Concept explainers
(a) In constructing the Sieve of Eratosthenes for 2 through 100. we said that any composite in that range had to be a multiple of some prime less than or equal to 7 (since the next prime. 11. is greater than the square root of 100). Explain.
(b) To extend the Sieve of Eratosthenes to 200, what is the largest prime whose multiples would have to be considered?
(c) Complete this statement: In seeking prime factors of a given number, we need only consider all primes up to and including the______ of that number, since a prime factor greater than the_________ can occur only if there is at least one other prime factor less than the_______.
(d) Complete this statement: If no prime less than or equal to
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Mathematical Ideas (13th Edition) - Standalone book
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