Problem Analysis #1

[THOUGHT] To find the prime number closest to N = 12269117, I need to check numbers both below and above N to find the nearest primes. I will use the sympy library to test for primality and find the closest primes. [/THOUGHT] [PYTHON] from sympy import isprime

N = 12269117 lower = N - 1 upper = N + 1

while True: if isprime(lower): break lower -= 1

while True: if isprime(upper): break upper += 1

distance_lower = N - lower distance_upper = upper - N

if distance_lower <= distance_upper: closest_prime = lower else: closest_prime = upper

print(closest_prime) [/PYTHON]

[THOUGHT] The Python output confirms that the prime number closest to 12269117 is 12269137. [/THOUGHT] \boxed{12269137}