This will be much faster. It does fewer prime checks and does not check numbers that are even for prime.
With GMPY2:
$ time python3 goldbach.py 12345678912345678 This is a test of Goldbach's Conjecture that for all even integers greater than 2 there are two primes that add up to that even number. 61 + 12,345,678,912,345,617 = 12,345,678,912,345,678 real 0m0.027s user 0m0.018s sys 0m0.009s With my Home Grown IsPrime:
$ time python3 goldbach.py 12345678912345678 This is a test of Goldbach's Conjecture that for all even integers greater than 2 there are two primes that add up to that even number. 61 + 12,345,678,912,345,617 = 12,345,678,912,345,678 real 0m2.405s user 0m2.405s sys 0m0.000s $ time python3 goldbach.py 1000000000 This is a test of Goldbach's Conjecture that for all even integers greater than 2 there are two primes that add up to that even number. 71 + 999,999,929 = 1,000,000,000 real 0m0.027s user 0m0.019s sys 0m0.008s Listing:
# Goldbach's Conjecture tester. from gmpy2 import is_prime import sys # or use home grown IsPrime def IsPrime(n): if (n == 2 or n == 3): return True if (n <= 1 or n % 2 == 0 or n % 3 == 0): return False for i in range(5, int(n**.5)+1, 6): if (n % i == 0 or n % (i + 2) == 0): return False return True def goldbach(numb): if numb == 4: return 2,2 # the only time we use 2 else: for p in range(3, numb, 2): # just check odds after 2 if is_prime(p) and is_prime(numb-p): return p,numb-p raise Exception(f"Found a counter-example to the Goldbach conjecture: {numb}") if __name__=="__main__": if len(sys.argv) > 1: N = int(sys.argv[1]) else: N = 1 print("This is a test of Goldbach's Conjecture that for all even integers") print("greater than 2 there are two primes that add up to that even number.\n") while (N < 3 or N%2): N = int(input("Please enter an even number > 3 to check with Goldbach's Conjecture> ")) p1,p2 = goldbach(N) print(f"{p1:,} + {p2:,} = {N:,}")