Count Prime Number.py

class Solution:
    prime_numbers = [2,3,5,7,11,13,17,19,23,29,31]
    def countPrimes(self, n: int) -> int:
        return Solution.countPrime(n)
    @staticmethod
    def countPrime(n: int):
        if n <= 2: return 0
        m = Solution.prime_numbers[-1]
        
        while n > m:
            m += 2
            prime_p = True
            for prime in Solution.prime_numbers:
                if m % prime == 0:
                    prime_p = False
                    break
            if prime_p: Solution.prime_numbers.append(m)
                
        p = len(Solution.prime_numbers)
        if Solution.prime_numbers[p-1] < n:
            return p
        l = 0
        while not (Solution.prime_numbers[p-1] >= n and Solution.prime_numbers[p-2] < n):
            t = ((p - l) // 2) + l
            print(f"p:{p}, l:{l}, t:{t} => {Solution.prime_numbers[t]}")
            if Solution.prime_numbers[t] > n:
                p = t+1
            elif Solution.prime_numbers[t] == n:
                p = t+1
                break
            else:
                l = t
        
        return p-1