4186

Number
$4186$ (four thousand, one hundred and eighty-six) is:


 * $2 \times 7 \times 13 \times 23$


 * The second of the $5$th pair of triangular numbers whose sum and difference are also both triangular:
 * $1485 = T_{54}$, $4186 = T_{91}$, $1485 + 4186 = T_{106}$, $4186 - 1485 = T_{73}$


 * The $46$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$, $3321$, $3486$, $3655$, $3828$, $4005$:
 * $4186 = \ds \sum_{k \mathop = 1}^{46} \paren {4 k - 3} = 46 \paren {2 \times 46 - 1}$


 * The $91$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3655$, $3741$, $3828$, $3916$, $4005$, $4095$:
 * $4186 = \ds \sum_{k \mathop = 1}^{91} k = \dfrac {91 \times \paren {91 + 1} } 2$