89 (number)

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88 89 90
Cardinal eighty-nine
Ordinal 89th
Factorization prime
Prime 24th
Divisors 1, 89
Roman numeral LXXXIX
Binary 10110012
Ternary 100223
Quaternary 11214
Quinary 3245
Senary 2256
Octal 1318
Duodecimal 7512
Hexadecimal 5916
Vigesimal 4920
Base 36 2H36

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

== In mathematics == 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]

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Eighty-nine is also:

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  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/2010/what-does-china-censor-online/ retrieved 28 May 2015