← 126 127 128 →
Cardinalone hundred twenty-seven
Ordinal127th
(one hundred twenty-seventh)
Factorizationprime
Prime31st
Divisors1, 127
Greek numeralΡΚΖ´
Roman numeralCXXVII
Binary11111112
Ternary112013
Senary3316
Octal1778
DuodecimalA712

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 the largest known Mersenne prime exponent for a Mersenne number, $2^{127}-1$ , 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.
• $2^{127}-1$ is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime.
• Furthermore, 127 is equal to $2^{7}-1$ , and 7 is equal to $2^{3}-1$ , 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 $p={\frac {x^{3}-y^{3)){x-y))$ , $x=y+1$ . 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 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 $127=2^{7}-1\,$ , as well as binary since $1111111=(1+1)^{111}-1\,$ .
• 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: $127=3+5+7+11+13+17+19+23+29$ .
• 127 is the smallest odd number that cannot be written in the form $p+2^{x)$ , 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 = 1*prime(1) + 2*prime(2) + 7*prime(7). Where prime(n) is the n-th prime number. There are only two numbers with that property, the other one is 43.
• 127 is the number of different ways in which 10,000 can be expressed as the sum of two prime numbers.