127 (number) - in Mathematics

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 (2127 - 1 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 because 7 is also a Mersenne prime, this makes 127 a double Mersenne prime.

• 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's a strong prime.

• 127 is a centered hexagonal number.

• It is the 7th Motzkin number.

• 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.