2Exponent127

2exponent127 refers to the mathematical expression 2^127, meaning two raised to the 127th power. It is a large power of two that is exactly representable in binary, since it equals a 1 followed by 127 zero bits.

The decimal value of 2^127 is 170141183460469231731687303715884105728. In scientific notation, it is approximately 1.7014 × 10^38. It is also the halfway point to 2^128, since 2^127 is half of 2^128. In binary, 2^127 has a simple representation: a 1 followed by 127 zeros.

A related and notable number is 2^127 − 1, which is a Mersenne prime. Mersenne primes are primes of the form 2^p − 1 where p itself is prime; 2^127 − 1 is among the historically significant large primes used in primality testing and the study of prime distributions. The Lucas–Lehmer test is commonly employed to verify such primes.

In computing, 2^127 marks a boundary in fixed-width arithmetic. In 128-bit two’s complement systems, the maximum positive signed value is 2^127 − 1, so 2^127 itself lies just outside the range of a signed 128-bit integer; the unsigned 128-bit range goes up to 2^128 − 1.

See also: Mersenne prime, 128-bit integer, exponent notation, binary representation.