127 (number)

Short description: Natural number
 ← 126 127 128 →
Cardinalone hundred twenty-seven
Ordinal127th
(one hundred twenty-seventh)
Factorizationprime
Prime31st
Divisors1, 127
Greek numeralΡΚΖ´
Roman numeralCXXVII
Binary11111112
Ternary112013
Quaternary13334
Quinary10025
Senary3316
Octal1778
DuodecimalA712
Vigesimal6720
Base 363J36

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 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 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.

• 127th (disambiguation)
• List of highways numbered 127
• United Nations Security Council Resolution 127

References

1. "Sloane's A002407 : Cuban primes". OEIS Foundation.
2. "Sloane's A051634 : Strong primes". OEIS Foundation.
3. "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation.
4. "Sloane's A001006 : Motzkin numbers". OEIS Foundation.
5. Sloane, N. J. A., ed. "Sequence A071148". OEIS Foundation. . Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
6. Sloane, N. J. A., ed. "Sequence A137985". OEIS Foundation. . Complementing any single bit in the binary representation of these primes produces a composite number.
7. Sloane, N. J. A., ed. "Sequence A065577 (Number of Goldbach partitions of 10^n)". OEIS Foundation. Retrieved 2023-08-31.
8. Esther 1:1
• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138