# 353

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## Number

$353$ (three hundred and fifty-three) is:

The $71$st prime number

The $1$st positive integer such that its fourth power is the sum of $4$ other fourth powers of positive integers with no common factors:
$353^4 = 30^4 + 120^4 + 272^4 + 315^4$

The $11$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$, $193$, $241$, $257$:
$353 = 11 \times 2^5 + 1$

The $12$th palindromic prime:
$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $\ldots$