The SHOCKING Truth About Prime Numbers and Optimization скачать в хорошем качестве

The SHOCKING Truth About Prime Numbers and Optimization

Prime Number Logic Explained | O(n) → O(√n) → 6k±1 | Mathematical Proof + Code Optimization Fastest Prime Check in Java | Mathematical Proof + 6k±1 Optimization | Prime Number Logic How to Check Prime Number Efficiently | From Brute Force to 6k±1 | DSA + Math Logic Prime Number Algorithm Explained Mathematically | O(n) → O(√n) → 6k±1 Given a number n, determine whether it is a prime number or not. Note: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. In this lecture, we’ll go from the basic prime number checking algorithm to the most optimized version using mathematical reasoning and code efficiency. You’ll understand why we check up to √n, how the 6k±1 pattern works, and what happens inside each optimization step — both logically and mathematically. What You’ll Learn: What makes a number prime (mathematical definition) The brute-force approach — O(n) time complexity Why we only need to check divisibility till √n (mathematical proof) The 6k±1 rule — number theory behind prime numbers The final optimized prime-checking function in Java Time complexity comparison of all three approaches Mathematical Concepts Covered: Factor pairs & sqrt(n) relationship proof Division algorithm and number forms (6k,6k+1,…,6k+5) Why primes greater then 3 are always 6k±1 Complexity analysis and performance insight Perfect For Students learning DSA or competitive programming Anyone who wants to understand mathematical logic behind algorithms Developers looking to optimize prime number checks YouTubers / Teachers explaining math in code Prime number logic, prime number algorithm, prime number check in Java, prime number mathematical proof, O(n) O(√n) 6k±1, prime number optimization, math logic in code, coding interview, DSA prime number, competitive programming, number theory in programming, primality test, check if number is prime, 6k ± 1 rule, sqrt n prime check, fast prime check algorithm, mathematical proof in programming, prime number Java, DSA explained with math, algorithm optimization, prime number program in c, prime number and composite number prime number program in java, prime numbers 1 to 100 Mathematical Algorithms | Math Logic in Code | DSA Fundamentals #dsa #education #codinginterview #engineering #correctcoding #leetcode #datastructures #coding #geeksforgeeks #maths #sde #algorithm #algo #interviewpreparation #interviewquestion #primenumber