127 (number)

← 126 127 128 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
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
Senary	3316
Octal	1778
Duodecimal	A712
Hexadecimal	7F16

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, $2^{127}-1$ $2^{127}-1$ , 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.
- $2^{127}-1$ is the largest prime ever discovered by hand calculations as well as the largest known double Mersenne prime.
- Furthermore, 127 is equal to $2^{7}-1$ , and 7 is equal to $2^{3}-1$ , 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 $p={\frac {x^{3}-y^{3}}{x-y}}$ , $x=y+1$ .[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 $127=2^{7}-1\,$ , as well as binary since $1111111=(1+1)^{111}-1\,$ .
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: $127=3+5+7+11+13+17+19+23+29$ .[6]
127 is the smallest odd number that cannot be written in the form $p+2^{x}$ , for $p$ is a prime number, and $x$ is an integer, since $127-2^{0}=126,$ $127-2^{1}=125,$ $127-2^{2}=123,$ $127-2^{3}=119,$ $127-2^{4}=111,$ $127-2^{5}=95,$ and $127-2^{6}=63$ are all composite numbers.[7]
127 is an isolated prime where neither $p-2$ nor $p+2$ 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 $127=1\cdot {\textrm {prime}}(1)+2\cdot {\textrm {prime}}(2)+7\cdot {\textrm {prime}}(7),$ where ${\textrm {prime}}(n)$ is the $n$ th prime number. There are only two numbers with that property; the other one is 43.
127 is equal to ${\textrm {prime}}^{6}(1),$ where ${\textrm {prime}}(n)$ is the $n$ th prime number.
127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers[9]

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.

References

"Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
"Sloane's A051634 : Strong primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
"Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
"Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
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.
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.
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.
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.
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.
"Sara". Catholic Encyclopedia. Retrieved September 8, 2015.
Esther 1:1
"Declaration 127".

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138

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[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".