127 (nombre)

127 (one hundred [and] twenty-seven') is the natural number following 126 and preceding 128. It is also a prime number. As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also the largest known Mersenne prime exponent for a Mersenne number, , which is also a Mersenne prime. It was discovered by Édouard Lucas in 1876 and held the record for the largest known prime for 75 years. is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime. Furthermore, 127 is equal to , and 7 is equal to , and 3 is the smallest Mersenne prime, making 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime. There are a total of 127 prime numbers between 2,000 and 3,000. 127 is also a cuban prime of the form , . 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. 127 is a centered hexagonal number. It is the seventh Motzkin number. 127 is a palindromic prime in nonary and binary. 127 is the first Friedman prime in decimal. It is also the first nice Friedman number in decimal, since , as well as binary since . 127 is the sum of the sums of the divisors of the first twelve positive integers. 127 is the smallest prime that can be written as the sum of the first two or more odd primes: . 127 is the smallest odd number that cannot be written in the form , for p is a prime number, and x is an 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. 127 is an isolated prime where neither p-2 nor p+2 are prime. 127 is the smallest digitally delicate prime in binary. 127 is the 31st prime number and therefore it is the smallest Mersenne prime with a Mersenne prime index. 127 is the largest number with the property 127 = 1prime(1) + 2prime(2) + 7*prime(7). Where prime(n) is the n-th prime number.