I have no ports opened on my router and it only shows up on my Mac.

Internet search shows the IP range is all from HP.

Could it be coming from the printer?

Wed Apr 13 05:42:28 2011 |  | GUI RPC request from non-allowed address 16.2.192.0
Wed Apr 13 06:24:23 2011 | SETI@home Beta Test | Computation for task 07mr11ah.23742.18881.206158430211.14.144_1 finished
Wed Apr 13 06:24:25 2011 | SETI@home Beta Test | Started upload of 07mr11ah.23742.18881.206158430211.14.144_1_0
Wed Apr 13 06:24:31 2011 | SETI@home Beta Test | Finished upload of 07mr11ah.23742.18881.206158430211.14.144_1_0
Wed Apr 13 08:30:08 2011 |  | GUI RPC request from non-allowed address 16.2.193.225
Wed Apr 13 08:58:39 2011 | SETI@home Beta Test | update requested by user
Wed Apr 13 08:58:42 2011 | SETI@home Beta Test | Sending scheduler request: Requested by user.
Wed Apr 13 08:58:42 2011 | SETI@home Beta Test | Reporting 4 completed tasks, not requesting new tasks
Wed Apr 13 08:58:45 2011 | SETI@home Beta Test | Scheduler request completed
Thu Apr 14 09:37:53 2011 |  | GUI RPC request from non-allowed address 16.2.239.33

I forwarded your post to the developers, hope they have more insight.
In the mean time, I do think it might be coming from your printer. Although I just set up a HP 3050 All-in-One for myself on our home network and I haven't seen anything like that from it, I do have to ask, how did you set up your printer?

What model printer is it?
Is it connected to your computer?
--If so how, by printer cable, USB cable or Ethernet cable?
Or is it on your network?
--If so how, by printer cable, USB cable or Ethernet cable to your Router or to something else?

---

Connected by USB, HP Deskjet F355. AIO.

It is shared to the other computers via Bonjour.

Networking doesn't work this way. If the host (with those suspicious connections) has no outgouing connections to those IP addresses, then your router must not let them in your network at all. That how NAT works.

But those connections are present. I believe, that some equipment on your network spits on your ethernet broken frames. That equipment, most probably, is either dieing or is broken out-of-the-box (the latter happens too, trust me). By accident, only boinc exhibits that noise; however, that doesn't mean that only boinc suffers that noise. I'd experienced something like this myself (dieing ethernet card).

I suggest you join some forum, IRC channel, newsgroup, whatever else that has somehting to do with networking and your operating system. I hope, regulars there could ask right questions and point to right tools that could help to find answers.

---

I'm counting for science,
points just make me sick.

With that said, the developers don't know either.
Yet there's one but: Normally you won't see GUI RPC requests showing in your messages, so do you have <gui_rpc_debug> (or <guirpc_debug> in pre-6.11 versions) on in cc_config.xml?

You could disable that (set to zero, or remove the line), save changes and let BOINC read the config file again. At least then you don't see these requests. They don't seem to be harmful either.

---

With that said, the developers don't know either.
Yet there's one but: Normally you won't see GUI RPC requests showing in your messages, so do you have <gui_rpc_debug> (or <guirpc_debug> in pre-6.11 versions) on in cc_config.xml?

You could disable that (set to zero, or remove the line), save changes and let BOINC read the config file again. At least then you don't see these requests. They don't seem to be harmful either.

I might have had them set at one time, but I removed them for one reason or the other.

All that is in the cc_config.xml is

<cc_config>
    <log_flags>
    </log_flags>
    <options>
    </options>
</cc_config>

Nothing has been logged since then either.