Problem 46
Goldbach’s other conjecture
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
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?
哥德巴赫的另一个猜想
克里斯蒂安·哥德巴赫曾经猜想，每个奇合数可以写成一个素数和一个平方的两倍之和。
9 = 7 + 2×12
15 = 7 + 2×22
21 = 3 + 2×32
25 = 7 + 2×32
27 = 19 + 2×22
33 = 31 + 2×12
最终这个猜想被推翻了。
最小的不能写成一个素数和一个平方的两倍之和的奇合数是多少？