193

Number
$193$ (one hundred and ninety-three) is:


 * The $44$th prime number


 * The $2$nd of the $14$th pair of twin primes, with $191$


 * The $8$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$:
 * $193 = 3 \times 2^6 + 1$


 * The $17$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$, $97$, $109$, $113$, $131$, $149$, $167$, $179$, $181$


 * The $32$nd happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $130$, $133$, $139$, $167$, $176$, $188$, $190$, $192$:
 * $193 \to 1^2 + 9^2 + 3^2 = 1 + 81 + 9 = 91 \to 9^2 + 1^2 = 81 + 1 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$


 * The $37$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $133$, $135$, $141$, $151$, $159$, $163$, $169$, $171$, $189$, $193$, $\ldots$

Also see