Primes Expressible as x^2 + n y^2 for all n from 1 to 10/Examples/1009

Example of Prime Expressible as $x^2 + n y^2$ for all $n$ from $1$ to $10$

\(\ds 1009\)

\(=\)

\(\ds 15^2 + 1 \times 28^2 = 28^2 + 1 \times 15^2\)

\(\ds \)

\(=\)

\(\ds 19^2 + 2 \times 18^2\)

\(\ds \)

\(=\)

\(\ds 31^2 + 3 \times 4^2\)

\(\ds \)

\(=\)

\(\ds 15^2 + 4 \times 14^2\)

\(\ds \)

\(=\)

\(\ds 17^2 + 5 \times 12^2\)

\(\ds \)

\(=\)

\(\ds 25^2 + 6 \times 8^2\)

\(\ds \)

\(=\)

\(\ds \ \, 1^2 + 7 \times 12^2\)

\(\ds \)

\(=\)

\(\ds 19^2 + 8 \times 9^2\)

\(\ds \)

\(=\)

\(\ds 18^2 + 9 \times 5^2\)

\(\ds \)

\(=\)

\(\ds 3^2 + 10 \times 10^2\)