← 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

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

## References

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. ^
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. ^
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. ^