In [4]:
every_other = 0
for num in range(1,101):
    prime = True
    for i in range(2,num):
        if (num%i==0):
            prime = False
    if prime:
        every_other += 1
        if (every_other%2==0):
            print(num)


2
5
11
17
23
31
41
47
59
67
73
83
97

I think this should be faster, but it's hard to tell:


In [19]:
every_other = 0
primes = []
for num in range(2,101):
    prime = True
    for i in primes:
        if (num%i==0):
            prime = False
    if prime:
        every_other += 1
        primes.append(num)
        if (every_other%2==1):
            print(num)


2
5
11
17
23
31
41
47
59
67
73
83
97

In [ ]: