In the show notes for Network+ episode 2.3 they go into more detail about it:
A = N.H.H.H - 1st Number = 1-126 - Starts with 0 16,777,214 Usable IPs
? = Loopback - 1st Number = 127 - Starts with 01111111
B = N.N.H.H - 1st Number = 128-191 - Starts with 10 65,534 Usable IPs
C = N.N.N.H - 1st Number = 192-223 - Starts with 110 254 Usable IPs
D = ?.?.?.? - 1st Number = 224-239 - Starts with 1110
E = ?.?.?.? - 1st Number = 240-254 - Starts with 11110
In the early days of networking, there probably was a reason for this. It's too perfect to be an accident. Remember that the computers don't see the decimal numbers and they don't see the dots, they just see a stream of binary digits. What we see as 192.168.1.100, the machine sees as: 11000000101010000000000101100100
So 25 years ago some very expensive yet underpowered system could look at this address flying by and when it sees the "110" at the front, it knows how to treat this, even without a subnet mask.
The Hamachi guys were smart and resourceful. They needed a cheap and dirty way to create VPN connections on the public internet. They did not want to use RFC-1918 addresses as many routers on the live internet will just drop these packets. Also, they needed a system that for sure would not collide with any of the current IP Address assigned to any machine their users might install on.
History lesson: In the early days of the Internet, class A blocks were handed out all over the place. I know that Don talks about this in some of the shows. Pretty much anyone could get a class A block. Apple computer still owns the entire 184.108.40.206/8 address space to this day, and we gave up the entire 127.0.0.0/8 block just for loopback addresses. (I guess even computers love to hear themselves talk)
The Hamachi guys figured out that the class A network 220.127.116.11/8 had been assigned to someone but was not in use on the public internet -- so they essentially hijacked these addresses for their VPN service. At some point, the IANA pulled this block back and re-allocated it to a company called RIPE. This left Hamachi with a problem that they were going to have IP address conflicts, but they were able to search around and find another block of suitable addresses. It turns out that the 18.104.22.168/8 network was assigned to the British defense department, who does not just hang all of their systems off the public backbone with public IPs. So the 22.214.171.124/8 block is assigned but not in real use on the public internet. Hamachi switched from using 5.x.x.x addresses to using 25.x.x.x addresses a few years ago.
Hamachi also supports IPv6 addresses, which are available in bulk, but the above IPv4 hack is useful for people playing older LAN based games over a Hamachi VPN. If you are a fan of any of the old LAN games (Quake, UT, AOE, etc) then Hamachi is a way that you can play these with your friends without having to do the old LAN party.
Wikipedia of course has an entry on Hamachi, but if you are interested in more deep details then you can check out the Security Now guys at:
They have done a few deep dives into Hamachi in the past.