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Understanding: Sieve of Eratosthenes Video Lecture | Mathematics & Pedagogy - CTET & State TET

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FAQs on Understanding: Sieve of Eratosthenes Video Lecture - Mathematics & Pedagogy - CTET & State TET

1. What is the Sieve of Eratosthenes?
Ans. The Sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to a given limit. It works by iteratively marking the multiples of each prime, starting from 2, as composite numbers. The remaining numbers that are not marked as composites are considered prime.
2. How does the Sieve of Eratosthenes algorithm work?
Ans. The algorithm starts by assuming all numbers from 2 to a given limit as potential primes. It then iterates through each number, starting from 2, and marks all its multiples as composites. After going through all the numbers, the remaining unmarked numbers are considered prime.
3. What are the advantages of using the Sieve of Eratosthenes algorithm?
Ans. The Sieve of Eratosthenes algorithm is highly efficient for finding prime numbers up to a specific limit. It has a time complexity of O(n log log n), making it significantly faster than other methods for larger limits. It also provides all the prime numbers within the given range, allowing for further analysis or computations.
4. Can the Sieve of Eratosthenes algorithm be used for very large prime numbers?
Ans. The Sieve of Eratosthenes algorithm is most suitable for finding prime numbers up to a specific limit or range. It becomes less efficient and impractical for very large prime numbers as the memory requirements increase significantly. For such cases, other algorithms like the Miller-Rabin primality test or the elliptic curve primality proving algorithm are more commonly used.
5. Are there any limitations or drawbacks of using the Sieve of Eratosthenes algorithm?
Ans. While the Sieve of Eratosthenes algorithm is efficient for finding prime numbers within a given range, it requires a substantial amount of memory to store all the potential primes. The memory usage increases with the limit or range specified. This makes it less suitable for extremely large ranges or when memory resources are limited. Additionally, the algorithm is not efficient for finding a single prime number, as it computes all primes up to the limit.
151 videos|108 docs|69 tests
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