Finding Prime Numbers From 1 to N Using Iterations

Introduction

Prime numbers are an essential concept in number theory and have numerous applications in various fields, including computer science and cryptography. Given a range from 1 to N, finding all prime numbers within this range is a common problem. In this article, we will explore an iterative approach to solving this problem. We will discuss the understanding, approach, step-by-step solution, and provide sample code to illustrate the process.

Understanding Prime Numbers

Prime numbers are positive integers greater than 1 that have no divisors other than 1 and themselves. They play a crucial role in number theory and are often used in algorithms and mathematical calculations. Identifying prime numbers helps in factorizing numbers, optimizing algorithms, and improving the efficiency of various computations.

Approach

The iterative approach to finding prime numbers from 1 to N involves checking each number in the range to determine if it is prime or not. To do this, we need to iterate through each number and verify if it is only divisible by 1 and itself. The approach is straightforward and can be optimized to some extent by reducing the number of iterations.

Step-by-Step Solution

1. Input the value of N, which represents the upper limit of the range.

2. Iterate through each number from 2 to N: 

   • For each number, check if it is divisible by any number from 2 to the square root of the number (inclusive). If there is a divisor greater than square root of number then there will also be a divisor less than the square root of the number. So, iterating till square root of number will be sufficient for validating if a number is prime or not

   • If it is divisible by any number other than 1 and itself, it is not a prime number. Move to the next number. 

   • If it is not divisible by any number other than 1 and itself, it is a prime number. Output the number as one of the prime numbers in the range.

Code 

Here's an example implementation  for finding prime numbers from 1 to N using iterations: