How many prime numbers are there that are strictly less than 40? Select the correct count.

Introduction / Context:Counting primes under a bound checks recall of small primes and understanding that 1 is not prime. Careful enumeration avoids double-counting and mistakes with composites like 21 or 35.

Given Data / Assumptions:

• List primes p with 2 <= p < 40.
• Exclude 1 (not prime) and composite numbers.
• Use divisibility checks for small bases (2, 3, 5, 7).

Concept / Approach:Enumerate systematically and confirm each candidate’s primality by testing divisibility up to its square root. This is feasible for small ranges like under 40.

Step-by-Step Solution:

Verification / Alternative check:Quick sieve mentally: cross out multiples of 2, 3, 5, 7; remaining in range match the list above.

Why Other Options Are Wrong:15, 17, 18, and 13 overcount or undercount due to including composites or missing primes.

Common Pitfalls:Mistaking 1 as prime or including 39 as prime (it equals 3 * 13).

Final Answer:12