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# Prime Detection II: Find Correct One

NUMTH-ERARBM

Among the following algorithms, find all that can detect all primes.

Select ALL that apply.

A

Divide $n$ by all integers $m$ with $1< m < n$. Record "$n$ is prime." if there is no such $m$ that divides $n$.

B

Divide $n$ by all integers $m$ with $1< m < \sqrt n$. Record "$n$ is prime." if there is no such $m$ that divides $n$.

C

Divide $n$ by all integers $m$ with $1 < m\leq\sqrt n$. Record "$n$ is prime." if there is no such $m$ that divides $n$.

D

Divide $n$ by all integers $m$ with $1 < m \leq \sqrt n$ and $m\in \{2, 3, 5, 7\}$. Record "$n$ is prime." if there is no such $m$ that divides $n$.