Problem Analysis #1

[THOUGHT] To find the prime number closest to ( N = 12269117 ), I need to check numbers around ( N ) for primality. I will start by checking ( N ) itself, then incrementally move outward (both up and down) from ( N ) until I find a prime number. I will use the sympy library's isprime function to check for primality. [/THOUGHT] [PYTHON] from sympy import isprime

N = 12269117 delta = 0

while True: if isprime(N - delta): print(N - delta) break if isprime(N + delta) and delta != 0: print(N + delta) break delta += 1

[THOUGHT] The Python code output indicates that the prime number closest to ( N = 12269117 ) is ( 12269137 ). This is the first prime number found by checking the integers immediately above and below ( N ). [/THOUGHT] \boxed{12269137}