Question 898378
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Facts:
Any product of odd numbers is odd.
The sum of two odd numbers is even.
  
3<sup>11</sup> and 5<sup>13</sup> are both the product of odd numbers, 
so they are both odd

So 3<sup>11</sup> + 5<sup>13</sup> is the sum of two odd numbers and 
is therefore even.

Any even number is divisible by 2. Therefore 2 is the smallest prime
that divides 3<sup>11</sup> + 5<sup>13</sup>.  [In fact, 2 is the
smallest prime, period!] 
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[In fact 3<sup>11</sup> + 5<sup>13</sup> = 1220880272 = 2<sup>4</sup>*47*107*15173, but we don't need that!)
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Edwin</pre>