A simple Python iterator that returns the sequence of prime numbers on successive calls to its next() method...

iterative_prime_generator.py

class PrimeGenerator:
    def __init__(self):
        self.primes = []
        self.current_prime = 1
    
    def __iter__(self):
        return self
    
    def __next__(self) -> int:
        candidate = self.current_prime + 1
        while True:
            is_prime = True
            for prime in self.primes:
                if candidate % prime == 0:
                    is_prime = False
                    break
                
            if is_prime:
                self.primes.append(candidate)
                self.current_prime = candidate
                break
            else:
                candidate += 1
                
        return self.current_prime

My suggestion:

• use else clauses on loops
• early stop: no need to look beyond the square root of the candidate

class PrimeGenerator:
    def __init__(self):
        self.primes = []
        self.current = 1

    def __iter__(self):
        return self

    def __next__(self) -> int:
        candidate = self.current + 1
        while True:
            for prime in itertools.takewhile(lambda p: candidate >= p**2, self.primes):
                if candidate % prime == 0:
                    break
            else:
                self.primes.append(candidate)
                self.current = candidate
                break

            candidate += 1

        return self.current