# 518

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## Number

$518$ (five hundred and eighteen) is:

$2 \times 7 \times 37$

The $49$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $386$, $394$, $404$, $412$, $436$, $466$, $470$, $474$, $482$, $490$:
$\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 518$
where $\phi \left({m}\right)$ denotes the Euler $\phi$ function

The $40$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $324$, $326$, $336$, $342$, $372$, $406$, $408$, $426$, $430$, $448$, $472$, $474$, $498$, $516$

The $14$th number after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $89$, $135$, $175$ which is the sum of the increasing powers of its digits taken in order:
$5^1 + 1^2 + 8^3 = 518$

The $11$th even integer after $2$, $4$, $94$, $96$, $98$, $400$, $402$, $404$, $514$, $516$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes

The $4$th integer after $0$, $1$, $2$ such that its double factorial plus $1$ is prime:
$518!! + 1$ is prime