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8. Primes (a) Prove there are infinitely many primes

8. Primes (a) Prove there are infinitely many primes

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Primes (a) Prove there are infinitely many primes (b) Using the Sieve of Eratosthenes, what is the worst case complexity for finding the prime factors of a number of magnitude N. (c) Consider the previous question for a number written in binary where b bits are required to encode a number of magnitude N, so the length of the number is 2°, what is the complexity in terms of b.
Transcribed Image Text:8. Primes (a) Prove there are infinitely many primes (b) Using the Sieve of Eratosthenes, what is the worst case complexity for finding the prime factors of a number of magnitude N. (c) Consider the previous question for a number written in binary where b bits are required to encode a number of magnitude N, so the length of the number is 2°, what is the complexity in terms of b.
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