127 (number)

127 prime 31st 1, 127 127 (one hundred [and] twenty-seven) is the natural number following 126 and preceding 128. It is also a prime number. In mathematics thumb|127 as a centered hexagonal 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 , .https://oeis.org/A002407 Sloane's A002407 : Cuban primes The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-05-27 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.A109611 Chen primes: primes p such that p + 2 is either a prime or a semiprime. 127 is greater than the arithmetic mean of its two neighboring primes; thus, it is a strong prime.https://oeis.org/A051634 Sloane's A051634 : Strong primes The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-05-27 127 is a centered hexagonal number.https://oeis.org/A003215 Sloane's A003215 : Hex (or centered hexagonal) numbers The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-05-27 It is the seventh Motzkin number.https://oeis.org/A001006 Sloane's A001006 : Motzkin numbers The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-05-27 127 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.A024916 sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n 127 is the smallest prime that can be written as the sum of the first two or more odd primes: .A071148. Partial sums of a sequence of odd primes; a(n) = sum of the first n 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 and are all composite numbers.A006285 Odd numbers not of form p + 2^x (de Polignac numbers) 127 is an isolated prime where neither nor is prime. 127 is the smallest digitally delicate prime in binary.A137985. Complementing any single bit in the binary representation of these primes produces a composite number. 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 nth prime number. There are only two numbers with that property; the other one is 43. 127 is equal to where is the nth prime number. 127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers.A065577 Number of Goldbach partitions of 10^n 2023-08-31 127 is the integer as floor of the imaginary part of the 42th non-trivial zero of the Riemann zeta-function.A013629. Floor of imaginary parts of nontrivial zeros of 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".A000959. Lucky numbers 127 is the 8th term in the prime number variation of Flavius's sieve.A099243. A variation on Flavius's sieve. 127 is a Fortunate number which is linked to the primorials.A005235. Fortunate numbers: least m > 1 such that m + prime(n)# is prime, where p# denotes the product of all primes <= p. 127 is the 11th super-prime. In Wilson's primeth recurrence, 127 is the sixth featuring prime, it being the 31st prime number and 31 being the fifth featuring. In other fields The non-printable "Delete" (DEL) control character in ASCII. Linotype (and Intertype) machines used brass matrices with one of 127 possible combinations punched into the top to enable the matrices to return to their proper channel in the magazine. References Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138 1 Category:Integers Category:Prime numbers