32767

32767 is a decimal integer that follows 32766 and precedes 32768. It equals 2^15 − 1, and its binary form is 0111111111111111, with hexadecimal representation 0x7FFF.

Mathematically, 32767 factors as 7 × 31 × 151. It is a composite Mersenne number (2^15 − 1), since the exponent 15 is not prime, so it is not a Mersenne prime.

In computing, 32767 is significant as the maximum positive value of a signed 16-bit integer in two's complement representation. The corresponding minimum is −32768, and many programming environments expose this limit as a constant (for example, the Java Short.MAX_VALUE and the C macro INT16_MAX).

In digital audio, 16-bit PCM samples use a range from −32768 to +32767. Therefore, 32767 represents the largest positive sample value, a common boundary in audio processing and storage formats.

Outside of these contexts, 32767 often appears as a boundary or sentinel in testing, edge-case scenarios, or demonstrations involving 16-bit integer arithmetic. Its role as a well-known fixed upper bound for signed 16-bit values makes it a reference point across programming, digital audio, and legacy hardware discussions.