Exercise 2: Sieve of Eratosthenes Up to 30 — Possible Solution
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STEP 1: START WITH EVERY NUMBER 2 THROUGH 30 MARKED AS "PRIME"
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2 is the first unmarked number - it's prime. Cross out every
multiple of 2 (starting from 2*2=4):
  4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

STEP 2: NEXT UNMARKED NUMBER IS 3 - IT'S PRIME
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Cross out every multiple of 3 (starting from 3*3=9) that isn't
already crossed out:
  9, 12, 15, 18, 21, 24, 27, 30
(12, 18, 24, 30 were already crossed out by 2 - crossing them again
changes nothing)

STEP 3: NEXT UNMARKED NUMBER IS 5 - IT'S PRIME
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Cross out every multiple of 5 (starting from 5*5=25) that isn't
already crossed out:
  25, 30
(30 was already crossed out)

STEP 4: STOPPING POINT
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sqrt(30) is approximately 5.48, so once every prime up to 5 has
been used to cross out its own multiples, the sieve is complete -
any remaining unmarked number greater than 5 cannot have a factor
small enough to have been missed, by the same sqrt(n) reasoning
this chapter used for trial division.

RESULT
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Primes up to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

(7, 11, 13, 17, 19, 23, 29 were never crossed out by 2, 3, or 5,
so they remain marked prime.)

WHY THIS WORKS AS AN ANSWER
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Each prime's own crossing-out pass is shown explicitly and in the
correct order (2, then 3, then 5), duplicate crossings are
explicitly noted rather than silently ignored, and the stopping
point at sqrt(30) is justified using the same reasoning this
chapter already established for trial division, rather than just
sieving arbitrarily far.