# Corners of a Number Spiral

**Number Theory**Level 3

The integers from \(0\) to \(1000000\) are written in order in a spiral pattern, as shown below.

\(\begin{array}{cccccccc} 6 &\rightarrow & 7 &\rightarrow & 8 & \rightarrow & 9\\ \uparrow&&&&&&\downarrow\\ 5 && 0 & \rightarrow & 1 & &10\\ \uparrow&&&&\downarrow&&\downarrow\\ 4 & \leftarrow & 3 & \leftarrow & 2&&11\\ &&&&&&\downarrow\\ 15 & \leftarrow & 14 & \leftarrow & 13&\leftarrow&12\\ \end{array}\)

A number is considered to be in a **bottom-right corner** if it has a downward arrow pointing into it and a leftward pointing arrow coming out of it. As we can see from the spiral, the first bottom-right corner number is 2 and the second is 12. What is the \(15\)th bottom-right corner number?

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