in the sieve of Eratosthenes for numbers less than 100, explain why after we cross our the multiples of 2 3 5 and 7 the remaining numbers are primes
Homework Answers
It is easy to understand if we consider n to be composite, which has to have at least two factors other than 1 or n, and if the smallest factor is greater than √n, then the product of the factors will exceed (√n)² > n.
Using this theorem, the largest prime factor less than √100 is 7 (8,9,10 are composite). So using the sieve, we only need to cross out multiples of prime numbers less than or equal to 10, which is 7.
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in the sieve of Eratosthenes for numbers less than 100, explain why after we cross our the multiples of 2 3 5 and 7 the remaining numbers are primes
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to...
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite lie., not prime) the multiples of each prime, starting with the multiples of 2 The sieve of Eratosthenes can be expressed in pseudocode, as follows: Input: an integer n Let A be an array of 8oo1ean values, indexed by integers 2 to n, initially all set to true. for t - 2, 3,...
PYTHON! The Sieve of Eratosthenes THANKS FOR HELP! A prime integer is any integer greater than...
PYTHON! The Sieve of Eratosthenes THANKS FOR
HELP!
A prime integer is any integer greater than 1 that is evenly
divisible only by itself and 1. The Sieve of Eratosthenes is a
method of finding prime numbers. It operates as follows:
Create a list with all elements initialized to 1 (true). List
elements with prime indexes will remain 1. All other elements will
eventually be set to zero.
Starting with list element 2, every time a list element is found...
in visual studio build a masm program that prints out the prime numbers in a array...
in visual studio build a masm program that prints out the
prime numbers in a array
L1001-Sieve of Eratosthenes Please use your textbook as a reference. Goal: Use what we have learned to generate prime numbers. Prime numbers have many applications in computer science and as such, efficient ways to discover prime numbers can be very useful. Mathematicians have been intrigued by the concept for ages including the Greek mathematician, Eratosthenes of Cyrene (famous for calculating the circumference o the...
One way to find prime numbers less than n is to treat them as array indices....
One way to find prime numbers less than n is to treat them as array indices. Mark each position as True initially, assuming that all numbers are prime. Then, starting with index 2, mark all multiples of 2 (greater than 2) as not prime (False). Repeat this for multiples of 3, then multples of 4, etc. When the algorithm terminates, only prime indices will still be True; everything else will be False. The following function takes an integer n as...
1. Let A be 1 more than the product of the primes 3, 5, and 7....
1. Let A be 1 more than the product of the primes 3, 5, and 7. Factor A into a product of primes and check how many of 3, 5,7 are factors of A. 2. Make a list consisting of a few of your favorite primes and let B be 1 more than the product of these primes. Factor B into a product of primes and check how many of the primes on your list are factors of B.
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using t...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
Use phyton TheSieve of Eratosthonesis an algorithm to find all the prime numbers between 1 andsome integerN. It can be implemented with nestedforloops:(a) Make a list of all the integers from 2 throug...
Use phyton TheSieve of Eratosthonesis an algorithm to find all the prime numbers between 1 andsome integerN. It can be implemented with nestedforloops:(a) Make a list of all the integers from 2 throughN.(b) Cross off all the multiples of 2 (except for 2 itself). The smallest number that remains(after 2) is 3.(c) Cross off all the multiples of 3 (except for 3 itself). The smallest number that remainsis 5.(d) Cross off all the multiples of 5 (except for 5 itself)....
Python Program Eratosthenes of Cyrene lived approximately 275-195 BC. He was the first to accurately estimate...
Python Program Eratosthenes of Cyrene lived approximately 275-195 BC. He was the first to accurately estimate the diameter of the earth. For several decades he served as the director and chief librarian of the famous library in Alexandria. He was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. The algorithm described for this assignment is known as the Sieve of Eratosthenes. The algorithm is designed to find all prime numbers within a given...
4.3 Ch 4 Ex 14 - sieve of Erotosthenes In this lab, you will write a...
4.3 Ch 4 Ex 14 - sieve of Erotosthenes In this lab, you will write a program to compute all the prime numbers between 2 and some other integer, using an algorithm called the Sieve of Erotosthenes. First you will read, from standard input, the integer that will be the upper limit of the range of primes. Call it max. Then, create a vector<int> with max elements, and call it is_composite. The result of the Sieve will be that is_composite[i]...
4.3 Ch 4 Ex 14 - sieve of Erotosthenes In this lab, you will write a...
4.3 Ch 4 Ex 14 - sieve of Erotosthenes In this lab, you will write a program to compute all the prime numbers between 2 and some other integer, using an algorithm called the Sieve of Erotosthenes. First you will read, from standard input, the integer that will be the upper limit of the range of primes. Call it max. Then, create a vector<int> with max elements, and call it is_composite. The result of the Sieve will be that is_composite[i]...
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite lie., not prime) the multiples of each prime, starting with the multiples of 2 The sieve of Eratosthenes can be expressed in pseudocode, as follows: Input: an integer n Let A be an array of 8oo1ean values, indexed by integers 2 to n, initially all set to true. for t - 2, 3,...
PYTHON! The Sieve of Eratosthenes THANKS FOR
HELP!
A prime integer is any integer greater than 1 that is evenly
divisible only by itself and 1. The Sieve of Eratosthenes is a
method of finding prime numbers. It operates as follows:
Create a list with all elements initialized to 1 (true). List
elements with prime indexes will remain 1. All other elements will
eventually be set to zero.
Starting with list element 2, every time a list element is found...
in visual studio build a masm program that prints out the
prime numbers in a array
L1001-Sieve of Eratosthenes Please use your textbook as a reference. Goal: Use what we have learned to generate prime numbers. Prime numbers have many applications in computer science and as such, efficient ways to discover prime numbers can be very useful. Mathematicians have been intrigued by the concept for ages including the Greek mathematician, Eratosthenes of Cyrene (famous for calculating the circumference o the...
2. How many positive integers less than 1000 are multiples of 5 or 7? Explain your answer using the inclusion-exclusion principle 3. For the purpose of this problem, a word is an ordered string of 5 lowercase letters from the English alphabet (i.e., the 26 letters from a to z). For example, "alpha" and "zfaxr" are words. A subword of a word is an ordered string that appears as consecutive letters anywhere within the given word. For example, "cat" is...
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