Exercise 1: Trial Division for n = 221 — Possible Solution
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STEP 1: DETERMINE THE BOUND, USING THIS CHAPTER'S OWN PROOF
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sqrt(221) is approximately 14.87. Per this chapter's own proof, if
221 has any factor at all, its SMALLER factor must be at most
sqrt(221) - so only candidate divisors up to 14 (the integer part
of sqrt(221)) need to be checked. Checking any further would be
redundant, since any factor larger than 14 would have to be
"the larger of the pair," already implied once its smaller partner
is found.

STEP 2: TRIAL DIVISION UP TO 14
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Testing i = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 - none divide 221
evenly.

Testing i = 13: 221 / 13 = 17 exactly. A factor is found.

RESULT
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221 is NOT prime. Its factors are 13 and 17 (221 = 13 x 17).

The search stopped at i=13, well within the required bound of 14 -
confirming the sqrt(n) bound was sufficient (in fact, more than
sufficient here, since the factor was found before even reaching
the full bound).

WHY THIS WORKS AS AN ANSWER
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The search bound is derived directly from this chapter's own proof
rather than just picking an arbitrary stopping point, and the trial
division is carried out fully and in order up to the point a factor
is actually found, correctly identifying both factors rather than
just reporting "not prime."