Primes Expressible as x^2 + n y^2 for all n from 1 to 10/Examples
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Examples of Primes Expressible as $x^2 + n y^2$ for all $n$ from $1$ to $10$
1009
| \(\ds 1009\) | \(=\) | \(\ds 15^2 + 1 \times 28^2 = 28^2 + 1 \times 15^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 19^2 + 2 \times 18^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 31^2 + 3 \times 4^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 15^2 + 4 \times 14^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 17^2 + 5 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 25^2 + 6 \times 8^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \ \, 1^2 + 7 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 19^2 + 8 \times 9^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 18^2 + 9 \times 5^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3^2 + 10 \times 10^2\) |
1129
| \(\ds 1129\) | \(=\) | \(\ds 20^2 + 1 \times 27^2 = 27^2 + 1 \times 20^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 29^2 + 2 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 19^2 + 3 \times 16^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 27^2 + 4 \times 10^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^2 + 5 \times 15^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 23^2 + 6 \times 10^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 11^2 + 7 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 29^2 + 8 \times 6^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 20^2 + 9 \times 9^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 33^2 + 10 \times 2^2\) |
1201
| \(\ds 1201\) | \(=\) | \(\ds 24^2 + 1 \times 25^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 7^2 + 2 \times 24^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^2 + 3 \times 20^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 25^2 + 4 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 34^2 + 5 \times 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 5^2 + 6 \times 14^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 33^2 + 7 \times 4^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 7^2 + 8 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 25^2 + 9 \times 8^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 29^2 + 10 \times 6^2\) |
1801
| \(\ds 1801\) | \(=\) | \(\ds 35^2 + 1 \times 24^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^2 + 2 \times 30^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 37^2 + 3 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 35^2 + 4 \times 12^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 26^2 + 5 \times 15^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 25^2 + 6 \times 14^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3^2 + 7 \times 16^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^2 + 8 \times 15^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 35^2 + 9 \times 8^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 19^2 + 10 \times 12^2\) |