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 $48$th emirp after $13$, $17$, $31$, $37$, $\ldots$, $1061$, $1069$, $1091$, $1097$, $1103$, $1109$, $1151$, $1153$, $1181$, $1201$
Also see
- Previous ... Next: Prime Number
- Previous ... Next: Emirp
- Previous ... Next: Prime Gaps of 8
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1201$