127 (number) explained

Number:	127
Factorization:	prime
Prime:	31st
Divisor:	1, 127

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 , 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 = (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 is a prime number, and 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.

• 127 is an isolated prime where neither

p -2 nor p +2 is prime.

• 127 is the smallest digitally delicate prime in binary.^[7]
• 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 ⋅ rm{prime}(1) + 2 ⋅ rm{prime}(2) + 7 ⋅ rm{prime}(7), where rm{prime}(n) is the th prime number. There are only two numbers with that property; the other one is 43.

• 127 is equal to

rm{prime} ^{6} ( 1 ), where rm{prime}(n) is the th prime number.

• 127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers^[8]
• 127/50 = 2.54, the number of centimeters in one inch.

In the military

• • was a Mission Buenaventura-class fleet oilers during World War II was a United States Navy transport ship
• was a United States Navy
• was a United States Navy in World War II
• was a United States Navy
• was a United States Navy for removing naval mines

In religion

• The biblical figure Sarah died at the age of 127.^[9]
• According to the Book of Esther, the Persian Empire under Ahasuerus consisted of 127 provinces "from India to Ethiopia".^[10]
• Havamal Stanza 127 is used as a declaration against folkish traditions of Heathenry and specifically the Asatru Folk Assembly.^[11]

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

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

Notes and References

1. Web site: Sloane's A002407 : Cuban primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-27.
2. Web site: Sloane's A051634 : Strong primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-27.
3. Web site: Sloane's A003215 : Hex (or centered hexagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-27.
4. Web site: Sloane's A001006 : Motzkin numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-27.
5. sum_ sigma(k) where sigma(n) = sum of divisors of n.
6. . Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
7. . Complementing any single bit in the binary representation of these primes produces a composite number.
8. A065577. Number of Goldbach partitions of 10^n. 2023-08-31.
9. News: Sara. . September 8, 2015.
10. 1:1 HE
11. Web site: Declaration 127.