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Simple Sieve - DSA
- The Sieve of Eratosthenes is a classic algorithm to find all prime numbers less than a given integer n by marking the multiples of each prime starting from 2.
- Time Complexity: O(n log log n). Space Complexity: O(n).
- Create a boolean array of size n + 1, mark multiples of each prime as false to identify primes.
- Java implementation fixed and provided for the Sieve algorithm including input handling and correction of syntax errors.
- Real-life applications of prime numbers include cryptography, random number generation, hashing algorithms, procedural generation in graphics, and mathematical research.
- Prime numbers are crucial in public-key encryption algorithms such as RSA for secure key generation.
- Primes are used in random number generators and hashing algorithms to ensure uniform randomness and reduce hash collisions.
- In graphics, prime intervals aid in generating less predictable world seeds and layouts in games.
- The study of prime numbers contributes to significant mathematical research and theories, leading to breakthroughs like Goldbach's conjecture and the Riemann Hypothesis.
- The code for the Sieve of Eratosthenes algorithm in Java has been fixed for correct functionality and can be used for finding prime numbers up to a specified limit.
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