Goldbach Conjecture in Python

The Goldbach Conjecture is a famous unsolved problem in number theory that dates back to 1742. It was first proposed by the German mathematician Christian Goldbach, who wrote a letter to the famous mathematician Leonhard Euler in which he stated that “every positive even integer greater than 2 can be expressed as the sum of two prime numbers.”.

            
            
                # Program to check if a number is prime or not
                num = 3
                prime = []
                
                # To take input from the user
                # num = int(input("Enter a number: "))
                
                while num != 100:
                    if num > 1:
                        # check for factors
                        for i in range(2, num):
                            if (num % i) == 0:
                                num = num + 1
                                break
                        else:
                            print(num, " is prime!")
                            prime.append(num)
                            num = num + 1
                
                    # Check for 1, but this program starts at 3 so no need for this.
                    else:
                        num = num + 1
                
                
                end = False
                
                while end == False:
                    # get first number in list
                    first = prime[0]
                
                    # print list of prime numbers
                    print(prime)
                
                    # Iterate through the list of prime numbers
                    for x in prime:
                        # calculate and print sum of x numbers in list and first number in list
                        sum = x + first
                        print(str(x), ' + ',  str(first),  ' = ',  x + first)
                
                        # if the sum is even, continue with the program
                        if sum % 2 == 0:
                            continue
                        else:
                            print("STOP")
                            end = True
                            break
                    # get rid of first number in list
                    prime.pop(0)
                
                    # if the list of prime numbers is empty, exit while loop
                    if not prime:
                        end = True