security so I think it's unlikely that anyone would be able to get ahold of it or brute-force their way in.

 

I guess I need to get BFD installed. Usually the only thing in this log is 127.0.0.1 and every now and then maybe one other that tried to connect once. The last couple of days though it's been full of them and looked like this:

Code:

--------------------- Connections (secure-log) Begin ------------------------ 

Connections:
   Service imap:
      60.164.127.2: 2 Time(s)
      67.15.62.16: 420 Time(s)
      81.220.165.125: 2 Time(s)
      82.48.107.11: 2 Time(s)
      82.56.16.189: 2 Time(s)
      82.56.20.227: 2 Time(s)
      82.67.210.110: 2 Time(s)
      83.50.98.133: 2 Time(s)
      84.0.246.135: 2 Time(s)
      84.97.58.52: 2 Time(s)
      84.121.70.190: 2 Time(s)
      84.164.95.209: 3 Time(s)
      86.125.16.122: 2 Time(s)
      127.0.0.1: 173 Time(s)
      134.39.120.248: 1 Time(s)
      218.7.13.217: 2 Time(s)
      218.16.129.221: 2 Time(s)
      222.11.219.8: 1 Time(s)
      222.83.232.234: 2 Time(s)
      222.86.62.33: 2 Time(s)
      222.95.172.54: 2 Time(s)

How do you tell if a connection was actually successful and not just an invalid log-in attempt?