751

Number
$751$ (seven hundred and fifty-one) is:


 * The $133$rd prime number


 * The index (after $2$, $3$, $6$, $30$, $75$, $81$, $115$, $123$, $249$, $362$, $384$, $462$, $512$) of the $14$th Woodall prime:
 * $751 \times 2^{751} - 1$


 * The $23$rd trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $375$, $376$, $499$, $501$, $624$, $625$, $749$:
 * $751^3 = 423 \, 563 \, \mathbf {751}$


 * The larger of the $11$th pair of primes whose prime gap is $8$:
 * $751 - 743 = 8$


 * The $20$th of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 19^2 + 29 = 751$