The following code will print the prime numbers between 1 and 100. Modify the code so it prints every other prime number from 1 to 100



In [21]:

    
from timeit import default_timer as timer

start = timer()
other = True
for num in range(1,101): # for-loop through the numbers
    prime = True # boolean flag to check the number for being prime
    for i in range(2,num): # for-loop to check for "primeness" by checking for divisors other than 1
        if (num%i==0): # logical test for the number having a divisor other than 1 and itself
            prime = False # if there's a divisor, the boolean value gets flipped to False
    if prime: # if prime is still True after going through all numbers from 1 - 100, then it gets printed
        if other == True:
            print(num)
            other = False
        else:
            other = True
end = timer()
exec_time_1 = end - start
print("Time:", exec_time_1)









    



1
3
7
13
19
29
37
43
53
61
71
79
89
Time: 0.0013584190000983654

Extra Credit: Can you write a procedure that runs faster than the one above?



In [115]:

    
from timeit import default_timer as timer

#import collections
#other_prime = collections.deque()

start = timer()
other = True
other_prime = []

for num in range(1,101):
    prime = True # boolean flag to check the number for being prime
    
    if (num & 1) == 0 and num > 2: # fast test for even numbers
        continue
    
    for i in range(2,num): # for-loop to check for "primeness" by checking for divisors other than 1
        if (num%i==0): # logical test for the number having a divisor other than 1 and itself
            prime = False # if there's a divisor, the boolean value gets flipped to False
            break
    if prime: # if prime is still True after going through all numbers from 1 - 100, then it gets printed
        if other == True:
            other_prime.append(num)
            other = False
        else:
            other = True

print(*other_prime, sep="\n")
end = timer()
exec_time_2 = end - start
print("Time:", exec_time_2)
diff = (exec_time_1 - exec_time_2)/exec_time_1
if diff > 0:
    print("The second code ran {0:.2f}% faster.".format(100*diff))
else:
    print("The second code ran {0:.2f}% slower.".format(-100*diff))









    



1
3
7
13
19
29
37
43
53
61
71
79
89
Time: 0.0005376940007408848
The second code ran 60.42% faster.