577

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


 * The $106$th prime number


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


 * 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 $13$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$, $193$, $241$, $257$, $353$, $449$:
 * $577 = 9 \times 2^6 + 1$


 * The $33$rd minimal prime base $10$ after $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$, $71$, $73$, $79$, $83$, $89$, $97$, $227$, $251$, $257$, $277$, $281$, $349$, $409$, $449$, $499$, $521$, $557$


 * The $40$th long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $383$, $389$, $419$, $433$, $461$, $487$, $491$, $499$, $503$, $509$, $541$, $571$

Also see