89 (number): Difference between revisions

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{{Infobox number

[[Link title]]'''89''' ('''eighty-nine''') is the [[natural number]] following [[88 (number)|88]] and preceding [[90 (number)|90]].

| number = 89

| factorization = [[prime number|prime]]

<table border=1 style="float: right; border-collapse: collapse;">

| prime = 24th

<tr><td colspan=2>{{Numbers_80s}}

| divisor = 1, 89

<tr><td>[[Cardinal number|Cardinal]]<td>89<br>eighty-nine

}}

<tr><td>[[Ordinal number|Ordinal]]<td>89th<br>eighty-ninth

[[Link title]]'''89''' ('''eighty-nine''') is the [[natural number]] following [[88 (number)|88]] and preceding [[90 (number)|90]].

<tr><td>[[Factorization]]<td><math>prime</math>

<tr><td>[[Divisor]]s<td> 1, 89

<tr><td>[[Roman numeral]]<td>LXXXIX

<tr><td>[[Binary numeral system|Binary]]<td>01011001

<tr><td>[[Hexadecimal]]<td>59

</table>

== In mathematics ==

'''89''' is:

'''Eighty-nine''' is the 24th [[prime number]], following [[83 (number)|83]] and preceding [[97 (number)|97]]. 89 is a [[Chen prime]]. It is the smallest [[Sophie Germain prime]] to start a [[Cunningham chain]] of the first kind of six terms, {89, 179, 359, 719, 1439, 2879}. 89 is an [[Eisenstein prime]] with no imaginary part and real part of the form <math>3n - 1</math>.

* the 24th [[prime number]], following [[83 (number)|83]] and preceding [[97 (number)|97]].

89 is a [[Fibonacci number]]. Its reciprocal has a curious relationship to the Fibonacci sequence F(n):

* a [[Chen prime]].<ref>{{Cite web|url=https://oeis.org/A109611|title=Sloane's A109611 : Chen primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>

* a [[Pythagorean prime]].<ref>{{Cite web|url=https://oeis.org/A002144|title=Sloane's A002144 : Pythagorean primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref>

* the smallest [[Sophie Germain prime]] to start a [[Cunningham chain]] of the first kind of six terms, {89, 179, 359, 719, 1439, 2879}.

* an [[Eisenstein prime]] with no imaginary part and real part of the form {{nowrap|3''n'' − 1}}.

* The 11th [[Fibonacci number]] and thus a [[Fibonacci prime]] as well.<ref>{{Cite web|url=https://oeis.org/A005478|title=Sloane's A005478 : Prime Fibonacci numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-29}}</ref> The first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity

::<math>\frac{1}{89}=\sum_{n=1}^\infty{F(n)\times 10^{-(n+1)}}=0.011235955..\dots\ .</math>

89 is also* a [[Markov number]], appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers.

''M''₈₉ is the 10th [[Mersenne prime]].

<math>\frac{1}{89}=\sum_{n=1}^\infty{F(n)\times 10^{-(n+1)}}=0.011235955...</math>

Although 89 is not a [[Lychrel number]] in base 10, it is unusual that it takes 24 iterations of the reverse and add process to reach a [[palindrome]]. Among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations. The palindrome reached is also unusually large: 8813200023188.<ref>Weisstein, Eric W. "196-Algorithm." From MathWorld, a Wolfram Web Resource. [http://mathworld.wolfram.com/196-Algorithm.html http://mathworld.wolfram.com/196-Algorithm.html]</ref>

89 is also a [[Markov number]], appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers.

There are exactly 1000 prime numbers between 1 and 89²=7921.<ref>{{Cite web |title=Prime Curios! 89 |url=https://primes.utm.edu/curios/page.php/89.html |access-date=2022-12-19 |website=primes.utm.edu}}</ref>

Being the solution to ''x'' - &phi;(''x'') more often than any lower number, 89 is a [[highly cototient number]].

== In sports ==

Although 89 is not a [[Lychrel number]] in base 10, it is unusual that it takes 24 iterations of the reverse and add process to reach a palindrome. Among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations.

* The [[Oklahoma Redhawks]], an American [[minor league baseball]] team, were formerly known as the Oklahoma 89ers (1962–1997). The number alludes to the [[Land Run of 1889]], when the [[Unassigned Lands]] of Oklahoma were opened to [[White American|white]] settlement. The team's home of [[Oklahoma City]] was founded during this event.

* In [[List of rugby union terms|Rugby]], an "89" or eight-nine move is a phase following a scrum, in which the number 8 catches the ball and transfers it to number 9 (scrum half).

==In [[astronomy]]==

*[[Messier object]] [[M89]], a [[visual magnitude|magnitude]] 11.5 [[elliptical galaxy]] in the [[constellation]] [[Virgo (constellation)|Virgo]].

*The [[New General Catalogue]] [http://www.ngcic.com/ object] [[NGC 89]], a magnitude 13.5 [[peculiar galaxy|peculiar]] [[spiral galaxy]] in the constellation [[Phoenix (constellation)|Phoenix]] and a member of [[Robert's Quartet]].

*The [[Saros]] number of the [[solar eclipse]] series which began on [[18]] [[February 4]] and ended on [[1316]] [[March 24]]. The duration of Saros series 89 was 1298.1 years, and it contained 73 solar eclipses. Further the Saros number of the [[lunar eclipse]] series which began on [[67]] [[June 15]] and ended on [[1347]] [[July 23]]. The duration of Saros series 89 was 1280.1 years, and it contained 72 lunar eclipses.

== In other fields ==

[[Image:TIDiaethria clymena or Cramer's Eighty-89eight.jpg underside Tr.jpg|thumb|80px|''[[TI-89Diaethria clymena]]'' eyespots]]

'''Eighty-nine''' is also:

* ''[[Information Is Beautiful]]'' cites [[Tiananmen Square protests of 1989|eighty-nine]] as one of the words censored on the [[Internet in China|Chinese internet]].<ref>{{cite web |url=http://www.informationisbeautiful.net/2010/what-does-china-censor-online/ |title=What Does China Censor Online? |website=www.informationisbeautiful.net |access-date=28 May 2015}}</ref>

==See also==

*The [[atomic number]] of [[actinium]].

*[[Hellin's law]]

*the model number of [[CBU-89 Gator]] and the [[TI-89]] graphing calculator

*part of the name of the baseball team [[Oklahoma City 89ers]] (1962-1997)

==References==

*the number of the [[French department]] [[Yonne]]

<references/>

*the designation of [[Interstate 89]], a freeway that runs from [[New Hampshire]] to [[Vermont]]

*The [[ISBN]] Group Identifier for books published in [[Korea]]

{{Integers|zero}}

*The capital letter Y in [[ASCII]]

*The year AD '''[[89]]''', [[89 BC]], [[1989]], or [[1789]] starting year of the [[French Revolution]].

[[Category:Integers]]

[[es:Ochenta y nueve]]

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