# 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 smaller of the smallest pair of primes whose prime gap is $8$:
$97 - 89 = 8$

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 $n$