# 89 (number)

 ← 88 89 90 →
Cardinaleighty-nine
Ordinal89th
(eighty-ninth)
Factorizationprime
Prime24th
Divisors1, 89
Roman numeralLXXXIX
Binary10110012
Ternary100223
Quaternary11214
Quinary3245
Senary2256
Octal1318
Duodecimal7512
Vigesimal4920
Base 362H36

 ← 88 89 90 →
Cardinaleighty-nine
Ordinal89th
(eighty-ninth)
Factorizationprime
Prime24th
Divisors1, 89
Roman numeralLXXXIX
Binary10110012
Ternary100223
Quaternary11214
Quinary3245
Senary2256
Octal1318
Duodecimal7512
Vigesimal4920
Base 362H36

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]

## In other fields

Eighty-nine is also: