Question

So I decided to learn python this weekend and I started with my default hello world, the prime solver. This code shouldn’t work… But for whatever reason it does (for numbers 5 and higher.)

#!/usr/bin/python
a = 2
while a < 65535:
    c = 0
    a = a + 1
    b = 2
    while b != a:
        if a % b == 0:
            #print a, "is not prime. LCD is ", b
            break
        b = b + 1
     if a - 1 == b: c = 1
 if c == 1: print a, " is prime"

The next to the last conditional should always be false, and yet somehow a -1 == b for all primes 5 and up.

Can someone point out this noob’s mistake, because I’m obviously missing something easily described.

Answers further below.

Answer 1

If a is not prime, it has atleast two proper divisors, and of one of them must be smaller than the square root (or both are the square root). If b reaches sqrt(a)+1, then a must be prime. So if b reaches a - 1, you can be pretty sure it’s prime. You could also replace it by if a - 3 == b, or a / 2 (but this might not work for the smaller primes).