感谢dlpangong网友提供的一万亿以内的素数

柳林 · 发表于 2018-7-18 17:45

n 区间素数个数素数值下界个数误差率
N n实 P n下 %
250 1312500 100909 1312471 94106.82 -6.7409
251 1323021 101664 1323017 94801.92 -6.7498
252 1333584 102397 1333583 95499.35 -6.7362
253 1344189 103160 1344181 96198.95 -6.7478
254 1354836 103889 1354823 96900.80 -6.7266
255 1365525 104654 1365503 97604.97 -6.7356
256 1376256 105407 1376237 98311.30 -6.7317
257 1387029 106182 1387021 99019.96 -6.7451
258 1397844 106951 1397839 99731.07 -6.7507
259 1408701 107715 1408699 100445.02 -6.7493
260 1419600 108458 1419589 101161.28 -6.7277
261 1430541 109234 1430521 101879.78 -6.7325
262 1441524 110034 1441523 102600.44 -6.7557
263 1452549 110810 1452541 103324.07 -6.7556
264 1463616 111602 1463611 104049.94 -6.7670
265 1474725 112373 1474721 104777.98 -6.7588
266 1485876 113161 1485871 105508.47 -6.7625
267 1497069 113967 1497061 106241.48 -6.7787
268 1508304 114763 1508303 106976.66 -6.7847
269 1519581 115559 1519561 107714.28 -6.7885
270 1530900 116339 1530871 108454.29 -6.7774
271 1542261 117128 1542259 109196.59 -6.7716
272 1553664 117921 1553653 109941.20 -6.7671
273 1565109 118720 1565099 110688.11 -6.7654
274 1576596 119525 1576583 111437.74 -6.7662
275 1588125 120312 1588121 112189.67 -6.7511
276 1599696 121110 1599691 112943.84 -6.7428
277 1611309 121945 1611307 113700.16 -6.7611
278 1622964 122747 1622953 114458.98 -6.7521
279 1634661 123588 1634657 115220.24 -6.7707
280 1646400 124391 1646387 115984.01 -6.7585
281 1658181 125216 1658161 116750.14 -6.7610
282 1670004 126052 1670003 117518.92 -6.7695
283 1681869 126882 1681853 118290.26 -6.7714
284 1693776 127696 1693763 119063.90 -6.7599
285 1705725 128534 1705721 119839.76 -6.7642
286 1717716 129366 1717687 120617.78 -6.7624
287 1729749 130194 1729747 121398.01 -6.7561
288 1741824 131028 1741811 122180.40 -6.7524
289 1753941 131894 1753931 122965.21 -6.7697
290 1766100 132697 1766099 123752.52 -6.7405
291 1778301 133552 1778299 124542.10 -6.7464
292 1790544 134399 1790539 125333.98 -6.7449
293 1802829 135265 1802821 126128.54 -6.7545
294 1815156 136126 1815131 126925.25 -6.7590
295 1827525 136992 1827509 127724.59 -6.7649
296 1839936 137834 1839923 128526.07 -6.7530
297 1852389 138712 1852373 129330.36 -6.7634
298 1864884 139590 1864879 130136.94 -6.7720
299 1877421 140469 1877401 130945.87 -6.7795

柳林 · 发表于 2018-7-18 17:46

n 区间素数个数素数值下界个数误差率
N n实 P n下 %
300 1890000 141338 1889999 131757.08 -6.7787
301 1902621 142207 1902619 132570.50 -6.7764
302 1915284 143090 1915267 133386.06 -6.7817
303 1927989 143982 1927979 134203.83 -6.7912
304 1940736 144860 1940713 135023.95 -6.7900
305 1953525 145742 1953517 135846.33 -6.7899
306 1966356 146619 1966343 136671.12 -6.7848
307 1979229 147478 1979227 137498.05 -6.7671
308 1992144 148375 1992139 138327.39 -6.7718
309 2005101 149286 2005079 139159.25 -6.7835
310 2018100 150198 2018077 139993.52 -6.7940
311 2031141 151094 2031137 140830.05 -6.7931
312 2044224 152005 2044201 141669.05 -6.7997
313 2057349 152884 2057333 142510.19 -6.7854
314 2070516 153805 2070479 143353.52 -6.7953
315 2083725 154695 2083721 144198.99 -6.7850
316 2096976 155598 2096971 145046.85 -6.7810
317 2110269 156526 2110267 145897.17 -6.7905
318 2123604 157428 2123603 146749.62 -6.7830
319 2136981 158354 2136977 147604.65 -6.7882
320 2150400 159272 2150399 148461.82 -6.7872
321 2163861 160226 2163859 149321.24 -6.8059
322 2177364 161139 2177363 150182.86 -6.7992
323 2190909 162065 2190901 151046.60 -6.7988
324 2204496 162975 2204483 151912.72 -6.7877
325 2218125 163901 2218121 152781.16 -6.7845
326 2231796 164839 2231791 153652.25 -6.7865
327 2245509 165773 2245501 154526.16 -6.7845
328 2259264 166725 2259241 155402.27 -6.7913
329 2273061 167695 2273059 156280.64 -6.8066
330 2286900 168613 2286883 157161.31 -6.7917
331 2300781 169567 2300777 158044.56 -6.7952
332 2314704 170504 2314699 158929.94 -6.7881
333 2328669 171449 2328653 159817.50 -6.7842
334 2342676 172395 2342671 160707.37 -6.7796
335 2356725 173330 2356699 161599.81 -6.7675
336 2370816 174309 2370811 162494.38 -6.7780
337 2384949 175262 2384911 163391.12 -6.7732
338 2399124 176241 2399119 164290.18 -6.7810
339 2413341 177185 2413339 165191.48 -6.7689
340 2427600 178169 2427599 166095.03 -6.7767
341 2441901 179128 2441867 167000.75 -6.7702
342 2456244 180108 2456243 167908.91 -6.7732
343 2470629 181081 2470621 168819.18 -6.7715
344 2485056 182049 2485037 169732.20 -6.7657
345 2499525 183036 2499521 170647.45 -6.7684
346 2514036 184025 2514019 171564.82 -6.7709
347 2528589 185012 2528587 172484.43 -6.7712
348 2543184 185998 2543171 173406.21 -6.7698
349 2557821 186985 2557817 174330.23 -6.7678

柳林 · 发表于 2018-7-18 19:45

n 区间素数个数素数值下界个数误差率
N n实 P n下 %
350 2572500 187990 2572489 175256.74 -6.7734
351 2587221 189019 2587217 176185.48 -6.7895
352 2601984 190006 2601979 177116.39 -6.7838
353 2616789 191008 2616787 178049.41 -6.7843
354 2631636 192005 2631631 178984.66 -6.7812
355 2646525 193018 2646517 179922.08 -6.7848
356 2661456 194044 2661427 180861.73 -6.7934
357 2676429 195039 2676419 181803.79 -6.7859
358 2691444 196062 2691443 182748.08 -6.7907
359 2706501 197085 2706481 183694.59 -6.7942
360 2721600 198118 2721577 184643.58 -6.8012
361 2736741 199102 2736737 185594.74 -6.7841
362 2751924 200127 2751907 186548.11 -6.7851
363 2767149 201158 2767147 187503.90 -6.7877
364 2782416 202178 2782411 188461.98 -6.7841
365 2797725 203191 2797723 189422.27 -6.7762
366 2813076 204272 2813071 190384.73 -6.7984
367 2828469 205307 2828461 191350.02 -6.7981
368 2843904 206384 2843903 192317.89 -6.8155
369 2859381 207405 2859377 193288.12 -6.8064
370 2874900 208444 2874881 194260.62 -6.8044
371 2890461 209481 2890457 195235.29 -6.8005
372 2906064 210517 2906053 196212.18 -6.7951
373 2921709 211568 2921689 197191.17 -6.7954
374 2937396 212617 2937391 198172.37 -6.7937
375 2953125 213670 2953123 199156.28 -6.7926
376 2968896 214725 2968891 200142.58 -6.7912
377 2984709 215788 2984701 201130.98 -6.7923
378 3000564 216849 3000553 202121.90 -6.7914
379 3016461 217918 3016417 203115.09 -6.7929
380 3032400 218971 3032399 204110.45 -6.7865
381 3048381 220033 3048359 205108.19 -6.7830
382 3064404 221082 3064367 206108.39 -6.7729
383 3080469 222183 3080461 207110.92 -6.7836
384 3096576 223284 3096571 208115.55 -6.7933
385 3112725 224343 3112721 209122.33 -6.7846
386 3128916 225437 3128893 210131.39 -6.7893
387 3145149 226510 3145147 211142.65 -6.7844
388 3161424 227603 3161407 212156.13 -6.7868
389 3177741 228704 3177739 213171.76 -6.7914
390 3194100 229805 3194069 214189.48 -6.7951
391 3210501 230934 3210479 215209.34 -6.8092
392 3226944 232034 3226939 216231.42 -6.8105
393 3243429 233143 3243397 217255.75 -6.8144
394 3259956 234234 3259933 218282.24 -6.8102
395 3276525 235355 3276523 219310.80 -6.8170
396 3293136 236463 3293123 220341.57 -6.8177
397 3309789 237559 3309763 221374.66 -6.8128
398 3326484 238673 3326471 222409.83 -6.8140
399 3343221 239783 3343217 223447.31 -6.8127

柳林 · 发表于 2018-7-18 19:46

n 区间素数个数素数值下界个数误差率
N n实 P n下 %
400 3360000 240853 3359989 224487.06 -6.7950
401 3376821 241987 3376819 225528.94 -6.8012
402 3393684 243115 3393683 226573.26 -6.8041
403 3410589 244255 3410587 227619.89 -6.8106
404 3427536 245393 3427513 228668.90 -6.8152
405 3444525 246546 3444521 229719.98 -6.8247
406 3461556 247655 3461551 230773.26 -6.8166
407 3478629 248757 3478627 231828.67 -6.8052
408 3495744 249872 3495743 232886.16 -6.7978
409 3512901 251000 3512869 233946.13 -6.7944
410 3530100 252103 3530099 235008.54 -6.7807
411 3547341 253240 3547331 236073.07 -6.7789
412 3564624 254379 3564623 237139.80 -6.7770
413 3581949 255524 3581927 238208.77 -6.7764
414 3599316 256684 3599279 239279.94 -6.7803
415 3616725 257872 3616721 240353.23 -6.7936
416 3634176 259053 3634171 241429.06 -6.8032
417 3651669 260163 3651653 242507.14 -6.7865
418 3669204 261321 3669187 243587.52 -6.7861
419 3686781 262506 3686747 244670.09 -6.7945
420 3704400 263694 3704387 245754.85 -6.8030
421 3722061 264860 3722053 246841.85 -6.8029
422 3739764 266052 3739763 247931.15 -6.8110
423 3757509 267226 3757471 249022.80 -6.8119
424 3775296 268354 3775201 250116.88 -6.7959
425 3793125 269540 3793121 251213.07 -6.7993
426 3810996 270719 3810979 252311.46 -6.7995
427 3828909 271916 3828901 253412.02 -6.8050
428 3846864 273115 3846863 254514.65 -6.8104
429 3864861 274293 3864841 255620.10 -6.8076
430 3882900 275460 3882899 256727.61 -6.8004
431 3900981 276667 3900943 257837.41 -6.8059
432 3919104 277851 3919099 258949.46 -6.8028
433 3937269 279063 3937267 260063.62 -6.8083
434 3955476 280272 3955459 261180.20 -6.8119
435 3973725 281448 3973691 262298.89 -6.8038
436 3992016 282628 3992011 263419.82 -6.7963
437 4010349 283832 4010339 264543.10 -6.7959
438 4028724 285047 4028723 265668.55 -6.7983
439 4047141 286305 4047101 266796.35 -6.8139
440 4065600 287498 4065599 267926.27 -6.8076
441 4084101 288717 4084081 269058.37 -6.8090
442 4102644 289934 4102603 270193.03 -6.8088
443 4121229 291148 4121213 271329.99 -6.8069
444 4139856 292339 4139831 272469.00 -6.7969
445 4158525 293577 4158521 273610.47 -6.8011
446 4177236 294805 4177231 274754.66 -6.8012
447 4195989 296061 4195973 275900.98 -6.8094
448 4214784 297296 4214779 277049.36 -6.8103
449 4233621 298521 4233613 278200.08 -6.8072
450 4252500 299756 4252489 279352.97 -6.8065
451 4271421 300989 4271417 280507.98 -6.8046
452 4290384 302201 4290373 281665.33 -6.7954
453 4309389 303446 4309369 282824.85 -6.7957
454 4328436 304684 4328419 283986.59 -6.7931
455 4347525 305924 4347521 285150.45 -6.7904
456 4366656 307153 4366643 286316.54 -6.7837
457 4385829 308431 4385819 287485.23 -6.7911
458 4405044 309668 4405043 288655.98 -6.7853
459 4424301 310946 4424297 289828.84 -6.7913
460 4443600 312248 4443599 291003.77 -6.8036
461 4462941 313520 4462921 292181.02 -6.8063
462 4482324 314781 4482323 293361.03 -6.8047
463 4501749 316062 4501733 294543.11 -6.8084
464 4521216 317314 4521173 295727.35 -6.8029
465 4540725 318565 4540687 296913.76 -6.7965
466 4560276 319837 4560263 298102.34 -6.7955
467 4579869 321134 4579859 299293.02 -6.8012
468 4599504 322411 4599493 300485.87 -6.8004
469 4619181 323709 4619179 301680.77 -6.8049
470 4638900 324979 4638899 302877.99 -6.8007
471 4658661 326239 4658659 304077.32 -6.7931
472 4678464 327539 4678397 305278.98 -6.7961
473 4698309 328868 4698299 306482.68 -6.8068
474 4718196 330151 4718191 307688.66 -6.8037
475 4738125 331469 4738099 308896.68 -6.8098
476 4758096 332733 4758077 310107.13 -6.8000
477 4778109 334028 4778107 311319.63 -6.7983
478 4798164 335317 4798163 312534.56 -6.7943
479 4818261 336635 4818241 313751.65 -6.7977
480 4838400 337960 4838399 314971.26 -6.8022
481 4858581 339249 4858577 316193.30 -6.7961
482 4878804 340565 4878799 317417.55 -6.7968
483 4899069 341927 4899067 318643.91 -6.8094
484 4919376 343237 4919363 319872.31 -6.8072
485 4939725 344565 4939717 321102.82 -6.8092
486 4960116 345881 4960097 322335.37 -6.8074
487 4980549 347247 4980539 323570.50 -6.8183
488 5001024 348579 5001023 324807.83 -6.8194
489 5021541 349895 5021537 326047.48 -6.8156
490 5042100 351224 5042099 327289.28 -6.8147
491 5062701 352557 5062697 328533.34 -6.8141
492 5083344 353891 5083343 329779.45 -6.8133
493 5104029 355228 5104013 331027.65 -6.8126
494 5124756 356568 5124683 332278.00 -6.8122
495 5145525 357917 5145521 333530.40 -6.8135
496 5166336 359253 5166331 334784.94 -6.8108
497 5187189 360584 5187181 336041.74 -6.8063
498 5208084 361953 5208079 337300.58 -6.8109
499 5229021 363300 5229011 338561.72 -6.8093
500 5250000 364685 5249989 339825.11 -6.8168

柳林 · 发表于 2018-7-18 19:51

n 区间素数个数素数值下界个数误差率
N n实 P n下 %
100380 2.116E+11 8452398129 2.116E+11 7974891265.59 -5.6494
102562 2.20898E+11 8808725055 2.209E+11 8311581841.16 -5.6438
104745 2.304E+11 9172116737 2.304E+11 8655104682.90 -5.6368
106927 2.401E+11 9542585532 2.401E+11 9005263147.65 -5.6308
109109 2.5E+11 9920079604 2.5E+11 9362107331.86 -5.6247
111291 2.601E+11 10304627621 2.601E+11 9725627973.06 -5.6188
113473 2.704E+11 10696202934 2.704E+11 10095815920.30 -5.6131
146206 4.489E+11 17407448715 4.489E+11 16443372391.71 -5.5383
170210 6.084E+11 23317152986 6.084E+11 22036200585.12 -5.4936
176757 6.561E+11 25072614748 6.561E+11 23698013301.43 -5.4825
183303 7.056E+11 26889370314 7.056E+11 25418059946.61 -5.4717
185485 7.225E+11 27508535894 7.225E+11 26004322626.17 -5.4682
187667 7.396E+11 28134510924 7.396E+11 26597034616.00 -5.4647
189850 7.569E+11 28767273539 7.569E+11 27196177416.15 -5.4614
192032 7.744E+11 29406803035 7.744E+11 27801770193.87 -5.4580
194214 7.921E+11 30053094294 7.921E+11 28413795609.59 -5.4547
196396 8.1E+11 30706162642 8.1E+11 29032250781.78 -5.4514
198578 8.281E+11 31365996441 8.281E+11 29657128761.76 -5.4482
200760 8.464E+11 32032574113 8.464E+11 30288430079.90 -5.4449
202943 8.649E+11 32705908011 8.649E+11 30926136665.26 -5.4417
205125 8.836E+11 33385994030 8.836E+11 31570263830.29 -5.4386
207307 9.025E+11 34072815815 9.025E+11 32220793456.68 -5.4355
209489 9.216E+11 34766377806 9.216E+11 32877727413.71 -5.4324
211671 9.409E+11 35466674593 9.409E+11 33541061856.05 -5.4294
213854 9.60404E+11 36173704275 9.604E+11 34210929252.54 -5.4260
216037 9.80112E+11 36887443015 9.801E+11 34887304916.82 -5.4223
218218 1E+12 37607912018 1E+12 35569405754.01 -5.4204

这时，已经接近下限值的极限了。

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