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127 (number)

From Wikipedia, the free encyclopedia

Natural number

127

←120 121 122 123 124 125 126 127 128 129 →

←0 100 200 300 400 500 600 700 800 900 →

one hundred twenty-seven

127th
(one hundred twenty-seventh)

31st

1, 127

ΡΚΖ´

CXXVII,cxxvii

1111111₂

11201₃

331₆

177₈

A7₁₂

7F₁₆

127 (one hundred [and] twenty-seven) is thenatural number following126 and preceding128. It is also a prime number.

In mathematics

127 as a centered hexagonal number

As aMersenne prime, 127 is related to theperfect number8128. 127 is also thelargest known Mersenne prime exponent for a Mersenne number, $2^{127}-1$ , which is also a Mersenne prime. It was discovered byÉdouard Lucas in 1876 and held the record for thelargest known prime for 75 years.
- $2^{127}-1$ is the largest prime ever discovered by hand calculations as well as the largest knowndouble 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 127prime numbers between2,000 and3,000.
127 is also acuban prime of the form $p={\frac {x^{3}-y^{3}}{x-y}}$ , $x=y+1$ .^[1] The next prime is 131, with which it comprises acousin prime. Because the nextodd number, 129, is asemiprime, 127 is aChen prime.^[2] 127 is greater than the arithmetic mean of its two neighboring primes; thus, it is astrong prime.^[3]
127 is acentered hexagonal number.^[4]
It is the seventhMotzkin number.^[5]
127 is apalindromic prime innonary andbinary.
127 is the firstFriedman 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 twelvepositive integers.^[6]
127 is the smallest prime that can be written as the sum of the first two or more odd primes: $127=3+5+7+11+13+17+19+23+29$ .^[7]
127 is the smallest odd number that cannot be written in the form $p+2^{x}$ , forp is aprime number, andx is aninteger, 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 allcomposite numbers.^[8]
127 is an isolated prime where neither $p-2$ nor $p+2$ is prime.
127 is the smallest digitally delicate prime in binary.^[9]
127 is the 31st prime number and therefore it is the smallestMersenne prime with a Mersenne prime index.
127 is the largest number with the property $127=1\cdot {\textrm {prime}}(1)+2\cdot {\textrm {prime}}(2)+7\cdot {\textrm {prime}}(7),$ where ${\textrm {prime}}(n)$ is thenth prime number. There are only two numbers with that property; the other one is43.
127 is equal to ${\textrm {prime}}^{6}(1),$ where ${\textrm {prime}}(n)$ is thenth prime number.
127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers.^[10]

In other fields

The non-printable "Delete" (DEL) control character inASCII.
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.

References

^"Sloane's A002407 : Cuban primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^Sloane, N. J. A. (ed.)."Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^"Sloane's A051634 : Strong primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A003215 : Hex (or centered hexagonal) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A001006 : Motzkin numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^Sloane, N. J. A. (ed.)."Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A071148".TheOn-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))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A137985".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-08-31.

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

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