PE[46]:the smallest odd composite that cannot be written as....

jimogsh

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 + 2×1^(2)
15 = 7 + 2×2^(2)
21 = 3 + 2×3^(2)
25 = 7 + 2×3^(2)
27 = 19 + 2×2^(2)
33 = 31 + 2×1^(2)

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?

有人假设所有奇数都可以表示为一个素数和一个平方的2倍之和。现在知道这个假设是不成立的。要求找出最小的一个不能写成这种形式的数。

jimogsh

1. In[27]:= Timing[s = 3;
   
2. While[Or @@ (PrimeQ[s - 2 #^2] & /@ Range[0, Sqrt[s/2], 1]) == True,
   
3.   s += 2]; s]
   
4. 
   
5. Out[27]= {0.703, 5777}

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这种写法是否比较简练？

FreddyMusic

还可以把 Range 里面的 1 省掉。