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The classical prime number theorem states that the prime counting function $$\pi(X) := \# \{ p \leq X \ | \ \text{$p$ prime} \}$$ is asymptotically equal to $X/\log(X)$. It is also known (and much ...

猜想:不存在两个长度为k且一共含有k个不同素因子的连续合数序列的素因子集合相等。例如 24 25 26 27 (2 3 5 13) 其余长度为4的连续合数序列要么素因子个数大于4 要么素因子集合不等于{2 3 5 13} 这个连续合数猜想的重大特定情况下的猜想。难度可与哥德巴赫猜想匹敌，非天才误入。再比如2 3 5 唯一决定了8 9 10 除此之外再无其他。总之经过计算机验证没有找到反例。 ...

Let $K$ be a number field, $\mathcal O_K$ be its ring of integers, and $\mathfrak p$ be a prime ideal of $\mathcal O_K$. Let $x\in \mathbb R^+$, and $N(\mathfrak p)$ be the norm of the prime ideal $\...