论文标题
一种可以找到连续素数的算法
An Algorithm to Find Sums of Powers of Consecutive Primes
论文作者
论文摘要
我们介绍并分析了一种算法，以列举所有整数$ n \ le x $，这些算法可以写为连续的$ k $ th primes的总和，价格为$ k> 1 $。我们表明，此类整数$ n $的数量是由常量$$ c_k \ frac {x^{2/（k+1）}} {（\ log x）^{2k/（k+1）}} {$ c_k $不在$ c_k $ boct $ k $ k $ k^2 $ k^2 $ k^2 $ k^2 $ k^2 $ k^2 $ k^2 $ k^2 $ k^2 $ k.这也界定了我们算法的渐近运行时间。我们还提供了相同数量级的下限，以及一种非常快的算法，该算法计算出这种$ n $。我们的作品扩展了Tongsomporn，Wananiyakul和Steuding（2022）的先前作品，他们检查了连续素数正方形的总和。
We present and analyze an algorithm to enumerate all integers $n\le x$ that can be written as the sum of consecutive $k$th powers of primes, for $k>1$. We show that the number of such integers $n$ is asymptotically bounded by a constant times $$ c_k \frac{ x^{2/(k+1)} }{ (\log x)^{2k/(k+1)} }, $$ where $c_k$ is a constant depending solely on $k$, roughly $k^2$ in magnitude. This also bounds the asymptotic running time of our algorithm. We also give a lower bound of the same order of magnitude, and a very fast algorithm that counts such $n$. Our work extends the previous work by Tongsomporn, Wananiyakul, and Steuding (2022) who examined sums of squares of consecutive primes.
