# 89

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## Number

$89$ (**eighty-nine**) is:

- The $24$th prime number

- The $10$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$:
- $2 \times 89 + 1 = 179$, which is prime.

- The $11$th Fibonacci number, after $1$, $1$, $2$, $3$, $5$, $8$, $13$, $21$, $34$, $55$:
- $89 = 34 + 55$

- The $5$th Fibonacci prime after $2$, $3$, $5$, $13$

- The index of the $10$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$:
- $M_{89} = 2^{89} - 1 = 618 \, 970 \, 019 \, 642 \, 690 \, 137 \, 449 \, 562 \, 111$

- The $6$th prime $p$ such that $p \# - 1$, where $p \#$ denotes primorial (product of all primes up to $p$) of $p$, is prime:
- $3$, $5$, $11$, $13$, $41$, $89$

- The $1$st term of the smallest Cunningham chain of the first kind of length $6$:
- $\left({89, 179, 359, 719, 1439, 2879}\right)$

- The $11$th number after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ which is the sum of the increasing powers of its digits taken in order:
- $8^1 + 9^2 = 89$

- The $34$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
- $1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $89$, $\ldots$

- The $45$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $61$, $65$, $66$, $67$, $72$, $77$, $80$, $81$, $84$ which cannot be expressed as the sum of distinct pentagonal numbers.

- With $98$, gives the longest reverse-and-add sequence of any $2$-digit integers, of $24$ terms.

- The $7$th prime number after $2$, $3$, $5$, $7$, $23$, $67$ consisting of a string of consecutive ascending digits

- The $11$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$ such that the Fibonacci number $F_n$ ends in $n$

## Also see

*Previous ... Next*: Numbers which are Sum of Increasing Powers of Digits*Previous ... Next*: Fibonacci Prime*Previous ... Next*: Sequence of Prime Primorial minus 1*Previous ... Next*: Fibonacci Number*Previous ... Next*: Index of Mersenne Prime*Previous ... Next*: Prime Numbers Composed of Strings of Consecutive Ascending Digits*Previous ... Next*: Prime Number*Previous ... Next*: Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares*Previous ... Next*: Sophie Germain Prime*Previous ... Next*: Numbers not Expressible as Sum of Distinct Pentagonal Numbers*Previous ... Next*: Sequence of Fibonacci Numbers ending in Index

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $89$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $89$