The Best Estimate of A Big Number!

Algebra Level pending

Let \(A\), \(B\) and \(N\) be real numbers. We say that \(A\) is a better estimate of \(N\) than \(B\) if \(|N - A| < |N - B|\) is fulfilled.

Which of the following is the best estimate of \(689^{1679} \)?


Side-note: both 689 and 1679 have special meanings in the minds of Hong Kong people.
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