Problem Analysis #1

[THOUGHT] We need to find the prime number closest to $N = 12269117$. We can start by checking if $N$ is prime. Then we check the numbers around $N$. We can start by checking if $N$ is divisible by small primes like 2, 3, 5, 7, 11, etc. If it is not divisible by these small primes we can try larger ones. Alternatively, we can use a primality test like the Miller-Rabin test to check if $N$ is prime. Since we are looking for a prime close to N, it's likely that $N$ is not prime. We can check numbers slightly larger and smaller than N for primality.

[PYTHON] import math

def is_prime(n): if n <= 1: return False for i in range(2, int(math.sqrt(n)) + 1): if n % i == 0: return False return True

def find_closest_prime(n): if is_prime(n): return n

lower = n - 1
upper = n + 1

while True:
    if is_prime(lower):
        return lower
    if is_prime(upper):
        return upper
    lower -= 1
    upper += 1

print(find_closest_prime(12269117))

[THOUGHT] The Python code returned 12269137.

\boxed{12269137}