What will be the next number in the following series? 3, 5, 7, 11, 13, 17, ____

Concept: A number series of primes lists prime numbers (numbers with exactly two divisors, 1 and themselves) in increasing order. Solving it means recognizing that each given term is prime and predicting the next prime in the sequence.

Application:

1. Check each given term for primality: 3, 5, 7, 11, 13, 17 are all prime (each is divisible only by 1 and itself).

2. List the primes in order starting from 3: 3, 5, 7, 11, 13, 17, 19, 23, … — the given series exactly matches this sequence.

3. The next prime after 17 is 19 (no integer between 2 and 18 divides 19 evenly), so 19 is the next term.

Cross-check: Testing the other options for primality — 20 (divisible by 2), 21 (divisible by 3 and 7), and 25 (divisible by 5) — shows all three are composite, confirming that only 19 continues the pattern.

Result: The next number in the series is 19.