arXiv 1306.30912013-06cs.CCcs.DMmath.NT

小因子和素元的直线复杂性

The straight line complexity of small factorials and primorials

Klas Markström

备注：: V4: Published version. Reformatted to journal format. Minor typos corrected. v3: Updated acknowledgments, improved some of the lower bounds after recomputing all data with a new program, corrected two incorrect lower bounds due a damaged datafile from the original 10 year old computation. V2: Corrected typos and a mistake in table 2

摘要：

本文确定了$n!$对于$n\leq 22$的直线复杂度，并给出了直到$n=46$的直线复杂度的界.以同样的方式，我们确定的直线复杂性的产品的第一个素数的$p=31$和给界$p\leq 43$。我们的结果是基于一个详尽的计算机搜索的短长度直线程序。

英文摘要：

In this paper we determine the straight-line complexity of $n!$ for $n\leq 22$ and give bounds for the complexities up to $n=46$. In the same way we determine the straight-line complexity of the product of the first primes up to $p=31$ and gives bounds for $p\leq 43$. Our results are based on an exhaustive computer search of the short length straight-line programs.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。