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P#1. Sieve of Eratosthenes. Popular algorithms to find primes are eith er Sieve of Eratosthenes or Trial Position Primes 1 2 Division. Most of you in the CP#1 used the Trial Division algorith m. The objective of the current program is to implement an old algorithm, the Sieve of Eratosthenes. Primes are positive integers which have no other divisors except 1 and itself. When a number has more than two factors it is called a 3 3 4 7 composite number. The program will create the array of prime numbers less than N in ascending order and print them. 12,3,5, 7, 11, 13, 17, 19, 23, 29,., N. Answer shou ld contain a table of the prime numbers less than N and the specified position in the prime array <N n Test the program with N-100. Program prints also how many primes are in the range of 2 to N Page 4 of 12 Instructor will explain the Sleve of Eratosthene’s algorithm in class, be present. SIEVE OF ERATOTHENES Let’s start with a list of numbers from 2, 3,N. For N 20 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 Start with the first prime, i.e. 2, and eliminate the multiples af 2 10 11 12 13 14 15 18 19 20 2 7 16 17 Increse 2 by one, e. 3, which is the next prime number and eliminate multiples of 3 12 13 14 15 16 10 11 19 20 2 3 5 17 18 This is repeated until 4, because sqrt(20)-4.47 which raunded is 4. PLEASE note that since 4 was eliminated when testing the prime 2, the multiples af 4 were already eliminated. The remaining number are primes: 2,3,5, 7,11, 13, 17, 19 Hint: each time you find a multiple of each picked number in the initial list [1:n], make it zero. Elements not equal to zero are primes. This works a lot better than trying to ‘erase’ the element. Because each time you erase an element the remaining indexes roll over, i.e., they change. Show transcribed image text P#1. Sieve of Eratosthenes. Popular algorithms to find primes are eith er Sieve of Eratosthenes or Trial Position Primes 1 2 Division. Most of you in the CP#1 used the Trial Division algorith m. The objective of the current program is to implement an old algorithm, the Sieve of Eratosthenes. Primes are positive integers which have no other divisors except 1 and itself. When a number has more than two factors it is called a 3 3 4 7 composite number. The program will create the array of prime numbers less than N in ascending order and print them. 12,3,5, 7, 11, 13, 17, 19, 23, 29,., N. Answer shou ld contain a table of the prime numbers less than N and the specified position in the prime array

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Answer to P#1. Sieve of Eratosthenes. Popular algorithms to find primes are eith er Sieve of Eratosthenes or Trial Position Primes…