primes_to_30=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
least[12]=2; factors[12]=[2, 2, 3]; mark_count[12]=1
composite_marks=19; composite_count=19
without_break: primes_same=True; marks[12]=2; total_marks=24
break_before_mark: wrongly_lists_4_as_prime=True
limits_checked=303; number_checks=55848; invalid_inputs=5
PASS: trial divisors, prime lists, unique marks and factor products agree
