2147483647

2147483647 is a positive integer equal to 2^31 − 1, with a decimal representation of 2,147,483,647. In binary it is 0b01111111111111111111111111111111 and in hexadecimal it is 0x7FFFFFFF. It is a Mersenne prime, corresponding to the exponent p = 31, and is the eighth known Mersenne prime.

The number is most widely recognized for its role in computing as the maximum value of a 32-bit signed integer in two’s complement representation. On many systems and programming languages that use 32-bit ints, 2147483647 serves as INT_MAX. For example, Java defines the int type with a maximum value of 2147483647, and C/C++ libraries often define INT_MAX as this value on 32-bit platforms; on some systems int remains 32-bit even as other types widen.

In addition to its mathematical and programming significance, 2147483647 has practical implications in timekeeping. Some systems use a 32-bit signed time representation (time_t), where the value 2147483647 corresponds to 19 January 2038 03:14:07 UTC. Beyond that moment, time values may overflow, creating the so-called year 2038 problem on affected platforms.

Mathematically, 2147483647’s status as a prime number and a Mersenne prime contributes to its recognition in number theory. Its properties as a boundary value in fixed-width integer representations make it a common reference point in software design, testing, and compatibility discussions.