The naive implementation is our baseline: implement with no awareness of potential tweaks, improvements, or optimizations. This should be the worst performing when compared to any optimization.

START TIMEKEEPING
NUMBER: FROM 2 THROUGH UPPERBOUND:
    ISPRIME <- YES
    FACTOR: FROM 2 THROUGH NUMBER-1:
        SHOULD FACTOR DIVIDE EVENLY INTO NUMBER:
            ISPRIME <- NO
    PROCEED TO NEXT FACTOR
    SHOULD ISPRIME STILL BE YES:
        INCREMENT OUR PRIME TALLY
PROCEED TO NEXT NUMBER
STOP TIMEKEEPING

START TIMEKEEPING
NUMBER: FROM 2 THROUGH UPPERBOUND:
    SHOULD THE NUMBER SLOT BE TRUE:
        VALUE AT NUMBER IS PRIME, INCREMENT TALLY
        MULTIPLE: FROM NUMBER+NUMBER THROUGH UPPERBOUND:
            VALUE AT MULTIPLE IS NOT PRIME
            MULTIPLE IS MULTIPLE PLUS NUMBER
        PROCEED TO NEXT MULTIPLE
    INCREMENT NUMBER
PROCEED TO NEXT NUMBER
STOP TIMEKEEPING

START TIMEKEEPING
NUMBER: FROM 2 THROUGH NUMBER*NUMBER<UPPERBOUND:
    SHOULD THE NUMBER SLOT BE TRUE:
        VALUE AT NUMBER IS PRIME, INCREMENT TALLY
        MULTIPLE: FROM NUMBER*NUMBER THROUGH UPPERBOUND:
            VALUE AT MULTIPLE IS NOT PRIME
            MULTIPLE IS MULTIPLE PLUS NUMBER
        PROCEED TO NEXT MULTIPLE
    INCREMENT NUMBER
PROCEED TO NEXT NUMBER
STOP TIMEKEEPING