487

Number
$487$ (four hundred and eighty-seven) is:


 * The $93$rd prime number


 * The $2$nd prime number $p$ after $3$ which satisfies the equation $p^2 \divides \paren {10^p - 10}$:
 * $487^2 \divides \paren {10^{487} - 10}$


 * The $6$th positive integer $n$ after $157$, $262$, $367$, $412$, $472$ for which $\map \phi {2 n + 1} < \map \phi {2 n}$:
 * $\map \phi {2 \times 487 + 1} = 480, \map \phi {2 \times 487} = 486$


 * The larger of the $6$th pair of primes whose prime gap is $8$:
 * $487 - 479 = 8$


 * The $22$nd integer after $7$, $13$, $19$, $35$, $38$, $\ldots$, $223$, $253$, $285$, $305$, $350$, $380$, $410$, $475$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $487^2 = 237 \, 169$; $23 \, 716 = 154^2$, $9 = 3^2$


 * The $33$rd long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $269$, $313$, $337$, $367$, $379$, $383$, $389$, $419$, $433$, $461$

Also see