715

Number
$715$ (seven hundred and fifteen) is:


 * $5 \times 11 \times 13$


 * The $22$nd pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$, $287$, $330$, $330$, $376$, $425$, $477$, $532$, $590$, $651$:
 * $715 = \displaystyle \sum_{k \mathop = 1}^{22} \left({3 k - 2}\right) = \dfrac {22 \left({3 \times 22 - 1}\right)} 2$


 * The $43$rd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$:
 * $715 = \displaystyle \sum_{k \mathop = 1}^{22} \left({3 k - 2}\right) = \dfrac {22 \left({3 \times 22 - 1}\right)} 2$


 * The $10$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$:
 * $715 = \displaystyle \sum_{k \mathop = 1}^{10} \dfrac {k \left({k + 1}\right) \left({k + 2}\right)} 6 = \dfrac {10 \left({10 + 1}\right) \left({10 + 2}\right) \left({10 + 3}\right)} {24}$


 * The $2$nd of the $5$th (and largest known) pair of consecutive integers whose product is a primorial:
 * $714 \times 715 = 510 \, 510 = 17 \#$