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Problem 46


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?