65539

The number 65539 is a significant value in computing and mathematics, particularly in the context of data representation and cryptography. It is one of the largest unsigned 16-bit integer values, expressed in decimal, and is equivalent to 2^16 - 1 (or 65536 + 3). In binary, it is represented as a sequence of sixteen 1s (1111111111111111), which is often used to denote a full bitmask or a maximum value in 16-bit systems.

In networking, 65539 is notable as the highest port number in the Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) port ranges. Port numbers are 16-bit unsigned integers, and 65539 is the last available port in the ephemeral range (ports 49152–65535), which are dynamically assigned by systems for temporary use in client-server communications.

The number also appears in cryptographic contexts, such as in the design of certain encryption algorithms and key sizes. For example, some early cryptographic standards used 16-bit keys, where 65539 could represent a maximum possible key value. Additionally, it plays a role in modular arithmetic, particularly in finite fields where it may appear as a prime modulus or in pseudorandom number generation.

Beyond computing, 65539 is occasionally referenced in mathematical discussions involving bitwise operations, binary representations, and computational limits. Its simplicity as a power of two minus one makes it a useful reference point in discussions about binary systems and their constraints.