In the following prime-number series, select the missing number that correctly completes the sequence: 13, 17, 19, 23, 29, ?

Introduction / Context:
This question is based on prime numbers arranged in ascending order. The series tests basic knowledge of prime numbers and the ability to recall them sequentially. Prime-based series are frequently used in reasoning sections to check both memory and fundamental number theory understanding.

Given Data / Assumptions:
Given series: 13, 17, 19, 23, 29, ?The next term in the series is missing.We assume the sequence is made of consecutive prime numbers in increasing order.

Concept / Approach:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The series appears to list primes in ascending order. The strategy is to identify the primes already present and then determine the immediate next prime after 29. There is no need for complex calculations; the key is familiarity with prime lists and quick divisibility checks.

Step-by-Step Solution:
Step 1: Note the primes given: 13, 17, 19, 23, 29.Step 2: Recall the sequence of primes after 10: 11, 13, 17, 19, 23, 29, 31, 37, and so on.Step 3: Observe that the given series starts from 13 and simply follows the increasing order of primes up to 29.Step 4: The next prime after 29 is 31, since 31 is not divisible by any integer greater than 1 and less than its square root.Step 5: Therefore, the missing term must be 31.

Verification / Alternative check:
We can verify by checking alternative candidates. After 29, the next integers are 30 and 31. The number 30 is composite because it is divisible by 2, 3, 5, and other factors. The next number, 31, has no divisors other than 1 and 31, so it is prime. The following primes after 31 are 37, 41, and so on. This confirms that 31 is the immediate next prime and fits perfectly into the pattern of consecutive prime numbers.

Why Other Options Are Wrong:
Option 33 is not prime because it is divisible by 3 and 11.Option 35 is not prime because it is divisible by 5 and 7.Option 37 is prime, but it is not the immediate next prime after 29; it comes after 31, so it would skip 31 and disrupt the sequence of consecutive primes.

Common Pitfalls:
A common mistake is to pick the next odd number without checking whether it is prime, leading to choices like 33 or 35. Another error is to think that the gaps between primes must be constant; however, prime gaps vary and sometimes increase. The correct approach is always to test divisibility or rely on a memorized list of primes for small numbers.

Final Answer:
The missing number that continues the prime number series is 31.