在线时间 12 小时 最后登录 2021-8-30 注册时间 2018-6-5 听众数 2 收听数 0 能力 0 分 体力 12 点 威望 0 点 阅读权限 20 积分 11 相册 0 日志 0 记录 0 帖子 15 主题 4 精华 0 分享 0 好友 0
升级 6.32%
该用户从未签到
第n个素数不好求,一般用黎曼猜想公式反算,可以获得比较高的精度作为参考范围.6 T$ ]& V1 K* m; \5 B' X
这里不进行第n个素数的计算比赛,只对一个趋势做出预测,求出第n个素数的极限系数k值.6 a2 \6 l. M9 Q1 Z5 x" T
p(n)≈n×(lnn+lnlnn-k),这里n值和p(n)值都是已知的数据,只有k值未知,代人后+ u+ B6 [0 i, h! r
k=lnn+lnlnn-p(n)/n6 R& q; h8 j9 O% D* `
n值 p(n)参考范围 计算的k值
$ d2 M- ]) e! g7 }$ _9 A- L( [& H 4 10 -0.787071379
. d# M. F6 j: f% C4 n 10 29 0.2366175381 r: M; } |/ l; j
24 90 0.584322837- ^* K. q5 K6 v2 w* O# D, [1 d& v' o8 C5 M
25 100 0.387908001
3 F) o7 t+ H. |% s 100 541 0.7223498123 U. N! G4 @6 u9 _' W0 P9 r
154 900 0.809598015% l6 j9 x$ p. h6 a9 F1 L, k; I2 o
168 1000 0.805511381: s/ j/ m: w- f
500 3571 0.899510764
0 T" S: {) H- M$ L a4 C 1000 7919 0.921400013& F$ q7 r; m0 Y
1117 9000 0.909640998
0 v" V. w" j8 R5 K 1229 10000 0.939318112
5 ^8 |; A0 F6 Z0 ^/ y9 I 5000 48611 0.93708004; m, { b3 [+ r+ {$ |1 G+ o c, U
8713 90000 0.948434316
$ b# o8 d2 y2 A- @% l/ | 9592 100000 0.959124075& Q* U" S8 x! ?1 l, B% ]
9592 100000 0.959124075
9 ?; Y8 d( T; B! B" q 10000 104729 0.957767178: G- \4 I k/ v0 H
30000 350377 0.962732035
( o: I3 s- Z# x- G* q 50000 611953 0.9620940668 t, M( g- `' q. G
70000 882377 0.962864732/ J- W6 w# o. U% j: _
71274 900000 0.9605766765 Z; M# o3 R0 ]$ o0 F/ K! |5 g
78498 999983 0.9540847560 q1 c4 l7 ?6 h {
90000 1159523 0.958252788/ Y% F# ^ @1 v
100000 1299709 0.959305823! G0 E! U5 [! H- }
200000 2750159 0.957211231: ?* Q0 L' c. G9 T+ W3 D' e
300000 4256233 0.95870651' B' x; `. v( w' U& [: J
400000 5800079 0.956189157& Z4 }$ u- F W! {! _
500000 7368787 0.95910728
0 |7 K% \# H# q2 b 600000 8960453 0.958712825
/ t+ Z, t1 V" s5 c 602489 9000000 0.959219949; l% D0 [6 H9 I( F$ b6 C2 Y8 [/ q
664579 10000000 0.955559154
$ W' E/ y7 _; P: k7 D2 {; m 700000 10570841 0.957269999$ f2 W8 A k0 p9 y% G; t, j+ b* _
800000 12195257 0.957804142
3 ^2 d3 M9 b6 \ 900000 13834103 0.957060924
+ p* x, ^2 e5 d6 p. l4 U0 x2 t3 v 1000000 15485863 0.955439472
4 d- y- h0 v3 d; i. S6 A6 i 4310144 73473859 0.9560668568 U. v) ]$ i* L7 w6 O- C& P
5216954 90000000 0.954714458: t% j# [: f: E$ }9 I
5761455 100000000 0.955107932
0 b S+ J( p5 K/ x: I' M 10000000 179424673 0.955570945: y0 U: m8 p0 e$ E3 k
28944316 551987369 0.954016283/ A) k& G0 F6 d8 L
31255985 598608349 0.9541818832 [. U7 H4 Q( ^. o, _! _
46009215 900000000 0.9534692559 n4 x2 `; M7 u+ }1 M! `+ ?
50847534 1000000000 0.953771771
( O/ A) `, j9 B8 ~9 z, H4 f 62106578 1234567890 0.953423793
$ W' q0 D6 [6 h, [* `2 _ 100000000 2038074743 0.953407301
' Q9 _$ u- ]3 m& S 111111111 2276855641 0.953517847
# q) J9 y Z2 k9 S 123456789 2543568463 0.953345453. _% ~" |/ j3 X9 {) F; N
399487944 8724310144 0.952931638 L6 d4 w: ~5 ~% M, o) M* U
411523195 9000000000 0.9528727789 i% h, S; N5 g4 Z) h& h6 ^) g
449689285 9876543210 0.952957054% x. ^4 l- {& V# Z% J. o$ q/ F
455052511 10000000000 0.9529608655 c. l: ~0 @* f, X+ j! @3 r
498388617 11000000000 0.952836503
T- f5 F+ T9 H 541555851 12000000000 0.952792438
% `- R$ e3 W& h! b 551987369 12242181113 0.952827232
1 _, c) E; _ h5 t' o0 Z! e% j8 Q 675522133 15125167433 0.95280727
% }, k# I K( u# k& ^ 1000000000 22801763489 0.952759371
' `1 X- F! z3 c, u( x 1111111111 25458070277 0.952691408% F Q& Q# R* w: w
1234567890 28423087477 0.9526597977 U: m- a: @ p) O
2031255985 47824232591 0.952633346
0 U: D* K' {& k1 s4 v 3722428991 90000000000 0.952632842' m, D% _4 M7 \; s7 }
4118054813 100000000000 0.952661953& n [# H a! `4 w0 q4 u \& {/ D
4512105232 110000000000 0.952609693
) \. D- }, _0 L" r' u 4904759399 120000000000 0.952630576- X% e) L2 p7 h
8724310144 218695452037 0.9526889362 L, Y) I- [% o! v; k
9000000000 225898512559 0.952686974, O( ]4 I% w e: _0 M4 M
9876543210 248857367251 0.952697866$ M; G! @4 {, E$ |* v& V
10000000000 252097800623 0.952688406
7 u4 H( S( R: j9 i2 o5 Y. R 11111111111 281329920307 0.952701468! e' r- f- D3 W+ s
12345678910 313945524931 0.952711638
+ O2 z+ I* I8 \7 Z& x5 ^ 15125167433 387829275881 0.9527327474 K5 V, z9 @- Y" Z( q3 i
24188924259 632071564697 0.952803332
( u& d# w, K: T" ^, a: h 33981987586 900000000000 0.9528566279 q* N8 a* L7 u: x" ? {; V
37607912018 1000000000000 0.952882443
- I( v& w8 ?+ O 41220703418 1100000000000 0.952898557
' O. D' W2 r3 r! T4 z* |8 w 44821651132 1200000000000 0.952913749/ e$ `, p4 ?, Z# t" \7 b- p) R
48411812843 1300000000000 0.952928255
5 t; I4 o8 [0 Y, X- W0 y' ` 51992079337 1400000000000 0.952943276
9 [# u' ~: q& l6 b 55563209929 1500000000000 0.952959823
& A1 H; w- g: R8 w9 h/ k" k, n 59125832286 1600000000000 0.95296585# q. ^2 c# r" t, S5 f4 [
62680547806 1700000000000 0.952978131; X; R* K0 R! B% H
66227858344 1800000000000 0.952997051) n& y% ~2 N7 x* f! n' X; i
69768165361 1900000000000 0.953005511: T0 ]% K7 X) T3 ?" h+ }
73301896139 2000000000000 0.953018171, p- E8 q0 u1 \* q& o \
76829404177 2100000000000 0.953034877
. D# l" d( a% y' F2 n 80350940550 2200000000000 0.953031576
4 B6 H6 F( x$ f9 z/ {" g- y 83866890515 2300000000000 0.953043799
/ ^8 ~$ W) S: ~1 x' F. y 87377470252 2400000000000 0.95305485
) Q( z. m- A9 g) E. {5 v: U 90000000000 2474799787573 0.95305936
5 l7 f: r2 C+ E) x I" a! A9 L* }+ Q 90882915772 2500000000000 0.953063852
9 n, b) d1 L, ^, q! J {1 H 94383447111 2600000000000 0.95307122- u1 {! C1 D* g. O' b
97879280182 2700000000000 0.953081213, F# X/ m9 C4 s$ Y8 E+ b, H
98765432109 2725369633577 0.953083106 L8 u. ^$ i' e, A5 [( } v
100000000000 2760727302517 0.953090716; O& i) ] D- g
101370585277 2800000000000 0.953089006
- \9 B/ }" [3 ]9 u 104857545428 2900000000000 0.9530976529 _6 q: k2 K5 x0 V; G" O3 g
108340298703 3000000000000 0.953101171( S: [- S. v+ v4 X
111819048275 3100000000000 0.953113895
% e( o9 Y" g4 P9 ]- J 115293888086 3200000000000 0.953123695& @" k' V' g% |7 {1 s
118764942011 3300000000000 0.9531292670 q6 D7 W1 s- |/ o6 ]+ v
122232349643 3400000000000 0.953135088- x8 b+ s; S c( M
125696244675 3500000000000 0.95314551
) w2 b+ \: a3 d 129156678096 3600000000000 0.95314744
! C* j! R3 ~" N) r* z% x 132613795649 3700000000000 0.953151137
3 g) n2 H3 a0 }. ]( \% O/ g5 H 136067688083 3800000000000 0.953155352; I) W' e# l" U* V: L
139518461664 3900000000000 0.953163273- t# y3 l) L7 [1 G: s h9 K+ D: N
142966208126 4000000000000 0.953175813
, k; m6 K# e) i+ E3 i6 j1 H 146410910264 4100000000000 0.9531730826 T# j) L# ^( s+ c
149852773964 4200000000000 0.953181021( i' P& H) K2 |# _+ G7 W! \
153291810623 4300000000000 0.953187137
' g) E: l9 M5 a5 `% ? 156728136258 4400000000000 0.95320009
8 F7 s; r# R& O# q 160161747327 4500000000000 0.953206672
: }$ v% m( ~* j9 D0 | 163592692077 4600000000000 0.953204523, l5 s- ]/ I2 q, y
167021151370 4700000000000 0.953215136# e9 N' V+ \0 X( a* j
170447066694 4800000000000 0.953217788
/ ~% `# W7 w* V, O6 a d! ~ 173870573446 4900000000000 0.953226341- ?( }( ^+ h* G- @
177291661649 5000000000000 0.953230035
. z9 m$ d( N: u/ `; C" M' x) Q% ?! [7 { 180710431905 5100000000000 0.953237157- Y- l5 D2 l' q6 w6 k0 F- @9 i# ~
184126901158 5200000000000 0.953242428+ H) K% g& z q6 P7 f- y0 ]- h
187541119457 5300000000000 0.9532464157 t K t# X X+ ~5 U
190953126302 5400000000000 0.953248309% k! @8 M7 Q5 W
194362990637 5500000000000 0.9532520612 u8 H# Y. _) j, Y; w1 p4 q5 W4 L
197770743547 5600000000000 0.953255983( S$ V6 v5 M2 I+ G7 a
201176428961 5700000000000 0.953260598
# i8 h3 M7 ~% F/ l' r, B; \ 204580066580 5800000000000 0.953263125
# o( L1 n+ W3 @1 Q8 U# U9 a 207981734215 5900000000000 0.95326937: U7 j, P. i$ o0 X0 q3 o; r
211381427039 6000000000000 0.95327346
. d9 o* y% d) M: ]3 }! ? 214779167476 6100000000000 0.953273786& R0 b8 k q9 e @, }3 M5 j
218175058254 6200000000000 0.953279837
5 K# ^& M& o1 g. u! ~1 u$ R 221569102517 6300000000000 0.953287444
) ]" B' G- `2 P6 |5 x 224961273873 6400000000000 0.953288951
, v# l3 ?; z/ j( A+ S- l 228351698532 6500000000000 0.9532969886 \0 B+ o# p' P) `% W
231740339225 6600000000000 0.953302771
4 G4 ?- ]9 ]; w 235127223891 6700000000000 0.953306312: Y1 l3 C' X* L1 p
238512407609 6800000000000 0.953311095+ r9 v7 y2 W" g# W+ _" H4 L
241895851648 6900000000000 0.953309053
8 J: I0 ]2 k; Q7 A! B8 `0 F- H p5 X 245277688804 7000000000000 0.953313329
5 H- Q6 ^7 ~/ l8 o6 h 248657916582 7100000000000 0.953320369
`( s$ t! Y3 A0 _+ r 252036515078 7200000000000 0.953324842" X. g- t- P/ j, t; Q
255413505374 7300000000000 0.953326527" d5 \" ]1 e7 c4 n- F' g
258788925595 7400000000000 0.9533272427 I; s; o! `- c2 B7 Z
259656817434 7425719040829 0.9533292381 c4 |, A7 N9 K, C+ Y( B+ d
262162841215 7500000000000 0.953331879/ G3 u8 J" |/ C7 _
265535241952 7600000000000 0.9533367
% ~3 g+ [, }; `% P 268906152117 7700000000000 0.953342033 o/ [3 }6 v2 F
272275559525 7800000000000 0.953344261- o8 ^' c6 m) h1 C6 ~; x5 u
275643544693 7900000000000 0.953350004
D$ ~6 j9 L; t- o 279010070811 8000000000000 0.953353124
2 V+ v2 s+ _- J ~/ Q1 Z 282375171661 8100000000000 0.953355251
. A: n" u2 D, t! W" p4 V2 J 285738881494 8200000000000 0.953358042
& D/ X* i* P/ z. }9 ?2 P$ n 289101209285 8300000000000 0.953360526
+ a: N7 \2 V: M 292462199848 8400000000000 0.953365471
- U) j- G) v: W7 u: ^6 ?. _ 295821814466 8500000000000 0.953367157
& z5 w7 ]$ B; S6 H; n 299180106058 8600000000000 0.953369279
! [2 r/ l3 I6 X; h 302537108851 8700000000000 0.953373572
( x! A7 k8 j1 U6 ~7 @7 H* G 305892791866 8800000000000 0.953375383 g5 U! `+ @; F0 n
309247216816 8900000000000 0.95337922
& c, J+ o5 f$ R% M& ~* u- V 312600354108 9000000000000 0.95338074& ?# N5 h5 A, L3 ] l! V, j
315952260435 9100000000000 0.953383952( h) v" a1 @- e8 F; n- p6 x( z
319302948414 9200000000000 0.953388614' [8 L- [% O `1 l/ A) X
322652410741 9300000000000 0.953392682
3 @9 ~1 D7 _9 s) k 326000647688 9400000000000 0.953394916
8 A- S# j6 G: m% I' D# }; P 329347709593 9500000000000 0.9533986970 o8 M2 m ]" {# w; w6 E
332693561966 9600000000000 0.953399676
* r$ }& S, [. t$ ]1 G* L2 b W 336038264769 9700000000000 0.953402105
1 ~$ O! r9 r2 s7 a& ]9 t 339381817251 9800000000000 0.953404747
" E5 u: v Q+ n0 s 342724224549 9900000000000 0.953406947: E) {) _3 d5 J* \- u* O: Q$ }9 T' f
346065536839 10000000000000 0.953411996
8 }- U' v2 p9 \ 379418886337 11000000000000 0.9534386214 g$ `; f8 Q( g) d' y3 [& N9 ^3 k3 ^
511905471132 15000000000000 0.9535272630 w0 B4 h* {+ j) t
643217611048 19000000000000 0.953596753. E0 p' Y; v2 p% J( {& Z$ @6 I
675895909271 20000000000000 0.953610735
5 S/ o: x: b2 _, O 773621469799 23000000000000 0.953652834
' w; a/ w# T3 J# `2 w1 E1 r 886674661126 26486412297029 0.953696348' z2 p2 x) s4 o8 A! @* I1 x
887114276903 26500000000000 0.953696396
0 P! l8 l- F7 ?) a2 ^ 900000000000 26898370231697 0.953701247
: a1 K. p- ]0 ?$ P7 }" K 932911185326 27916701633581 0.953711916: k1 i% L) \1 V# D
967879555617 29000000000000 0.953724541
; j9 @' o3 k) Q0 H; U" B' V8 B 1000000000000 29996224275833 0.953735935. i7 F2 z; {. q# Q5 X+ K) _# G5 c
1000121668853 30000000000000 0.953735897
1 b" `! C5 c6 ^% W. T3 Z+ P1 n/ R 3204941750802 100000000000000 0.954126498
0 x' s; `1 ~+ n 10000000000000 323780508946331 0.954537117
% O+ X! A& k* Z. r& C 29844570422669 1000000000000000 0.954950335
. Y9 z5 a5 W# G5 z 100000000000000 3475385758524527 0.955423492! g5 K+ ^) f! w' h9 y2 C- ?
279238341033925 10000000000000000 0.955833997
Z1 I0 _8 ?4 v4 B3 N, A" D+ ~ 547863431950008 20000000000000000 0.956106462* J* [7 y9 R" z2 i! t
1000000000000000 37124508045065437 0.956350996
2 Q- u' A) I2 ?' c2 t% g( z7 p 1075292778753150 40000000000000000 0.956380556 _) K- u% o, M. E* [
2623557157654233 100000000000000000 0.956744527
j4 s( G: {3 F$ O2 U, G 3893882469583623 150000000000000000 0.956905884
: W& l- Q6 M; V# s 10000000000000000 394906913903735329 0.9572912654 O$ G1 @7 e: K
24739954287740860 1000000000000000000 0.957660554' B0 T- y: f: M; S! e
48645161281738535 2000000000000000000 0.95793517+ v: O& d1 f8 U |
72254704797687083 3000000000000000000 0.95809533
& f* A$ @0 L- B7 i5 B, Q 95676260903887607 4000000000000000000 0.9582087168 m0 u: N4 k! K; ^
100000000000000000 4185296581467695669 0.958226556
3 W+ m3 B) z a" ^( x1 p+ r, i 118959989688273472 5000000000000000000 0.958296529
+ Q' ?! O) ]4 d9 r" q! [5 O1 u 142135049412622144 6000000000000000000 0.958368158
8 p" X* L, W9 T6 |- i4 R0 e 165220513980969424 7000000000000000000 0.9584286468 ?% @" N4 Y! C- l
188229829247429504 8000000000000000000 0.958480986
, ?, z$ i$ g" j- O 211172979243258278 9000000000000000000 0.9585271
: d( W$ `; T! ~& X" v8 B' o5 ]' @! | 234057667276344607 10000000000000000000 0.958568315
7 R( M/ U: Q$ ` L5 y* A1 J 460637655126005490 20000000000000000000 0.958838542& H* D/ R- \0 O0 V7 C
684559920583084690 30000000000000000000 0.958995813: x8 @- U; C" ^4 {! M' Z+ I
706849401776940275 31000000000000000000 0.959008504# j1 D4 }2 a, v$ O) u# o3 C& C
906790515105576571 40000000000000000000 0.9591070225 }) Q" S; R( T$ z- @7 ~
1000000000000000000 44211790234832169331 0.959145642( q) R( P/ c4 U) r* ?# f) t
1127779923790184543 50000000000000000000 0.959193055) E, K+ s A1 i. t; n Y5 z
2220819602560918840 100000000000000000000 0.959458995" U* w, M+ t* r7 z4 d
3516585752930430595 160000000000000000000 0.9596381550 i' e) [* D# O; J! a0 V/ P
3731397829842461168 170000000000000000000 0.959661194
; {" G6 t: v0 l 3945938652811699917 180000000000000000000 0.9596829
4 v0 m5 ?& q3 s# v 4374267703076959271 200000000000000000000 0.959722871
1 `1 X7 R) t& q @- K$ E4 h 4588082544160859769 210000000000000000000 0.959741366
4 w3 Z! M+ e" c( @( \ 5654086442526321042 260000000000000000000 0.9598221912 S& m0 @5 ]: E n$ t# j
5866733862193360875 270000000000000000000 0.959836454
( p4 [( B5 f& M# N* G! R 6503696293016202398 300000000000000000000 0.95987623
8 E3 U ?1 Y0 o3 O4 v1 `( @ 6715709842660010419 310000000000000000000 0.9598886
% P2 p7 {! X/ G0 f' ?' U5 Q 6927578466326617308 320000000000000000000 0.959900571
& D- I; L- k) V! h! C- g, Q 8617821096373621600 400000000000000000000 0.959984581
6 {) l& A2 B6 ` m) H7 O3 | 10000000000000000000 465675465116607065549 0.96004168
4 Y, x2 _( s) G: G 10720710117789005897 500000000000000000000 0.960068355
0 D: N- X$ c1 f; f$ |2 f 12814731195053369962 600000000000000000000 0.960136628% P$ g; L3 N* ]0 l& u6 M
21127269486018731928 1000000000000000000000 0.960327059
$ N* W+ g2 ?) z 41644391885053857293 2000000000000000000000 0.960583407' U6 `& j) x/ z0 f! q7 [
82103246362658124007 4000000000000000000000 0.96083734
; l; m9 B' |5 u2 s1 C 100000000000000000000 4892055594575155744537 0.960910633
1 v) \/ ] v8 n2 C* P3 L 201467286689315906290 10000000000000000000000 0.961169232
3 q; {& e9 E1 e( E# ]' j 299751248358699805270 15000000000000000000000 0.9613146990 }5 b) ?9 T1 B" y) K: D% c
397382840070993192736 20000000000000000000000 0.9614173856 F' p; z) s* ?$ q) n
783964159847056303858 40000000000000000000000 0.961662996
# o3 k6 [" H! G$ j$ a* G/ F! O 1925320391606803968923 100000000000000000000000 0.96198374; o$ s% j9 n0 G& s+ O( M `: E, V" Y
18435599767349200867866 1000000000000000000000000 0.962769828
w2 \/ F5 n4 h2 y 176846309399143769411680 10000000000000000000000000 0.96352742281009973617214866335650
- P) a% A' x' J) ?; f* B 1699246750872437141327603 100000000000000000000000000 0.964256911769038367410632552188609 i. [: O# C2 _0 z/ `" S
从0.2一直上升,虽然区间有所反复,但总体趋势明显,就是趋向于1,即k值为1! m) L8 K" R, m
所以无穷大时p(n)≈n×(lnn+lnlnn-1)成立1 T" E. u# b3 ?3 a
如果一直大下去,比1大,比2大,直至大到lnlnn,这时后两项一减为0,变成了p(n)≈n×lnn这可能吗?
+ S5 _: L' L) b4 E8 r9 T 我坚持无穷大时p(n)≈n×(lnn+lnlnn-1)
# \' [6 a, N& G
zan