# 127 (number)

From HandWiki

__: Natural number__

**Short description**
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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 | 1111111_{2} | |||

Ternary | 11201_{3} | |||

Quaternary | 1333_{4} | |||

Quinary | 1002_{5} | |||

Senary | 331_{6} | |||

Octal | 177_{8} | |||

Duodecimal | A7_{12} | |||

Hexadecimal | 7F_{16} | |||

Vigesimal | 67_{20} | |||

Base 36 | 3J_{36} |

**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

Original source: https://en.wikipedia.org/wiki/127 (number).
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