Kattis prime reduction challenge
Some ideas:


is_prime_number doesn't scale well when dealing with bigger primes - the range of odd numbers 3..sqrt(number) is going to get very big. You'd be better off implementing a more sophisticated algorithm such as Eratosthenes' Sieve, where the cost of checking primality of subsequent primes grows slower.
sum_prime_factors duplicates the implementation of primality checking from is_prime_number.
[print_output(item, 1) for item in map(int, sys.stdin) if item != 4] is awkward. I would use a main method and any of the common

if __name__ == '__main__':
    main()


patterns for making the code reusable and testable.