1201

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Number

$1201$ (one thousand, two hundred and one) is:

The $197$th prime number


The $3$rd prime number after $1009$, $1129$ which can be expressed in the form $x^2 + n y^2$ for all values of $n$ from $1$ to $10$:
\(\ds 1201\) \(=\) \(\ds 24^2 + 1 \times 25^2\)
\(\ds \) \(=\) \(\ds 7^2 + 2 \times 24^2\)
\(\ds \) \(=\) \(\ds 1^2 + 3 \times 20^2\)
\(\ds \) \(=\) \(\ds 25^2 + 4 \times 12^2\)
\(\ds \) \(=\) \(\ds 34^2 + 5 \times 3^2\)
\(\ds \) \(=\) \(\ds 5^2 + 6 \times 14^2\)
\(\ds \) \(=\) \(\ds 33^2 + 7 \times 4^2\)
\(\ds \) \(=\) \(\ds 7^2 + 8 \times 12^2\)
\(\ds \) \(=\) \(\ds 25^2 + 9 \times 8^2\)
\(\ds \) \(=\) \(\ds 29^2 + 10 \times 6^2\)


The larger of the $18$th pair of primes whose prime gap is $8$:
$1201 - 1193 = 8$


The $48$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $1061$, $1069$, $1091$, $1097$, $1103$, $1109$, $1151$, $1153$, $1181$, $1201$


Also see


Sources