Use Python 3.6, for this problem we revisit the Sieve of Eratosthenes. Since we

Question

Use Python 3.6, for this problem we revisit the Sieve of Eratosthenes. Since we know that 2 is the only even prime, it is wasteful of memory to include information for even numbers. Instead our array should start with the information for 3 and then only keep track of the information for the odd numbers (3,5,7,9,...). The program should list the primes less that or equal to an input number, call it n. We may as well assume n is odd. Hints: Note that 2i + 3 runs through the odd numbers in question for i = 0,1,2,3,.... We can use slot i in our array to store the information for the odd number 2i + 3. Write a function that takes i and returns 2i + 3. Write the inverse function also. These functions should enable you to easily find the right places in the array and the corresponding numbers. Give some sample output of a value of n that’s pretty big, but the output will fit on one page. What is the biggest value of n you can process in less than or equal to one minute? Use Python 3.6, for this problem we revisit the Sieve of Eratosthenes. Since we know that 2 is the only even prime, it is wasteful of memory to include information for even numbers. Instead our array should start with the information for 3 and then only keep track of the information for the odd numbers (3,5,7,9,...). The program should list the primes less that or equal to an input number, call it n. We may as well assume n is odd. Hints: Note that 2i + 3 runs through the odd numbers in question for i = 0,1,2,3,.... We can use slot i in our array to store the information for the odd number 2i + 3. Write a function that takes i and returns 2i + 3. Write the inverse function also. These functions should enable you to easily find the right places in the array and the corresponding numbers. Give some sample output of a value of n that’s pretty big, but the output will fit on one page. What is the biggest value of n you can process in less than or equal to one minute? Since we know that 2 is the only even prime, it is wasteful of memory to include information for even numbers. Instead our array should start with the information for 3 and then only keep track of the information for the odd numbers (3,5,7,9,...). The program should list the primes less that or equal to an input number, call it n. We may as well assume n is odd. Hints: Note that 2i + 3 runs through the odd numbers in question for i = 0,1,2,3,.... We can use slot i in our array to store the information for the odd number 2i + 3. Write a function that takes i and returns 2i + 3. Write the inverse function also. These functions should enable you to easily find the right places in the array and the corresponding numbers. Give some sample output of a value of n that’s pretty big, but the output will fit on one page. What is the biggest value of n you can process in less than or equal to one minute?

Explanation / Answer

from array import *

def inputfunction():

return ((2 * i) + 3)

def reverse():

if (n%2) == 0:

return ((n-4)/2)

else:

return ((n-3)/2)

def printprime():

for k in range(0,num+1):

#print(num)

for j in range(2,odd[k]):  

if (odd[k] % j) == 0:

break

else:

print(odd[k])

odd = array("l");

n = input("Enter a number : ")

num=reverse()

for i in range(0,num+1):

odd.append(inputfunction())

printprime()

#65447 is the prime number approximately at one minute

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