127 (number)

Summary

127 (one hundred [and] twenty-seven) is the natural number following 126 and preceding 128. It is also a prime number.

← 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
Hexadecimal7F16

In mathematics edit

  • 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  ,  .[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.[2]
  • 127 is a centered hexagonal number.[3]
  • It is the seventh Motzkin number.[4]
  • 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.[5]
  • 127 is the smallest prime that can be written as the sum of the first two or more odd primes:  .[6]
  • 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.[7]
  • 127 is an isolated prime where neither   nor   is prime.
  • 127 is the smallest digitally delicate prime in binary.[8]
  • 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[9]
  • 127/50 = 2.54, the number of centimeters in one inch.

In the military edit

In religion edit

In transportation edit

In other fields edit

  • 127 Hours is a film released in 2010
  • The year AD 127 or 127 BC
  • 127 AH is a year in the Islamic calendar that corresponds to 744745 CE
  • 127 Johanna, a Main belt asteroid
  • 127 film, a film format
  • The atomic number of Unbiseptium, an element that has not yet been discovered
  • The LZ 127 Graf Zeppelin, a dirigible
  • Sonnet 127 by William Shakespeare
  • 127th Street Ensemble was a troupe of African-American actors which included Tupac Amaru Shakur
  • NCT 127, K-pop boy group under SM Entertainment
  • In IP (Internet Protocol) Version 4, it is the last Class A network and is also the subnet used for loopback functionality in computer networking
  • The highest signed 8-bit integer, using two's complement
  • 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.
  • 127 is the smallest positive integer, n, such that n centimeters is a whole number of inches. 127 cm is exactly 50 inches.
  • 127 is the total number of people, including self and all ancestors, in a 7-generation (back to 4-great grandparents) pedigree chart in genealogy.

See also edit

References edit

  1. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. ^ "Sloane's A051634 : Strong primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  3. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  4. ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A071148". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A006285 (Odd numbers not of form p + 2^x (de Polignac numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A137985". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Complementing any single bit in the binary representation of these primes produces a composite number.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A065577 (Number of Goldbach partitions of 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-08-31.
  10. ^ "Sara". Catholic Encyclopedia. Retrieved September 8, 2015.
  11. ^ Esther 1:1
  12. ^ "Declaration 127".