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Natural number
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
{\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}
.
[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 .
[2] 127 is greater than the arithmetic mean of its two neighboring primes; thus, it is a
strong prime .
[3]
127 is a
centered hexagonal number .
[4]
It is the seventh
Motzkin number .
[5]
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 .
[6]
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}
.
[7]
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 .
[8]
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.
[9]
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 n th 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 n th prime number.
127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers
[10]
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
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000