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<p>of  contain a divisor less than or equal to , so the algorithm need only search for divisors less than or equal to  to guarantee detection of all divisor pairs.</p>

<p>Also, 2 is a prime dividing 100, which immediately proves that 100 is not prime. Every positive integer except 1 is divisible by at least one prime number by the <a href="page.php?w=Fundamental_Theorem_of_Arithmetic">Fundamental Theorem of Arithmetic</a>. Therefore the algorithm need only search for prime divisors less than or equal to .</p>

<p>For another example, consider how</p><p>
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