What is the logic for generate prime numbers?

The implementation of this logic can be facilitated through various programming constructs, one of which is the for loop. Akin to the while loop, the for loop offers the capability to iterate through a sequence of operations until a specified condition is fulfilled.

The fundamental principle in determining whether a number is prime revolves around the process of division. This involves subjecting the number to division by a series of integers, commencing with the number 2.

The essence of this method lies in the absence of any remainder when the number is divided by any integer within its range, excluding 1 and itself. If such a scenario arises, the number in question can be confidently classified as prime.

In the context of identifying prime numbers, the for loop can be employed to systematically check the divisibility of the number in question by each integer within its range. This process continues until a divisor is found that results in a remainder, or until the loop reaches the number itself, indicating that no such divisor exists.

The efficiency of this approach is contingent upon the range within which the divisibility checks are performed. Ideally, the checks should extend only up to the square root of the number being tested, as any factor greater than this would necessarily have a corresponding factor less than or equal to the square root.