# 1891

Previous  ... Next

## Number

$1891$ (one thousand, eight hundred and ninety-one) is:

$31 \times 61$

The $8$th Fermat pseudoprime to base $5$ after $4$, $124$, $217$, $561$, $781$, $1541$, $1729$:
$5^{1891} \equiv 5 \pmod {1891}$

The $10$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$:
$3^{1891} \equiv 3 \pmod {1891}$

The $31$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$, $1770$:
$1891 = \ds \sum_{k \mathop = 1}^{31} \paren {4 k - 3} = 31 \paren {2 \times 31 - 1}$

The $61$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1830$:
$1891 = \ds \sum_{k \mathop = 1}^{61} k = \dfrac {61 \times \paren {61 + 1} } 2$