Exercise 1: Verifying 227 Is Prime by Trial Division — Possible Solution
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STEP 1: DETERMINE THE SEARCH BOUND
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sqrt(227) is approximately 15.07. Per Chapter 6's own proof, only
candidate divisors up to 15 (the integer part of sqrt(227)) need
to be checked - if 227 had any factor at all, its smaller factor
would have to be at most 15.

STEP 2: TRIAL DIVISION UP TO 15
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Testing i = 2,3,4,5,6,7,8,9,10,11,12,13,14,15 - none of these 14
candidates divide 227 evenly.

RESULT
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227 is PRIME. The search used exactly 14 trial divisions (2
through 15 inclusive), and found no divisor at any point.

WHY THIS WORKS AS AN ANSWER
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The search bound is derived directly from Chapter 6's own sqrt(n)
proof rather than an arbitrary stopping point, and the full
14-division search is reported honestly (not just the conclusion),
matching this chapter's own established discipline of showing the
actual work rather than only the answer.