1009

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Number

$1009$ (one thousand and nine) is:

The $169$th prime number


The $1$st prime number which can be expressed in the form $x^2 + n y^2$ for all values of $n$ from $1$ to $10$:
\(\displaystyle 1009\) \(=\) \(\displaystyle 15^2 + 1 \times 28^2 = 28^2 + 1 \times 15^2\)
\(\displaystyle \) \(=\) \(\displaystyle 19^2 + 2 \times 18^2\)
\(\displaystyle \) \(=\) \(\displaystyle 31^2 + 3 \times 4^2\)
\(\displaystyle \) \(=\) \(\displaystyle 15^2 + 4 \times 14^2\)
\(\displaystyle \) \(=\) \(\displaystyle 17^2 + 5 \times 12^2\)
\(\displaystyle \) \(=\) \(\displaystyle 25^2 + 6 \times 8^2\)
\(\displaystyle \) \(=\) \(\displaystyle \ \, 1^2 + 7 \times 12^2\)
\(\displaystyle \) \(=\) \(\displaystyle 19^2 + 8 \times 9^2\)
\(\displaystyle \) \(=\) \(\displaystyle 18^2 + 9 \times 5^2\)
\(\displaystyle \) \(=\) \(\displaystyle 3^2 + 10 \times 10^2\)


The $34$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $733$, $739$, $743$, $751$, $761$, $769$, $907$, $937$, $941$, $953$, $967$, $971$, $983$, $991$


Also see


Sources