This will be much faster. It does fewer prime checks, usually less than 100, and does not check numbers that are even for prime. 

**With GMPY2:**

 $ 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
 
 42 function calls in 0.000 seconds
 
 Ordered by: standard name
 
 ncalls tottime percall cumtime percall filename:lineno(function)
 1 0.000 0.000 0.000 0.000 <string>:1(<module>)
 1 0.000 0.000 0.000 0.000 goldbach.py:16(goldbach)
 1 0.000 0.000 0.000 0.000 {built-in method builtins.exec}
 1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
 37 0.000 0.000 0.000 0.000 {built-in method gmpy2.gmpy2.is_prime}
 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}


 $ python3 goldbach.py 4444444444444444444444
 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.
 
 
 257 + 4,444,444,444,444,444,444,187 = 4,444,444,444,444,444,444,444
 
 144 function calls in 0.000 seconds
 
 Ordered by: standard name
 
 ncalls tottime percall cumtime percall filename:lineno(function)
 1 0.000 0.000 0.000 0.000 <string>:1(<module>)
 1 0.000 0.000 0.000 0.000 goldbach.py:16(goldbach)
 1 0.000 0.000 0.000 0.000 {built-in method builtins.exec}
 1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
 139 0.000 0.000 0.000 0.000 {built-in method gmpy2.gmpy2.is_prime}
 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

**With my Home Grown IsPrime:**
 
 $ 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
 
 42 function calls in 3.869 seconds
 
 Ordered by: standard name
 
 ncalls tottime percall cumtime percall filename:lineno(function)
 1 0.000 0.000 3.869 3.869 <string>:1(<module>)
 1 0.000 0.000 3.869 3.869 goldbach.py:16(goldbach)
 37 3.869 0.105 3.869 0.105 goldbach.py:6(IsPrime)
 1 0.000 0.000 3.869 3.869 {built-in method builtins.exec}
 1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

 $ 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
 
 47 function calls in 0.001 seconds
 
 Ordered by: standard name
 
 ncalls tottime percall cumtime percall filename:lineno(function)
 1 0.000 0.000 0.001 0.001 <string>:1(<module>)
 1 0.000 0.000 0.001 0.001 goldbach.py:16(goldbach)
 42 0.001 0.000 0.001 0.000 goldbach.py:6(IsPrime)
 1 0.000 0.000 0.001 0.001 {built-in method builtins.exec}
 1 0.000 0.000 0.000 0.000 {built-in method builtins.print}
 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}

**Listing:**

 # Goldbach's Conjecture tester. 
 from gmpy2 import is_prime
 import sys
 import cProfile
 # 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(number):
 	if number == 4:
 		print("\n2 + 2 = 4\n")
 		return
 	elif IsPrime(number - 3):
 		print(f"\n3 + {number-3:,} = {number}\n")
 		return 
 	else:
 		for p in range(5, number, 6): # just odds after 3 
 			if IsPrime(p) and IsPrime(number-p): 
 				print(f"\n{p:,} + {number-p:,} = {N:,}\n")
 				return
 			elif IsPrime(p+2) and IsPrime(number-(p+2)):
 				print(f"\n{p+2:,} + {number-(p+2):,} = {N:,}\n")
 				return
 		raise Exception(f"Found a counter-example to the Goldbach conjecture: {number}")
 
 if __name__=="__main__":
 	N = 1
 	args = len(sys.argv)
 	if args > 1:
 		N = int(sys.argv[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> "))
 	cProfile.run('goldbach(N)')