契比雪夫界限定理的改进

Some Improvements of Chebyshev’ss Bound

选用较传统更贴切的组合数以优化半长区间上素数连乘积的上界估计,然后通过构造半长区间的有限序列来覆盖全区间上的素数,由此得到契比雪夫界限定理(Chebyshev’s Bound)中上界限(即控制函数)的若干改进,并给出改进后估计式的关键参数的控制范围和具体算法.

This paper shows some improvements of Chebyshev’ss Bound(i.e.upper control function)and presents the control area and algorithm of key parameters.Some combinatorial number better than the traditional one is chosen and estimated upper bound of continued product of prime numbers on half-length interval is optimized.Finally,all prime numbers in the given interval are covered by an infinite half-length sequence.