127 (number)
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | one hundred twenty-seven | |||
| Ordinal | 127th (one hundred twenty-seventh) | |||
| Factorization | prime | |||
| Prime | 31st | |||
| Divisors | 1, 127 | |||
| Greek numeral | ΡΚΖ´ | |||
| Roman numeral | CXXVII | |||
| Binary | 11111112 | |||
| Ternary | 112013 | |||
| Quaternary | 13334 | |||
| Quinary | 10025 | |||
| Senary | 3316 | |||
| Octal | 1778 | |||
| Duodecimal | A712 | |||
| Hexadecimal | 7F16 | |||
| Vigesimal | 6720 | |||
| Base 36 | 3J36 | |||
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]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ 2^{7}-1 }[/math], and 7 is equal to [math]\displaystyle{ 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]\displaystyle{ p=\frac{x^{3}-y^{3}}{x-y} }[/math], [math]\displaystyle{ 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]\displaystyle{ 127=2^{7}-1 \, }[/math], as well as binary since [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ p+2^{x} }[/math], for p is a prime number, and x is an integer, since [math]\displaystyle{ 127 - 2^0=126, }[/math] [math]\displaystyle{ 127 - 2^1=125, }[/math] [math]\displaystyle{ 127 - 2^2=123, }[/math] [math]\displaystyle{ 127 - 2^3=119, }[/math] [math]\displaystyle{ 127 - 2^4=111, }[/math] [math]\displaystyle{ 127 - 2^5=95, }[/math] and [math]\displaystyle{ 127 - 2^6=63 }[/math] are all composite numbers.[7]
- 127 is an isolated prime where neither [math]\displaystyle{ p-2 }[/math] nor [math]\displaystyle{ 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]\displaystyle{ 127 = 1\cdot\textrm{prime}(1) + 2\cdot\textrm{prime}(2) + 7\cdot\textrm{prime}(7), }[/math] where [math]\displaystyle{ \textrm{prime}(n) }[/math] is the nth prime number. There are only two numbers with that property; the other one is 43.
- 127 is equal to [math]\displaystyle{ \textrm{prime}^{6}(1), }[/math] where [math]\displaystyle{ \textrm{prime}(n) }[/math] 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
- USNS Mission San Luis Obispo (T-AO-127) was a Mission Buenaventura-class fleet oilers during World War II
- USS Admiral W. S. Sims (AP-127) was a United States Navy transport ship
- USS Allendale (APA-127) was a United States Navy Haskell-class attack transport
- USS Alnitah (AK-127) was a United States Navy Crater-class cargo ship in World War II
- USS Raccoon (IX-127) was a United States Navy Armadillo-class tanker
- USS Tumult (AM-127) was a United States Navy Auk-class minesweeper 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
- 127th (disambiguation)
- List of highways numbered 127
- United Nations Security Council Resolution 127
References
- ↑ "Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407.
- ↑ "Sloane's A051634 : Strong primes". OEIS Foundation. https://oeis.org/A051634.
- ↑ "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation. https://oeis.org/A003215.
- ↑ "Sloane's A001006 : Motzkin numbers". OEIS Foundation. https://oeis.org/A001006.
- ↑ Sloane, N. J. A., ed. "Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". OEIS Foundation. https://oeis.org/A024916.
- ↑ Sloane, N. J. A., ed. "Sequence A071148". OEIS Foundation. https://oeis.org/A071148.. Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
- ↑ Sloane, N. J. A., ed. "Sequence A006285 (Odd numbers not of form p + 2^x (de Polignac numbers))". OEIS Foundation. https://oeis.org/A006285.
- ↑ Sloane, N. J. A., ed. "Sequence A137985". OEIS Foundation. https://oeis.org/A137985.. Complementing any single bit in the binary representation of these primes produces a composite number.
- ↑ Sloane, N. J. A., ed. "Sequence A065577 (Number of Goldbach partitions of 10^n)". OEIS Foundation. https://oeis.org/A065577. Retrieved 2023-08-31.
- ↑ "Sara". Catholic Encyclopedia. http://www.newadvent.org/cathen/13468a.htm.
- ↑ Esther 1:1
- ↑ "Declaration 127". http://www.declaration127.com/.
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138
 |  |
