127 (number)
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127 (one hundred 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
{\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.
-
2
127
−
1
{\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
2
7
−
1
{\displaystyle 2^{7}-1}
, and 7 is equal to
2
3
−
1
{\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
p
=
x
3
−
y
3
x
−
y
{\displaystyle p={\frac {x^{3}-y^{3}}{x-y}}}
,
x
=
y
+
1
{\displaystyle x=y+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.
- 127 is a centered hexagonal number.
- It is the seventh Motzkin number.
- 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
{\displaystyle 127=2^{7}-1\,}
, as well as binary since
1111111
=
(
1
+
1
)
111
−
1
{\displaystyle 1111111=(1+1)^{111}-1\,}
.
- 127 is the sum of the sums of the divisors of the first twelve positive integers.
- 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
{\displaystyle 127=3+5+7+11+13+17+19+23+29}
.
- 127 is the smallest odd number that cannot be written in the form
p
+
2
x
{\displaystyle p+2^{x}}
, for p is a prime number, and x is an integer, since
127
−
2
0
=
126
,
{\displaystyle 127-2^{0}=126,}
127
−
2
1
=
125
,
{\displaystyle 127-2^{1}=125,}
127
−
2
2
=
123
,
{\displaystyle 127-2^{2}=123,}
127
−
2
3
=
119
,
{\displaystyle 127-2^{3}=119,}
127
−
2
4
=
111
,
{\displaystyle 127-2^{4}=111,}
127
−
2
5
=
95
,
{\displaystyle 127-2^{5}=95,}
and
127
−
2
6
=
63
{\displaystyle 127-2^{6}=63}
are all composite numbers.
- 127 is an isolated prime where neither
p
−
2
{\displaystyle p-2}
nor
p
+
2
{\displaystyle p+2}
is prime.
- 127 is the smallest digitally delicate prime in binary.
- 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
⋅
prime
(
1
)
+
2
⋅
prime
(
2
)
+
7
⋅
prime
(
7
)
,
{\displaystyle 127=1\cdot {\textrm {prime}}(1)+2\cdot {\textrm {prime}}(2)+7\cdot {\textrm {prime}}(7),}
where
prime
(
n
)
{\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
prime
6
(
1
)
,
{\displaystyle {\textrm {prime}}^{6}(1),}
where
prime
(
n
)
{\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
- 127/50 = 2.54, the number of centimeters in one inch.
In the military
In religion
In transportation
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
References
- ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "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".
Integers |
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≥1000 |
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- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
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