89 (number)
Encyclopedia : 8 : 89 : 89N : 89 (number)
89 (eighty-nine) is the natural number following 88 and preceding 90.
| Cardinal | 89 eighty-nine |
| Ordinal | 89th eighty-ninth |
| Factorization | [prime] |
| Roman numeral | LXXXIX |
| Binary | 01011001 |
| Hexadecimal | 59 |
In mathematics
Eighty-nine is the 24th prime number, following 83 and preceding 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 is an Eisenstein prime with no imaginary part and real part of the form [3n - 1].89 is a Fibonacci number. Its reciprocal has a curious relationship to the Fibonacci sequence F(n):
[\frac=\sum_^\infty}=0.011235955...]
89 is also a Markov number, appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers.
Being the solution to x - φ(x) more often than any lower number, 89 is a highly cototient number.
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.
