Английская Википедия:127 (number)
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Шаблон:Infobox number 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, <math>2^{127}-1</math>, 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.
- <math>2^{127}-1</math> is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime.
- Furthermore, 127 is equal to <math>2^{7}-1</math>, and 7 is equal to <math>2^{3}-1</math>, 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 <math>p=\frac{x^{3}-y^{3}}{x-y}</math>, <math>x=y+1</math>.[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 <math>127=2^{7}-1 \,</math>, as well as binary since <math>1111111 = (1 + 1)^{111} - 1 \,</math> .
- 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: <math>127 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29</math>.[6]
- 127 is the smallest odd number that cannot be written in the form <math>p+2^{x}</math>, for Шаблон:Mvar is a prime number, and Шаблон:Mvar is an integer, since <math>127 - 2^0=126,</math> <math>127 - 2^1=125,</math> <math>127 - 2^2=123,</math> <math>127 - 2^3=119,</math> <math>127 - 2^4=111,</math> <math>127 - 2^5=95,</math> and <math>127 - 2^6=63</math> are all composite numbers.[7]
- 127 is an isolated prime where neither <math>p-2</math> nor <math>p+2</math> 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 <math>127 = 1\cdot\textrm{prime}(1) + 2\cdot\textrm{prime}(2) + 7\cdot\textrm{prime}(7),</math> where <math>\textrm{prime}(n)</math> is the Шаблон:Mvarth prime number. There are only two numbers with that property; the other one is 43.
- 127 is equal to <math>\textrm{prime}^{6}(1),</math> where <math>\textrm{prime}(n)</math> is the Шаблон:Mvarth 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
- Шаблон:USNS was a Mission Buenaventura-class fleet oilers during World War II
- Шаблон:USS was a United States Navy transport ship
- Шаблон:USS was a United States Navy Шаблон:Sclass
- Шаблон:USS was a United States Navy Шаблон:Sclass in World War II
- Шаблон:USS was a United States Navy Шаблон:Sclass
- Шаблон:USS was a United States Navy Шаблон:Sclass for removing naval mines
In religion
- The biblical figure Sarah died at the age of 127.[10]
- According to the Book of Esther, the Persian Empire under Ahasuerus consisted of 127 provinces "from India to Ethiopia".[11]
- Havamal Stanza 127 is used as a declaration against folkish traditions of Heathenry and specifically the Asatru Folk Assembly.[12]
In transportation
- The small Fiat 127 automobile
- London Buses route 127 is a Transport for London contracted bus route in London
- 127 is the number of many roads, including U.S. Route 127
- STS-127 was a Space Shuttle Endeavour mission to the International Space Station which launched on June 15, 2009
In other fields
- 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 744 – 745 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
References
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite web
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS. Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite OEIS. Complementing any single bit in the binary representation of these primes produces a composite number.
- ↑ Шаблон:Cite OEIS
- ↑ Шаблон:Cite news
- ↑ Шаблон:Bibleverse
- ↑ Шаблон:Cite web
