Goldbach's other conjecture
Problem 46
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
9 = 7 + 2×12
15 = 7 + 2×22
21 = 3 + 2×32
25 = 7 + 2×32
27 = 19 + 2×22
33 = 31 + 2×12
15 = 7 + 2×22
21 = 3 + 2×32
25 = 7 + 2×32
27 = 19 + 2×22
33 = 31 + 2×12
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
from tools import is_prime
def is_conjecture(odd_num):
square = 0
while 2 * square**2 < odd_num:
if is_prime(odd_num - (2 * square**2)):
return True
square += 1
return False
def run():
odd = 3
while is_conjecture(odd):
odd += 2
return odd