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  • 09 - Sieve of Eratosthenes & Segmented Sieve Problems

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<h1 align='center'>SIEVE - OF - ERATOSTHENES - ALGORITHM</h1>
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This repository contains a collection of coding problems related to the **Sieve of Eratosthenes** algorithm, which is used to find all prime numbers up to a specified integer `n`. The problems here span across both **LeetCode** and **GeeksforGeeks (GFG)** platforms, offering a variety of challenges that will help you gain a deeper understanding of this efficient algorithm for prime number generation.
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### Sieve of Eratosthenes Overview:
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The **Sieve of Eratosthenes** is one of the most efficient ways to identify all prime numbers up to a given number `n`. The basic idea is to iteratively mark the multiples of each prime number starting from `2`, and the remaining unmarked numbers are the primes.
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### Repository Contents:
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This repository provides problems that focus on both the algorithm and its various applications, including:
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- **Prime Number Detection**
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- **Prime Factorization**
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- **Optimized Approaches** to the Sieve of Eratosthenes
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- **Applications in Competitive Programming**
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### Repository Content
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<p>
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<img src="https://img.shields.io/badge/problems%20count-02-orange?logo=leetcode" alt="LeetCode">
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<img src="https://img.shields.io/badge/problems%20count-03-darkgreen?logo=geeksforGeeks" alt="GeeksforGeeks">
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<img src="https://img.shields.io/badge/total%20problems%20count-04-blue" alt="Problem Count">
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</p>
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| No | Problem Name | Description | Leetcode | GFG |
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|-----|-------------------------------|-------------------|-------------------|-------|
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| 01 | [Count Primes](https://github.com/JawadSher/DSA-LeetCode-GFG-Problems-Repository/tree/main/09%20-%20Sieve%20of%20Eratosthenes%20%26%20Segmented%20Sieve%20Problems/01%20-%20Count%20Primes) | Counts the number of prime numbers less than a given number `n`. | [Link](https://leetcode.com/problems/count-primes/) | Non |
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| 02 | [Count Primes in Range](https://github.com/JawadSher/DSA-LeetCode-GFG-Problems-Repository/tree/main/09%20-%20Sieve%20of%20Eratosthenes%20%26%20Segmented%20Sieve%20Problems/02%20-%20Count%20Primes%20in%20Range) | Counts the number of prime numbers in a given range `[a, b]`. | Non | [Link](https://www.geeksforgeeks.org/count-primes-in-a-range/) |
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| 03 | [Sieve of Eratosthenes](https://github.com/JawadSher/DSA-LeetCode-GFG-Problems-Repository/tree/main/09%20-%20Sieve%20of%20Eratosthenes%20%26%20Segmented%20Sieve%20Problems/03%20-%20Seive%20of%20Eratosthenes) | Implements the Sieve of Eratosthenes algorithm to find all prime numbers up to `n`. | [Link](https://leetcode.com/problems/sieve-of-eratosthenes/) | [Link](https://www.geeksforgeeks.org/sieve-of-eratosthenes/) |
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| 04 | [Product of Primes](https://github.com/JawadSher/DSA-LeetCode-GFG-Problems-Repository/tree/main/09%20-%20Sieve%20of%20Eratosthenes%20%26%20Segmented%20Sieve%20Problems/04%20-%20Product%20of%20Primes) | Calculates the product of all primes up to a given number `n`. | Non | [Link](https://www.geeksforgeeks.org/problems/product-of-primes5328/1?itm_source=geeksforgeeks&itm_medium=article&itm_campaign=practice_card) |
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This table summarizes the problems with their brief descriptions and available links to LeetCode and GFG, if applicable.
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### Problems in this Repository:
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Each problem in this repository provides an opportunity to implement the **Sieve of Eratosthenes** in different contexts, such as:
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- Finding all prime numbers up to `n`.
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- Using the sieve to solve mathematical problems efficiently.
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- Optimizing algorithms that involve prime numbers.
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### Platforms:
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- **LeetCode**: A set of problems available on LeetCode that help solidify the understanding of the Sieve of Eratosthenes.
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- **GeeksforGeeks**: A collection of algorithmic challenges on GFG where the sieve technique is applied to solve various problems.
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Feel free to explore, solve, and contribute to any of the problems listed in this repository.
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---
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Happy Coding 😊

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