127 (number)

 ← 126 127 128 →
Cardinal one hundred twenty-seven
Ordinal 127th
(one hundred twenty-seventh)
Factorization prime
Prime 31st
Divisors 1, 127
Roman numeral CXXVII
Binary 11111112
Ternary 112013
Quaternary 13334
Quinary 10025
Senary 3316
Octal 1778
Duodecimal A712
Vigesimal 6720
Base 36 3J36

127 (one hundred [and] twenty-seven) is the natural number following 126 and preceding 128. It is also a prime number.

In mathematics

• As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 - 1, which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years - it is still the largest prime ever discovered by hand calculations. Furthermore, 127 is equal to 27 - 1, and 7 is equal to 23 - 1, and 3 is the smallest Mersenne prime, this makes 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime.
• 127 is also a cuban prime of the form ${\displaystyle p=(x^{3}-y^{3})/(x-y)}$, ${\displaystyle x=y+1}$.[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 is a strong prime.[2]
• 127 is a centered hexagonal number.[3]
• It is the 7th Motzkin number.[4]
• 127 is a palindromic prime in nonary and binary.
• It is the first nice Friedman number in base 10, since 127 = -1 + 27, as well as binary since 1111111 = (1 + 1)111 - 1 * 1.
• 127 is the sum of the sums of the divisors of the first 12 positive integers.[5]
• 127 is the smallest prime that can be written as the sum of the first two or more odd primes: 127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.[6]
• 127 is the smallest odd number that can't be written in the form p + 2x for p=prime number and x=integer, since 127 - 20 = 126, 127 - 21 = 125, 127 - 22 = 123, 127 - 23 = 119, 127 - 24 = 111, 127 - 25 = 95, and 127 - 26 = 63 are all composite numbers.[7]
• 127 is an isolated prime where both p-2 and p+2 isn't prime.

127 is also: