Problem Analysis #1

[THOUGHT] I will write a Python script to find the prime number closest to $N = 12269117$. I will check integers $N, N-1, N+1, N-2, N+2, \dots$ for primality using the sympy.isprime function. The first prime found will be the closest. If two are found at the same distance, I will note that, but typically one is closer or the question implies a unique answer.

[/THOUGHT] [PYTHON] from sympy import isprime

N = 12269117 found = False d = 0

while not found: # Check lower first, then higher, or check both and see which is closer (they are at distance d) # If d=0, check N if d == 0: if isprime(N): print(f"Found prime: {N} at distance {d}") found = True else: # Check N-d p_down = N - d if isprime(p_down): print(f"Found prime: {p_down} at distance {d}") found = True

    # Check N+d
    p_up = N + d
    if isprime(p_up):
        print(f"Found prime: {p_up} at distance {d}")
        found = True
        
if found:
    break
d += 1

[/PYTHON]

The prime number closest to $N = 12269117$ is \boxed{12269137}.