Goldbach Conjecture (Even as Sum of Two Primes)

Express even number as sum of two primes.

Logic BuildingAdvanced
Logic Building
# Helper function
def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    return True

# Take even number
num = int(input("Enter an even number (>2): "))

# Find two primes
found = False
for i in range(2, num // 2 + 1):
    if is_prime(i) and is_prime(num - i):
        print(f"{num} = {i} + {num - i}")
        found = True
        break

if not found:
    print("No representation found")

Output

Enter an even number (>2): 20
20 = 3 + 17

Find two primes that sum to even number.

Key Concepts:

  • Check if i and num-i are prime
  • Both must be prime
  • Goldbach conjecture