1031

Number
$1031$ (one thousand and thirty-one) is:


 * The $173$rd prime number


 * The index of the $5$th repunit prime after $R_2$, $R_{19}$, $R_{23}$, $R_{317}$


 * The larger of the $17$th pair of primes whose prime gap is $10$:
 * $1031 - 1021 = 10$


 * The $36$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $733$, $739$, $743$, $751$, $761$, $769$, $907$, $937$, $941$, $953$, $967$, $971$, $983$, $991$, $1009$, $1021$


 * The $1$st of the $36$th pair of twin primes:
 * $1033 - 1031 = 2$


 * The $40$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $653$, $659$, $683$, $719$, $743$, $761$, $809$, $911$, $953$, $1013$, $1019$:
 * $2 \times 1031 + 1 = 2063$, which is prime.