829

Number
$829$ (eight hundred and twenty-nine) is:


 * The $145$th prime number


 * The $4$th after $199$, $409$, $619$ of the smallest $10$ primes in arithmetic sequence:
 * $829 = 3 \times 210 + 199$


 * The smaller of the $15$th pair of primes whose prime gap is $10$:
 * $839 - 829 = 10$


 * The $21$st of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 20^2 + 29 = 829$


 * The $2$nd of the $33$rd pair of twin primes:
 * $829 - 827 = 2$