196 Separate Enumerations of Primes. [June 19, 



Third Million. 





Number of 

 4n + 1 

 primes. 



dumber of 

 4rc + 3 

 primes. 



Difference. 



Total number 

 of primes. 



2,000,000—2,010,000 



2,010,000—2,020,000 



2,020,000—2.030,000 



2,030,000—2,040.000 



2,040,000—2,050,000. . . . 

 2,050,000—2,060,000.. . . 

 2,060,000—2,070,000. . . . 

 2.070,000—2,080,000. . . . 

 2,080,000—2,090,000. . . . 

 2,090,000—2,100,000. . . . 



351 

 345 

 350 

 340 

 343 

 356 

 355 

 343 

 339 

 341 



354 

 346 

 343 

 350 

 328 

 340 

 339 

 331 

 347 

 333 



- 3 



- 1 

 + 7 

 -10 

 + 15 

 + 16 

 + 16 

 + 12 



- 8 

 + 8 



705 

 691 

 693 

 690 

 671 

 696 

 694 

 674 

 6S6 

 674 



2,000,000—2.100,000 



3.463 



3,411 





6.S74 



Fourth Million. 





Number of 

 4?* + l 

 primes. 



dumber of 

 4« + 3 

 primes. 



Difference. 



Total number 

 of primes. 



3,000,000—3,010,000. . . . 

 3,010,000—3,020,000. . . . 

 3,020,000—3.030,000. . . . 

 3,030,000—3,040.000. . . . 

 3,040,000—3,050,000. . . 

 3,050,000—3,060,000. . . . 

 3,060,000—3,070,000. . . . 

 3,070,000—3,080,000. . . . 

 3,080.000—3,090,000. . . . 

 3,090,000—3,100,000. . . . 



351 

 325 

 322 

 322 

 354 

 341 

 334 

 357 

 339 

 323 



319 

 334 

 341 

 335 

 317 

 316 

 330 

 338 

 347 

 331 



+ 32 



- 9 

 -19 

 -13 



+ 37 

 + 25 

 + 4 

 + 19 



- 8 



- 8 



S7( 

 659 

 663 

 657 

 671 

 657 

 664 

 695 

 6S6 

 654 



3,000,000—3,100,000. . . . 



3.368 



3,308 



+60 



I 



6,676 



Seventh Million. 





Number of 

 4?* + l 

 primes. 



]S umber of 

 4>? + 3 

 primes. 



Difference. 



Total number 

 of primes. 



6,000,000— 6,010,000.. .. 



341 



320 



+ 21 



661 



6,010,000—6,020,000. . . . 



317 



321 



- 4 



638 



6,020,000—6,030,000. . . . 



315 



349 



-34 



664 



6,030,000—6.040,000. . . . 



295 



306 



-11 



601 



6,040,000—6,050,000. . . . 



322 



305 



+ 17 



627 



6,050,000—6,060.000. . . . 



329 



337 



- 8 



666 



6.060.000—6,070,000. . . . 



322 



293 



+ 29 



615 



6,070,000—6,080,000. . . . 



326 



327 



- 1 



653 



6,080,000-0,090,000. . . . 



311 



317 



- 6 



62S 



6,090,000—6,100,000. . . . 



315 



329 



-14 



644 



6,000,000—6,100,000. . . . 



3,193 



3.204 



-11 



'5 I ■ - 



