Introduction / Context:
This is a prime-number recognition problem. The sequence lists consecutive odd primes in ascending order. We need the next prime after 19.
Given Data / Assumptions:
- Sequence: 7, 11, 13, 17, 19.
- All terms shown are prime numbers and increase.
Concept / Approach:
- Prime numbers are integers greater than 1 with no positive divisors other than 1 and themselves.
- Check the next odd integers after 19: 21 (composite), 23 (prime).
Step-by-Step Solution:
After 19, test 21: divisible by 3 and 7 ⇒ not prime.Next 23: not divisible by 2, 3, or 5; √23 < 5, so only small primes need testing ⇒ prime.
Verification / Alternative check:
Known list of primes confirms 23 follows 19 in the odd prime sequence after excluding 21 as composite.
Why Other Options Are Wrong:
- 21 and 27 are composite (21 = 3*7; 27 = 3^3).
- None of these: Incorrect because 23 is the correct next prime.
Common Pitfalls:
- Assuming every odd number is prime.
- Stopping checks too early without testing divisibility by small primes.
Final Answer:
23
Discussion & Comments