Prime number sequence continuation Given the primes: 11, 13, 17, 19, 23, 29, 31, 37, 41, what is the next prime?

Introduction / Context:
This is a straightforward prime sequence continuation problem. You are given a strictly increasing list of prime numbers and asked to identify the next prime. Recognizing primes and skipping composites is the key skill tested here.

Given Data / Assumptions:

• Sequence shown: 11, 13, 17, 19, 23, 29, 31, 37, 41.
• Task: choose the next prime greater than 41.
• We assume standard definition of prime: an integer greater than 1 with no positive divisors other than 1 and itself.

Concept / Approach:
List consecutive integers after 41 and test primality: 42, 43, 44, 45, 46, 47, etc. Eliminate even numbers and those divisible by small primes (3, 5). The first candidate that passes basic divisibility tests is the next prime.

Step-by-Step Solution:
42 is even ⇒ composite.43: test divisibility by primes ≤ √43 (2, 3, 5). Not divisible ⇒ 43 is prime.Thus, the next prime after 41 is 43.

Verification / Alternative check:
Continue checking: 44 is even; 45 divisible by 3 and 5; 46 even; 47 is also prime but it comes after 43. The immediate successor prime to 41 is indeed 43.

Why Other Options Are Wrong:
47 and 53 are primes but not the immediate next; 51 and 49 are composite (51 = 3 * 17, 49 = 7 * 7).

Common Pitfalls:
Jumping to a larger prime (like 47) without checking the smaller candidate 43, or forgetting that “next” means the first prime greater than 41, not any future prime.

Final Answer:
43