Prime Number Theorem |
x |
π(x) |
π(x) − x / ln x |
π(x) / (x / ln x) |
li(x) − π(x) |
x / π(x) |
10 |
4 |
−0.3 |
0.921 |
2.2 |
2.500 |
102 |
25 |
3.3 |
1.151 |
5.1 |
4.000 |
103 |
168 |
23 |
1.161 |
10 |
5.952 |
104 |
1,229 |
143 |
1.132 |
17 |
8.137 |
105 |
9,592 |
906 |
1.104 |
38 |
10.425 |
106 |
78,498 |
6,116 |
1.084 |
130 |
12.740 |
107 |
664,579 |
44,158 |
1.071 |
339 |
15.047 |
108 |
5,761,455 |
332,774 |
1.061 |
754 |
17.357 |
109 |
50,847,534 |
2,592,592 |
1.054 |
1,701 |
19.667 |
1010 |
455,052,511 |
20,758,029 |
1.048 |
3,104 |
21.975 |
1011 |
4,118,054,813 |
169,923,159 |
1.043 |
11,588 |
24.283 |
1012 |
37,607,912,018 |
1,416,705,193 |
1.039 |
38,263 |
26.590 |
1013 |
346,065,536,839 |
11,992,858,452 |
1.034 |
108,971 |
28.896 |
1014 |
3,204,941,750,802 |
102,838,308,636 |
1.033 |
314,890 |
31.202 |
1015 |
29,844,570,422,669 |
891,604,962,452 |
1.031 |
1,052,619 |
33.507 |
1016 |
279,238,341,033,925 |
7,804,289,844,393 |
1.029 |
3,214,632 |
35.812 |
1017 |
2,623,557,157,654,233 |
68,883,734,693,281 |
1.027 |
7,956,589 |
38.116 |
1018 |
24,739,954,287,740,860 |
612,483,070,893,536 |
1.025 |
21,949,555 |
40.420 |
1019 |
234,057,667,276,344,607 |
5,481,624,169,369,960 |
1.024 |
99,877,775 |
42.725 |
1020 |
2,220,819,602,560,918,840 |
49,347,193,044,659,701 |
1.023 |
222,744,644 |
45.028 |
1021 |
21,127,269,486,018,731,928 |
446,579,871,578,168,707 |
1.022 |
597,394,254 |
47.332 |
1022 |
201,467,286,689,315,906,290 |
4,060,704,006,019,620,994 |
1.021 |
1,932,355,208 |
49.636 |
1023 |
1,925,320,391,606,803,968,923 |
37,083,513,766,578,631,309 |
1.020 |
7,250,186,216 |
51.939 |