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Trial Division

Try all odd numbers $3, \ldots, \sqrt{n}$ to test n for primality.

Running Time $\Theta(\sqrt{n})$ , but $\beta \;=\; \lceil lg(n+1) \rceil \;\longrightarrow\; \sqrt{n} \;=\; \Theta(2^{\frac{\beta}{2}})$ (exponential).

This works well only for small n.

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