# 1129

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## Number

$1129$ (one thousand, one hundred and twenty-nine) is:

The $189$th prime number

The $2$nd prime number after $1009$ which can be expressed in the form $x^2 + n y^2$ for all values of $n$ from $1$ to $10$
 $\displaystyle 1129$ $=$ $\displaystyle 20^2 + 1 \times 27^2 = 27^2 + 1 \times 20^2$ $\displaystyle$ $=$ $\displaystyle 29^2 + 2 \times 12^2$ $\displaystyle$ $=$ $\displaystyle 19^2 + 3 \times 16^2$ $\displaystyle$ $=$ $\displaystyle 27^2 + 4 \times 10^2$ $\displaystyle$ $=$ $\displaystyle 2^2 + 5 \times 15^2$ $\displaystyle$ $=$ $\displaystyle 23^2 + 6 \times 10^2$ $\displaystyle$ $=$ $\displaystyle 11^2 + 7 \times 12^2$ $\displaystyle$ $=$ $\displaystyle 29^2 + 8 \times 6^2$ $\displaystyle$ $=$ $\displaystyle 20^2 + 9 \times 9^2$ $\displaystyle$ $=$ $\displaystyle 33^2 + 10 \times 2^2$
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