1.2. A Table of values of π(x)
1 10 42 100 25
3 1,000 168
4 10,000 1,229
5 100,000 9,592
6 1,000,000 78,498
7 10,000,000 664,579
8 100,000,000 5,761,455
9 1,000,000,000 50,847,534
10 10,000,000,000 455,052,511
11 100,000,000,000 4,118,054,813
12 1,000,000,000,000 37,607,912,018
13 10,000,000,000,000 346,065,536,839
14 100,000,000,000,000 3,204,941,750,802
15 1,000,000,000,000,000 29,844,570,422,669
16 10,000,000,000,000,000 279,238,341,033,925
17 100,000,000,000,000,000 2,623,557,157,654,233
18 1,000,000,000,000,000,000 24,739,954,287,740,860
19 10,000,000,000,000,000,000 234,057,667,276,344,607
20 100,000,000,000,000,000,000 2,220,819,602,560,918,840
21 1,000,000,000,000,000,000,000 21,127,269,486,018,731,928
22 10,000,000,000,000,000,000,000 201,467,286,689,315,906,290
23 100,000,000,000,000,000,000,000 1,925,320,391,606,803,968,923
24 1,000,000,000,000,000,000,000,000 18,435,599,767,349,200,867,866 (note)
25 10,000,000,000,000,000,000,000,000 176,846,309,399,143,769,411,680
用公式p·连乘q/(q-1),
(其中q最小4,最大q+1=p,p为小于根号下n的最大素数),计算的数值,一定少于比n小的素数。
如n=100,则7·4/2·6/4=21,小于25.更精确的是不小于p至n的素数个数。
订正:一定不少于比n小的素数个数。 请教,若用n(1-1/2)(1-1/3)(1-1/5)……(1-1/p)计算的素数个数,是不是都比您给的值要小 定理:熊一兵作诗祝贺的的那个哥猜证明的证明人鲁思顺是个二百五。
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