999

Number

$999$ (nine hundred and ninety-nine) is:

$3^3 \times 37$

The smallest integer which is the sum of a set of $3$ three-digit primes using all $9$ digits from $1$ to $9$ once each:

$149 + 263 + 587 = 999$

The smallest multiple of $27$ whose digits add up to $27$:

$999 = 37 \times 27$; $27 = 9 + 9 + 9$

The $8$th Kaprekar number after $1$, $9$, $45$, $55$, $99$, $297$, $703$:

$999^2 = 998 \, 001 \to 998 + 001 = 999$

The $25$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $501$, $624$, $625$, $749$, $751$, $875$:

$999^3 = 997 \, 002 \, \mathbf {999}$