Brute force

The brute force approach for determining the minimal odd composite number that does not satisfy the Goldbach's other conjecture can be separated into two steps:

Verify whether a number satisfies the Goldbach's other conjecture.
Iterate through all odd composite numbers.

The first step can be brute force by iterating through every \( i \leq n \) and verify if \( i \) is prime and \( \sqrt{\frac{n-i}{2}} \) is an integer.

From solution1.py:

def is_odd_goldbach(n):
    return any(isprime(i) and (((n - i) / 2) ** 0.5).is_integer() for i in range(1, n + 1))

Assuming the existence of a solution, the second part is straightforward and can be done by iterating through all odd composite numbers until a solution is found.

From solution1.py:

def goldbachs_other_conjecture():
    for i in itertools.count(7, 2):
        if not is_odd_goldbach(i):
            return i

Project Euler

Brute force