Number reference
127 explained.
127: one hundred twenty-seven, prime, mersenne prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred twenty-seven
- Classification
- prime
- Factors
- 1, 127
- Prime factorization
- 127
- Square root
- 11.269428
- Cube root
- 5.026526
- Binary
- 1111111
- Octal
- 177
- Hexadecimal
- 7F
- Roman numeral
- CXXVII
- Digit sum
- 10
- Digital root
- 1
What makes 127 notable
- Prime. 127 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Mersenne prime. 127 = 2^7 − 1 and is prime, making it a Mersenne prime. These are the primes that large prime searches concentrate on.
127 in everyday use
One hundred twenty-seven is the first number in the loopback address 127.0.0.1, which every computer uses to talk to itself, and the whole 127.x.x.x block is reserved for that purpose. It is the largest value a signed 8-bit integer can hold, so it turns up as a ceiling in old software, and it is the code of the DEL character in ASCII, the last of the 128 original codes. Both roles follow from the same fact: 127 is 2⁷ − 1, seven binary ones in a row.
That form also makes 127 a Mersenne prime, the fourth after 3, 7, and 31, and Euclid's recipe turns it into the perfect number 8128. Since 7 is itself a Mersenne prime, 127 is a double Mersenne prime, and 2¹²⁷ − 1 was the largest known prime for 75 years after Édouard Lucas proved it prime by hand in 1876. It is also the sum of the first seven powers of two, from 1 through 64.
Nearby numbers
How to read this page
Because 127 is prime, the factor list stops at 1 and 127 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 127 in its prime factorisation inherits it from here.
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