89 (number)

From Wikipedia, the free encyclopedia - View original article

888990
Cardinaleighty-nine
Ordinal89th
(eighty-ninth)
Factorizationprime
Prime24th
Divisors1, 89
Roman numeralLXXXIX
Binary10110012
Ternary100223
Quaternary11214
Quinary3245
Senary2256
Octal1318
Duodecimal7512
Hexadecimal5916
Vigesimal4920
Base 362H36
 
Jump to: navigation, search
888990
Cardinaleighty-nine
Ordinal89th
(eighty-ninth)
Factorizationprime
Prime24th
Divisors1, 89
Roman numeralLXXXIX
Binary10110012
Ternary100223
Quaternary11214
Quinary3245
Senary2256
Octal1318
Duodecimal7512
Hexadecimal5916
Vigesimal4920
Base 362H36

89 (eighty-nine) is the natural number following 88 and preceding 90.

In mathematics[edit]

Eighty-nine is the 24th prime number, following 83 and preceding 97. 89 is a Chen prime and a Pythagorean 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 3n - 1. M89 is the 10th Mersenne prime.

89 is a Fibonacci number and thus a Fibonacci prime as well. The first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity

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

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

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.[1]

In science[edit]

In astronomy[edit]

In sports[edit]

In other fields[edit]

Eighty-nine is also:

See also[edit]

References[edit]

  1. ^ Weisstein, Eric W. "196-Algorithm." From MathWorld, a Wolfram Web Resource. http://mathworld.wolfram.com/196-Algorithm.html
  2. ^ Greenberg, Jon (December 9, 2013). "Mike Ditka gets jersey retired". ESPN. Retrieved February 2, 2014. 
  3. ^ http://www.informationisbeautiful.net/ retrieved 16 January 2010[dead link]