Thank You All for helping me out & for the education! I appreciate it very much.
I MESSED UP & I OFFER MY APOLOGIES!
After re-reading everything I wrote here, I don't see that I mentioned that my telephone wiring is connected to this router with a RJ-45 cable into a special jack. We use the ISP for phone service. I totally forgot & I apologize for this. I'd have to guess this is an important detail!
Unplugging the phone didn't have an effect on the mystery IP address appearing in an IP Scan application.
I've started exploring & working on the suggestions you each provided. Hopefully today I will be able to do more, learning as I go.
Something I noticed today is that once you log into the router with the user name & password, you can change any of my settings- including network passwords without entering anymore password. The user name & password that the ISP set when installing were the defaults shown in the owner's manual. I changed the access password today.
I tried some of things that Lisa was kind enough to list in Post #13. (Thanks Lisa for those & the explanations!) Here's what I have so far:
Ping
Ping to the mystery IP address showed the pings returned. Pinging the normal IP showed the same results. Pinging my computer showed a timeout, indicating to me that the firewall is working. (If I understand this correctly...)
Traceroute
This showed the mystery IP address going back to itself & no packets were on the lst. The regular IP did the same. To my laptop, it showed packets going.
WhoIs
WhoIs showed no results for the mystery IP. For my laptop it showed:
Registrar: GMO Internet, Inc. dba Onamae.com
Registrar WHOIS Server: whois.discount-domain.com
Registrar URL:
http://www.onamae.com/
>>> Last update of whois database: 2017-11-25T13:57:45Z <<<
Port Scan
192.160.0.1 (The normal IP)
TCP 80 http
TCP 443 https
TCP 5000 Complex-Main
192.168.0.252 (The mystery address)
TCP 23 telnet
TCP 5150 ATMP showed on one scan, but not the next scan
In the router's configuration utility showed Active Access Points As:
2.4 Ghz Shows a list of the same nearby (neighboring houses & business') routers that Airport drop down list shows.
5 Ghz Shows “No data found” (We use the 5 Ghz)
Wireless Client List
2.4 Ghz Shows the computer I am using to access the router
Shows it twice with the same MAC Address but different IP address
One IP is 192.168.0.2
One IP is FE80:21B:63FF:FECC:4C06
5 Ghz Shows no one
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Is It Safe to Try This?
In the router's configuration page titled "LAN Setup Client List", is it safe to try deleting the mystery IP address?
The page shows it as "Offline" & shows a MAC Address of MAC Adress FF:FF;FF;FF;FF;FF (Different than what the IP Scan tools show)
Tried This Again
I plugged the laptop into the router directly
via an ethernet cord & removed the printer's cable and the telephone wire.
Logged into the router & turned off both 2.4 Ghz & 5 Ghz wireless.
Saved the changes & rebooted the router.
Rebooted the laptop.
The mystery IP address still showed up in the IP Scan applications.
I verified that wireless was off by trying to let a different laptop & an iPad find the network by using Airport. My network was not on the list.
Does this verify that the mystery IP address is not someone else plugged in?
I'll keep trying the items you all suggested & the items on Lisa's list. I sure am learning a lot & any day I can learn something new is a good day, indeed!
Paul
Unsolicited Editorial Comment
Some of these posts mentioned ISPs not liking Macs. I have to agree. As soon as I mention Mac, they say "Oh" followed by either a long silence or a transfer to someone else. They have a melt down if Mac Mail does not work & you have set up questions. Two of the agents I talked to about this mystery IP address question told me if I got a Windows computer, this would not happen because Macs are too easy to hack & Windows isn't (Huh?)
Most of my career was (and I still get called out) in designing & building power systems for sports, broadcast, entertainment and film. Way back in the early 1990's the rule-of-thumb was if broadcast on a NASCAR event went down, it costs over 10,000 dollars per second. And what were the only computers allowed to be used? Unix based- like a MAC.
Today, you will never see a non-Mac (or Unix) computer operating any broadcast equipment. The engineers say that is because they are very stable, can be easily paralleled for redundancy and it is simple (for them) to write custom applications. They also report very little bandwidth is used by Mac OS for communicating, making their setup simpler. (I am really uneducated on this, so I take their word for it.)
I have set often up multi-megawatt power systems for broadcast with an identical parallel system for automatic redundant backup. I have never been allowed to use any computer that is not Mac to operate the frequency synchronization and emergency switchover. I've seen computers fail while at the broadcast control station and the parallel computer ties in so fast that you can't even see a noise bar on the monitor. No one wold dare try that with a Windows based computer.