# 2047

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## Number

$2047$ (two thousand and forty-seven) is:

$23 \times 89$

The $1$st Mersenne number which is composite:
$2047 = 2^{11} - 1 = 23 \times 89$

The $5$th Mersenne number after $3$, $7$, $31$, $127$:
$2047 = 2^{11} - 1$

The $8$th Woodall number after $1$, $7$, $23$, $63$, $159$, $383$, $895$:
$2047 = 8 \times 2^8 - 1$

The $8$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$:
$2^{2047} \equiv 2 \pmod {2047}$: $2047 = 23 \times 89$

## Historical Note

$2047$ was the $1$st Mersenne number that was demonstrated to be composite.

This was done in $1636$ by Hudalrichus Regius, who demonstrated it to be $23 \times 89$.