primalitytest.py

# Prime numbers two factors 1 , Number Itself
# Approach One O(n)
# Aprroach Two: Base Case + Hint: O(1) -> O(root(N))
from math import *

def approach1(n):
    divcnt = 0
    for i in range(1,n+1): # [1,n]
        if n%i == 0:
            divcnt+=1

    print(divcnt)
    if divcnt == 2:
        return True
    else:
        return False

def approach2(n):
    
    if n == 0 or n == 1: # O(1)
        return False
    if n == 2 or n == 3:# O(1)
        return True
    if n%2 == 0 or n%3 == 0:# O(1)
        return False
    for i in range(5,int(sqrt(n))+1,6): # [1,root n] prime numbers are in the form of 6k-1 or 6k+1
        if n%i == 0 or n%(i+2) == 0:
            return False
    return True
    

# approach2 more effiecient


t = int(input())
while t:
    n = int(input())
    #print(approach1(n))
    print(approach2(n))
    t = t -1