# 257

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## Number

$257$ (two hundred and fifty-seven) is:

The $55$th prime number

The $4$th Fermat number and Fermat prime after $3$, $5$, $17$:
$257 = 2^{\left({2^3}\right)} + 1 = 2^8 + 1$

The $4$th Sierpiński number of the first kind after $2$, $5$, $28$:
$257 = 4^4 + 1$

The $7$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$, $37$, $101$, $197$:
$257 = 16^2 + 1$

The $3$rd (and largest known) prime Sierpiński number of the first kind after $2$, $5$:
$257 = 4^4 + 1$

The $6$th balanced prime after $5$, $53$, $157$, $173$, $211$:
$257 = \dfrac {251 + 263} 2$