257

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 $5, 53, 157, 173, 211$:
 * $257 = \dfrac {251 + 263} 2$

Also see

 * Construction of Regular $257$-Gon