127 (number)
127 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,, 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 is a prime number, and is an integer, since and are all composite numbers.
- 127 is an isolated prime where neither nor is 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 where is the th prime number. There are only two numbers with that property; the other one is 43.
- 127 is equal to where is the th prime number.
- 127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers.
- 127 is the integer as floor of the imaginary part of the 42th non-trivial zero of the Riemann zeta-function.
- 127 is the smallest prime number that results in a decimal greater than 4 when divided by its prime index. 127 divided by 31 is 4 with a remainder of 3.
- 127 is a Lucky number which is generated by a certain "sieve".
- 127 is the 8th term in the prime number variation of Flavius's sieve.
- 127 is a Fortunate number which is linked to the primorials.