577

Number
$577$ (five hundred and seventy-seven) is:


 * The $106$th prime number


 * The smaller of the $9$th pair of primes whose prime gap is $10$:
 * $587 - 577 = 10$


 * The $9$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$, $37$, $101$, $197$, $257$, $401$:
 * $577 = 24^2 + 1$


 * The $7$th positive integer $n$ after $157$, $262$, $367$, $412$, $472$, $487$ for which $\phi \left({2 n + 1}\right) < \phi \left({2 n}\right)$:
 * $\phi \left({2 \times 577 + 1}\right) = 480, \phi \left({2 \times 577}\right) = 576$