Question

I have a python class that generates the nth prime number by starting at the n-1th prime and increments. Then divides by all the primes already in the list up to floor(sqrt(candidate)).
But my class just gets into an infinite loops somewhere and I can’t figure out why.

class prime_list():
    def __init__(self):
        self.primelst = [1]
        self.n = 1

    def increment(self):
        self.n+=1
        candidate = self.primelst[-1]+1
        limit = int(math.floor(math.sqrt(candidate)))
        prime = True
        while True:
            for p in self.primelst:
                if p>limit:
                    break
                if (candidate % p) == 0:
                    prime = False
                    break
            if prime:
                self.primelst.append(candidate)
                return
            else:
                candidate += 1
                limit = int(math.floor(math.sqrt(candidate)))
                prime = True

if __name__=="__main__":
    p = prime_list():
    p.increment()

Answer 1

The problem is that you put 1 as a starting value in your prime list. The increment function then searches for numbers not divisible by 1. Since there are no such numbers, it searches forever.

You should start with 2 as the initial smallest prime number or add a special case handling the generation of the first prime.