关于p_(n),n∑k=1 kp_(k)的确界估计的进一步精确  

Further Refinement of Estimates of p_(n) and n∑k=1 kp_(k) True Bounds

作　　者：梁钟浩 杨仕椿 廖群英 LIANG Zhonghao;YANG Shichun;LIAO Qunying(School of Mathematical Science,Sichuan Normal University,Chengdu 610066,China;School of Mathematics,Aba Teachers University,Wenchuan Sichuan 623000,China)

机构地区：[1]四川师范大学数学科学学院,成都610066 [2]阿坝师范学院数学学院,四川汶川623000

出　　处：《大学数学》2025年第1期16-22,共7页College Mathematics

基　　金：国家自然科学基金(12361001);阿坝师范学院教学科研项目(AS-XJPT2023-02,AS-KCTD2023-02,20210301002)。

摘　　要：对于■k∈Z^(+)=1,2,3,…,记p_(k)表示第k个素数.利用与p_(k)的确界有关的不等式,对p_(n)的下确界以及n∑k=1 kp_(k)的上确界进行了更加精确的估计,即建立了与第n个素数有关的新的两个不等式:当n≥10^(8)时,p_(n)≥0.769n/lnn+n+n∑k=1 p_(k)/k;当n≥10^(6)时,n∑k=1 kp_(k)≤n^(2)/3 p_(n)-n^(3)/9-0.052n^(3)/lnn,进而改进了文献[1]中给出的部分估计.For any positive integer k,let’s call p_(k) the k-th prime number.By using the inequality related to the infimum of p_(k) and the supremum of n∑k=1 kp_(k) are estimated more accurately,establishing a new inequality bound related to the n-th prime number:When n is a positive integer greater than or equal to 108,the following a inequalities are true:p_(n)≥0.769n/lnn+n+n∑k=1 pk/k and When n is a positive integer greater than or equal to 10^(6),the following a inequalities are true:n∑k=1 kp_(k)≤n^(2)/3 p_(n)-n^(3)/9-0.052n^(3)/lnn.Furthermore,the estimate given in reference[1]is improved.

关 键 词：素数 不等式 确界估计 

分 类 号：O156.1[理学—数学]