512

Number
$512$ (five hundred and twelve) is:
 * $2^9$


 * In binary:
 * $1 \, 000 \, 000 \, 000$


 * In octal:
 * $1 \, 000$


 * The $3$rd cube after $0$, $1$ whose digits add up to its root:
 * $512 = 8^3$, while $5 + 1 + 2 = 8$


 * The $3$rd power of $8$ after $(1)$, $8$, $64$:
 * $512 = 8^3$


 * The $8$th cube number after $1$, $8$, $27$, $64$, $125$, $216$, $343$:
 * $512 = 8 \times 8 \times 8$


 * The $9$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$:
 * $512 = 2^9$


 * The $10$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$:
 * $\map \sigma {512} = 1023 = 2 \times 512 - 1$


 * The $10$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$, $432$, $448$, $480$ with $7$ or more prime factors:
 * $512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \paren {\times \, 2 \times 2}$


 * The index (after $2$, $3$, $6$, $30$, $75$, $81$, $115$, $123$, $249$, $362$, $384$, $462$) of the $13$th Woodall prime:
 * $512 \times 2^{512} - 1$


 * The $14$th positive integer after $200$, $202$, $204$, $205$, $206$, $208$, $320$, $322$, $324$, $325$, $326$, $328$, $510$ that cannot be made into a prime number by changing just $1$ digit


 * The $25$th positive integer after $64$, $96$, $128$, $144$, $\ldots$, $384$, $400$, $416$, $432$, $448$, $480$, $504$ with $6$ or more prime factors:
 * $512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \paren {\times \, 2 \times 2 \times 2}$


 * The $39$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $289$, $324$, $343$, $361$, $392$, $400$, $432$, $441$, $484$, $500$:
 * $512 = 2^9$

Also see