What is 2¹⁶, and why does it matter for networking?

65536 — the size of one port space: TCP has 65536 ports (0–65535) and UDP has its own separate 65536, because the port field in each header is 16 bits. More generally, the range of a 16-bit unsigned integer.

Chunk 65536 → 65 · 53 · 6 → shell · lamb · shoe: a lamb and a shoe tucked inside a giant sea shell. The port field in a TCP header and in a UDP header is 16 bits each, so each protocol has exactly 2¹⁶ = 65536 ports (0–65535). The two spaces are independent — TCP port 80 and UDP port 80 are different endpoints — and the highest port in either is 65535. (SCTP uses 16-bit ports too; ICMP has no ports at all.)

Tip: 65536 = 64 KiB, the addressable memory of many classic 8-bit and 16-bit machines.