1247

Number
$1247$ (one thousand, two hundred and forty-seven) is:


 * $29 \times 43$


 * The $11$th Fermat pseudoprime to base $4$ after $15$, $85$, $91$, $341$, $435$, $451$, $561$, $645$, $703$, $1105$:
 * $4^{1247} \equiv 4 \pmod {1247}$


 * The $29$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $477$, $532$, $590$, $651$, $715$, $782$, $852$, $925$, $1001$, $1080$, $1162$:
 * $1247 = \ds \sum_{k \mathop = 1}^{29} \paren {3 k - 2} = \dfrac {29 \paren {3 \times 29 - 1} } 2$


 * The $57$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $925$, $950$, $1001$, $1027$, $1080$, $1107$, $1162$, $1190$:
 * $1247 = \ds \sum_{k \mathop = 1}^{29} \paren {3 k - 2} = \dfrac {29 \paren {3 \times 29 - 1} } 2$