127 (number)
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127 is the natural number following 126 and preceding 128.
| Cardinal | One hundred [and] twenty-seven |
| Ordinal | 127th |
| Factorization | prime |
| Roman numeral | CXXVII |
| Binary | 1111111 |
| Hexadecimal | 7F |
In mathematics
127 is a Mersenne prime, 27 - 1, and as such, in binary it is a repunit prime, a permutable prime and a palindromic prime. This also means it is the largest integer that can be represented by a signed byte. As a Mersenne prime, 127 is related to the perfect number 8128, and 2127 - 1 is also a Mersenne prime, making it a double Mersenne prime. 127 is also a cuban prime of the form [p = (x^3 - y^3) / (x - y)], [x = y + 1]. The next prime is 131, with which it comprises a cousin prime. Because the next odd number, 129, is a semiprime, 127 is a Chen prime. 127 is greater than the arithmetic mean of its two neighboring primes, thus it's a strong prime.It is the sum of the sums of divisors of the first twelve integers.
127 is a centered hexagonal number.
It is the 7th Motzkin number.
It is a nice Friedman number in base 10, since 127 = -1 + 27, as well as binary since 1111111 = (1 + 1)111 - 1 * 1.
It should also be noted that 2127 - 1 is also a Mersenne prime, discovered by Lucas in 1876. 2127 - 1 held the record for the largest known prime for 75 years, and it is the largest prime ever discovered by hand calculations. 2127 - 1 is a double Mersenne prime.
In other fields
One hundred [and] twenty-seven is also:- ASCII and Unicode code point for delete.
- The number of provinces ruled by King Xerxes I, "from India to Ethiopia" (Bible, Esther 1:1).
- The number of sons of Bethlehem at the Census of men of Israel upon return from exile (Bible, Ezra 2:21).
- The year AD 127 or 127 BC.
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