120 REPORT-—1883. 
at intervals of 50,000 up to 9,000,000. ‘The comparisons are also given 
for the separate groups of 50,000, The deviations are given in separate 
tables. 
Table I., which is abridged from the more extended tables given in 
the Introduction, shows the numbers of primes counted and the numbers 
given by the formule (i.), (ii.), (ail.), at intervals of 100,000 up to 
9,000,000. Table II. shows the deviations in the case of the three 
formule. 
TasLe I. 
Number of Primes 
Calculated by 
x 
Counted 
Riemann’s Tchebycheft’s Legendre’s 
formula formula formula 
100,000 9,593 9,587 9,630 9,588 
200,000 17,985 17,982 18,036 17,982 
300,000 25,998 26,024 26,087 26,024 
400,000 33,861 33,852 33,923 33,854 
500,000 41,539 41,530 41,606 41,533 
600,000 49,099 49,091 49,173 49,096 
700,000 56,544 56,557 56,645 56,565 
800,000 63,952 63,945 64,037 63,955 
900,000 71,275 71,266 71,362 71,279 
1,000,000 78,499 78,528 78,628 78,543 
1,100,000 85,715 85,737 85,841 85,756 
1,200,000 92,940 92,899 93,007 92,921 
1,300,000 100,021 100,019 100,130 100,045 
1,400,000 107,124 107,100 107,214 107,129 
1,500,000 114,152 114,146 114,263 114,179 
1,600,000 121,125 121,159 121,279 121,195 
1,700,000 128,140 128,141 128,264 128,181 
1,800,000 135,072 135,095 135,221 1355539 
1,900,000 142,029 142,022 142,150 142,070 
2,000,000 148,932 148 924 149,055 148,976 
2,100,000 155,806 155,802 155,936 155,858 
2,200,000 162,663 162,658 162,794 162,718 
2,300,000 169,512 169,492 169,631 169,557 
2,400,000 176,303 176,307 176,448 176,376 
2,500,000 183,073 183,102 183,245 183,175 
2,600,000 189,882 189,878 190,024 189,956 
2,700,000 196,647 196,637 196,785 196,720 
2,800,000 203,363 203,380 203,530 203,467 
2,900,000 210,109 210,106 210,258 210,197 
3,000,000 216,817 216,816 216,971 216,913 
3,100,000 223,493 223,512 223,668 223,613 
3,200,000 230,210 230,193 230,351 230,299 
3,300,000 236,901 236,961 237,021 236,971 
3,400,000 243,540 243,514 243,677 243,629 
3,500,000 250,151 250,155 250,319 250,275 
3,600,000 256,726 256,784 256,950 256,908 
3,700,000 263,397 263,400 263,568 263,529 
3,800,000 269,987 270,004 270,174 270,139 
3,900,000 276,611 276,597 276,769 276,737 
4,000,000 283,146 283,179 283,352 283,323 
4,100,000 289,774 289,750 289,925 289,899 
