Why are USB hubs provided in 4- and 7-port varieties. What's special about these numbers? Why don't I see 3-, 5-, 6-, and 8-port hubs?
Is there something special about 4- and 7-port configurations that makes them more attractive?
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The reason is twofold:
Four-port hub is a mere manufacturing and user convenience. There are one-port hubs (as in active USB2 repeaters), two and tree-port hubs (mostly in "mobile" segment). People also mentioned 5 and 6-port hubs.
7-port hubs are due to specification constraints per single hub. While USB specifications allow for N ports per a single hub, the hub status change reporting is in bit-wise format, and the endpoint reporting granularity is defined as 1 byte (8 bits), see Section 11.12.4 of USB 2.0 Specs. As result, designers/manufacturers limit this reporting map to 1 byte. Upstream port is always Port0, which leaves only 7 ports for downstreams.
If you see more than a 7-port hub, it means that it contains two (or more) cascaded hub ICs inside the box.
Here's another aspect that is easily overlooked: Power!
USB 2.0 hub with 4 ports can directly run form host computer and provide minimum power to each port just form host.
On 7 port USB 2.0 hub, external power source is required to provide power for each port. Since each powered port needs 500 mA plus, we get 3.5 A power supply for external components (I'll assume that host computer can power the hub itself). At this point power supplies tend to get big and expensive and just the power supply can cost few times more that the hub itself.
As we are slowly moving to USB 3.0, power situation gets worse, since most basic unit load is 150 mA (up from 100 mA in USB 2.0) and each port can take up to 900 mA. So for 4 port hub, we'd need 3.6 A power supply.
Another interesting point is saturation of host port. As we get more and more ports on the hub, more and more devices will be connected meaning that the chances that several devices will try to use port at the same time increase. This could easily lead to performance problems.