- 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." Q: t6 v: I8 B1 O2 s( o* j) `
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.
5 v! L, _( @4 }+ Zp(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/ }% Z$ i+ R. v& |& H, E+ F
k=lnn+lnlnn-p(n)/n
/ X5 X$ t$ N) F* I. G! N+ K7 O! Hn值 p(n)参考范围 计算的k值, m. b, z/ |# i* C, y# M/ T
4 10 -0.7870713795 u8 ~5 L) w$ }( M3 P
10 29 0.2366175381 N8 K6 |; `4 ?- w* K: H
24 90 0.584322837 O9 c1 n0 O0 F* ?: ^9 }' m) J
25 100 0.3879080017 ?% G# z0 Z O {
100 541 0.7223498124 n7 i, U' R1 i/ @! `/ C. p! A4 d
154 900 0.809598015
e8 Y5 S9 g- H, g1 C* U! z, Q168 1000 0.8055113814 n+ ^; L3 d+ _4 f2 W+ h/ B/ t
500 3571 0.899510764
3 o/ r$ t5 A1 M( D* K* M+ f0 t; ^1000 7919 0.9214000134 T- k$ y; b+ a
1117 9000 0.9096409980 f6 d; @) h. x6 p( t6 u6 i) S
1229 10000 0.939318112- d& A/ i% }. @" {( [3 @
5000 48611 0.937080044 g5 X3 h6 {2 A3 h; M0 g
8713 90000 0.948434316" k0 \3 b1 V" H3 [) T' D; O
9592 100000 0.959124075% n# W: }8 k1 H6 L3 E0 a
9592 100000 0.9591240754 w, s% Y p! c: H: m& f
10000 104729 0.957767178/ w2 K' v8 m9 S( N
30000 350377 0.9627320355 w6 p/ b2 Y' v# D
50000 611953 0.962094066
$ J4 j0 f4 K0 e70000 882377 0.962864732, o" x! s/ i: e1 @4 g& M
71274 900000 0.960576676: z/ m% Y$ {4 i) ~+ N# v
78498 999983 0.954084756
2 H. j! y0 z4 A. L6 t1 B# r9 |90000 1159523 0.958252788& G. x! Q& S* Y* b q& [9 c
100000 1299709 0.959305823
1 _3 G( v1 c" w- t6 k' M5 {4 k200000 2750159 0.957211231
" c7 L' a4 u }1 i O' i300000 4256233 0.95870651
' X' a# L3 D6 r! j7 a6 D. m400000 5800079 0.956189157# g# i( W, f0 h: {7 R( d7 r
500000 7368787 0.95910728
3 {2 g# O1 c, ?* C- n3 z0 Q600000 8960453 0.958712825
4 [7 j, D1 K3 @4 k& J9 Y, Q0 b602489 9000000 0.9592199493 e* ~: J# b* S n& L; i
664579 10000000 0.955559154
' C# }. D% f$ y8 L/ G4 k700000 10570841 0.957269999
8 u0 E1 @ E/ }% y: e) J3 T800000 12195257 0.9578041425 u+ ?. i2 e; ~2 h& Y
900000 13834103 0.957060924
) g4 [/ j3 {4 Q A5 U1000000 15485863 0.9554394729 {0 l" P' o$ ~2 i
4310144 73473859 0.956066856
D5 e9 a1 }1 X3 G5 ?8 g- Z5216954 90000000 0.954714458
& ]. @# S, J# c( R+ M5 M" x% H5761455 100000000 0.955107932
- q$ I. E t% l Q; i10000000 179424673 0.955570945$ T: T7 i& G" B( G/ @
28944316 551987369 0.954016283
. B9 F3 B, g8 a" n: |31255985 598608349 0.954181883
- l. V0 J+ ~# D( `, c2 p46009215 900000000 0.953469255
6 r# Q( S4 k0 L6 w7 Z. c+ M; i8 u50847534 1000000000 0.953771771
, d4 `. N- r* b% J62106578 1234567890 0.953423793" k8 l1 e: T4 h; P! M
100000000 2038074743 0.953407301
' ?9 }" p& n* Q111111111 2276855641 0.953517847
Z8 w$ ]7 k7 ~- q9 M9 j123456789 2543568463 0.953345453
, B4 e9 d9 T% Y# D6 b( s; D6 d399487944 8724310144 0.95293163/ R4 X3 q; A- Y2 f" b
411523195 9000000000 0.952872778
+ h+ Z1 j6 J+ g6 c449689285 9876543210 0.952957054
7 Y; ]8 D, ~+ U g! w455052511 10000000000 0.9529608657 X( N% }" ? F% n! Z/ {% e( Q
498388617 11000000000 0.952836503% n$ ]% D, d: h& q
541555851 12000000000 0.952792438
+ x8 N) Q+ r+ N! y8 k; l$ T551987369 12242181113 0.952827232
$ a) C3 E" m! A( Y: J675522133 15125167433 0.952807270 k( ?. y X w9 P5 k' n
1000000000 22801763489 0.9527593713 P7 Z5 R3 t1 A q' M
1111111111 25458070277 0.952691408
" M/ m2 E9 q% ]( k7 s1234567890 28423087477 0.9526597974 |* n( X# `" e! @5 l
2031255985 47824232591 0.952633346 w: u6 @0 @3 ]' a! m
3722428991 90000000000 0.952632842% d3 y0 G& d9 q8 Q* X2 `* W# v
4118054813 100000000000 0.952661953
4 `& h* q7 i, a4512105232 110000000000 0.952609693
: |5 @1 q% K* Y5 H1 B4904759399 120000000000 0.952630576/ p3 a* U+ T( c! c4 |" R- r6 M
8724310144 218695452037 0.952688936
e6 D; ]: X0 C+ ] q* E# M( f9000000000 225898512559 0.952686974
2 W \, P" {% i) z- m' q4 `2 r9 H9876543210 248857367251 0.952697866' e) x& R+ x) L
10000000000 252097800623 0.9526884061 G! B! F# W1 @& T e
11111111111 281329920307 0.952701468, H x7 }& W: R0 L( L8 V
12345678910 313945524931 0.952711638
7 d; z' I1 a8 A3 o8 e15125167433 387829275881 0.952732747
; ?; b8 t# W7 V5 D ?4 e( s8 v24188924259 632071564697 0.9528033328 W0 i8 q3 }* t8 O! x' }
33981987586 900000000000 0.952856627
- n3 a% ^/ F- V" k37607912018 1000000000000 0.952882443
8 e: ~& v9 y& ^41220703418 1100000000000 0.952898557) y( n+ |* r7 Y9 Z$ F& y* ?
44821651132 1200000000000 0.952913749" ?+ W$ R4 X1 J: T* @2 T
48411812843 1300000000000 0.952928255
/ p- a2 i0 d7 q$ \4 u( S! W51992079337 1400000000000 0.9529432764 B2 b* M$ d, Z' ~6 h6 U
55563209929 1500000000000 0.952959823
2 c! \' K6 a( j5 E4 h$ P59125832286 1600000000000 0.95296585) W% h) k& l6 ]
62680547806 1700000000000 0.9529781315 i; q# l3 p0 W7 s/ n8 o
66227858344 1800000000000 0.9529970518 j. g5 M! z/ g q. G* i7 Z
69768165361 1900000000000 0.953005511
. I0 G1 ~* ^ I! [73301896139 2000000000000 0.953018171
. D. n8 N9 W) D \/ D5 ]76829404177 2100000000000 0.953034877
: `; O+ ~% c0 z4 n! [80350940550 2200000000000 0.9530315761 b$ e. Z* d& @3 S9 J9 Y
83866890515 2300000000000 0.9530437997 D, p/ x5 ~' B3 F7 h' v0 P
87377470252 2400000000000 0.95305485
- P+ e' V3 I' t" Y8 m8 [# |" \90000000000 2474799787573 0.95305936, D2 A) ?# C% `* f
90882915772 2500000000000 0.953063852
# M6 B# z' \5 m/ e/ _1 x1 z1 C: s94383447111 2600000000000 0.95307122# D2 [" B i% L
97879280182 2700000000000 0.953081213
. E2 S4 S6 R* W2 F. r. f3 {, v98765432109 2725369633577 0.953083106" g, L) s- [& _" ], L* l2 i" b! j8 u
100000000000 2760727302517 0.953090716
$ W" E+ b% r7 w( W. @% B101370585277 2800000000000 0.953089006" O8 F8 v8 W; O' [! M4 `
104857545428 2900000000000 0.953097652, `' `# A- F( W% v) s0 a' S
108340298703 3000000000000 0.953101171
- _0 K7 g* x* O5 G111819048275 3100000000000 0.953113895
6 l% q+ r* ^8 ]" @2 y115293888086 3200000000000 0.953123695' m( t7 C4 n! ]
118764942011 3300000000000 0.9531292675 q% `8 w2 C- c/ S4 r" O( K
122232349643 3400000000000 0.953135088) E/ c, h* S/ |+ ^4 v. V
125696244675 3500000000000 0.95314551
/ T9 i# T0 Y; i9 l129156678096 3600000000000 0.953147447 X/ I4 n# x, f. K+ _& ?8 u9 P
132613795649 3700000000000 0.953151137
3 ~6 ]0 k/ J2 Q) o136067688083 3800000000000 0.953155352
2 D$ O/ p. ~8 _% N7 i. O$ g0 i! p A139518461664 3900000000000 0.953163273
/ \3 |) [+ Q& I- \9 k142966208126 4000000000000 0.953175813
: c- M' z8 j' K6 y2 X" D% v146410910264 4100000000000 0.953173082
. y5 r; D# |* i% S% w" c! t149852773964 4200000000000 0.9531810211 G' T5 b0 u" j$ X( ]+ X( ]0 ]/ R
153291810623 4300000000000 0.953187137
# v) q3 R% y" h2 R156728136258 4400000000000 0.95320009
' ?7 N/ \7 e7 ] N( `& n' o160161747327 4500000000000 0.9532066726 H1 S9 h9 O+ u" J K* {8 j
163592692077 4600000000000 0.953204523
( O) N' V r* f: y. b* ?& Q. B167021151370 4700000000000 0.953215136
5 `: b! u$ ?, [' J* C9 F3 p170447066694 4800000000000 0.953217788
0 ^5 j- c8 G' g, b, z; r173870573446 4900000000000 0.953226341
- h5 d" D# V# D) f; F) ?) p# d( q* D) k& w177291661649 5000000000000 0.953230035
6 H! N- w! f0 f G k' [% D180710431905 5100000000000 0.953237157
% ^, o* S: Y1 v) o9 x# U184126901158 5200000000000 0.953242428) r- A7 n; J' w* q
187541119457 5300000000000 0.953246415
0 }& \- C+ ^, C190953126302 5400000000000 0.953248309! N! p% _ J( X# o
194362990637 5500000000000 0.953252061
- C" u$ C9 t% q. V) P* ]5 V% |4 S197770743547 5600000000000 0.953255983
0 E& ^4 G4 ?9 E5 K% U9 U201176428961 5700000000000 0.953260598
( j+ W7 M2 P% \0 U5 \- n204580066580 5800000000000 0.953263125
& i, X; S( l7 g' Y. r' X# l207981734215 5900000000000 0.95326937
: ~& X- a1 A: s1 P211381427039 6000000000000 0.95327346# d5 x c" ]4 [3 v4 A( l
214779167476 6100000000000 0.953273786
/ D2 ]: h0 r" K8 F218175058254 6200000000000 0.953279837
L7 ~+ ^6 k, N. R N221569102517 6300000000000 0.953287444
9 `8 B+ Z2 ^$ H224961273873 6400000000000 0.953288951! p/ @9 O" @ q! d' O
228351698532 6500000000000 0.953296988
! A7 A/ T5 K6 W6 U8 h* i" n231740339225 6600000000000 0.953302771
9 c% u- N* G2 E/ ^* O235127223891 6700000000000 0.953306312
" d! |9 Y( d. }$ V238512407609 6800000000000 0.9533110951 r: G! ?" u# L
241895851648 6900000000000 0.953309053$ A$ e/ ~8 G' v% p8 N/ b
245277688804 7000000000000 0.953313329
/ z& m' d p3 D0 l248657916582 7100000000000 0.953320369; I/ O* H3 }3 w5 h3 \ U
252036515078 7200000000000 0.953324842' k* C6 U8 ^4 w8 U! X
255413505374 7300000000000 0.9533265271 Y" Z5 r1 c6 W. s$ U- A5 I5 {
258788925595 7400000000000 0.953327242
" D! ? y& o+ ^9 @259656817434 7425719040829 0.953329238
! e3 {# Y6 o6 m$ k6 U" M4 `262162841215 7500000000000 0.9533318796 N+ N' z2 N6 ~1 [( h8 I
265535241952 7600000000000 0.9533367! Z# d5 \/ a: k- D8 k' g/ S
268906152117 7700000000000 0.95334203
/ F$ G7 j7 u. w, k" @6 n272275559525 7800000000000 0.953344261& I' _/ K% F+ }3 B
275643544693 7900000000000 0.9533500040 d) }+ ~7 p/ g
279010070811 8000000000000 0.953353124; C3 J3 o: R2 {. t' ?1 K
282375171661 8100000000000 0.9533552514 v$ Y' h4 u1 f8 T! s* g
285738881494 8200000000000 0.953358042. f3 _0 s# |# N8 Q
289101209285 8300000000000 0.953360526
2 J# F! `' s, i% G X292462199848 8400000000000 0.953365471
0 `* }0 ]- m3 L- K. q295821814466 8500000000000 0.953367157
$ l6 z7 q& J& d; f299180106058 8600000000000 0.9533692795 i: {; p/ b2 N( [8 @; r
302537108851 8700000000000 0.953373572) \) \- }/ v( @* A/ Y! H, t
305892791866 8800000000000 0.95337538
" V" |1 a V9 a- S' E& Z309247216816 8900000000000 0.95337922
. h. n3 g! W! ]2 _312600354108 9000000000000 0.95338074
+ [7 C0 {3 s5 s% m& r2 |" |315952260435 9100000000000 0.953383952
0 H' |2 N. v7 U0 v319302948414 9200000000000 0.9533886142 ]/ Q0 ?( C! V5 t, Q$ x( Y' E
322652410741 9300000000000 0.953392682% B; t& e1 q( G1 p5 F/ Y5 Q2 t
326000647688 9400000000000 0.953394916
/ V( H; U# L: T# l- N329347709593 9500000000000 0.9533986977 H6 v& V% `% N( x# t) h; Y
332693561966 9600000000000 0.953399676: S z2 |8 ?( D* S1 Y7 H
336038264769 9700000000000 0.953402105 W2 | j. n2 v8 U* I
339381817251 9800000000000 0.9534047473 X0 X: s2 ]8 p. A
342724224549 9900000000000 0.953406947
# a. D" v" w+ d" @346065536839 10000000000000 0.953411996
! o9 `- K5 E. E2 Z- J379418886337 11000000000000 0.953438621
( j" b& N' D, g+ c. v; ]6 q: @3 X511905471132 15000000000000 0.953527263
. a' f" p$ C3 S6 i# ]6 H643217611048 19000000000000 0.953596753) M1 D# E# j; y. \
675895909271 20000000000000 0.953610735
5 f* h/ S6 t! { S. _- o6 \ `773621469799 23000000000000 0.953652834
( x2 I% X* w. T6 m886674661126 26486412297029 0.953696348
& S: ?& J) w9 N- {% ^( h887114276903 26500000000000 0.953696396% m1 w2 Y1 |8 P) I: R! G6 p6 V8 y
900000000000 26898370231697 0.953701247
6 \2 w3 j7 S' r' e ?932911185326 27916701633581 0.9537119162 g+ ~; ^) @* K, U
967879555617 29000000000000 0.953724541
) E7 `; n0 x* E0 \# L5 V- S1000000000000 29996224275833 0.953735935; c+ k# c9 r+ ~. o/ L. n
1000121668853 30000000000000 0.953735897" i0 ]! w& ^% z
3204941750802 100000000000000 0.9541264985 m$ r1 k# d8 Z, R: J
10000000000000 323780508946331 0.954537117
) _$ A: ?( M& R- @5 |5 O: @6 ^29844570422669 1000000000000000 0.954950335
' o/ a% I1 M: s1 \1 W100000000000000 3475385758524527 0.955423492
* z+ |5 }% }! o* h: h+ K t8 R279238341033925 10000000000000000 0.955833997+ p/ k" J% s4 E2 L# y+ j, [2 t
547863431950008 20000000000000000 0.956106462
o" Q( W# v0 w2 a" p: J- Q1000000000000000 37124508045065437 0.9563509969 p# C2 Z, T- K# L" t) x! y
1075292778753150 40000000000000000 0.95638055& R/ ]6 O/ M9 y% V; d4 r; P9 K
2623557157654233 100000000000000000 0.9567445270 `1 h4 M/ D4 S- o; X# M
3893882469583623 150000000000000000 0.9569058843 I+ H4 d$ I$ P
10000000000000000 394906913903735329 0.957291265
4 B+ U# A( k; B7 [6 G( j' a0 F& |24739954287740860 1000000000000000000 0.957660554% _8 b( x( _& `( i+ ~
48645161281738535 2000000000000000000 0.957935178 Z3 d# K- k+ x9 g9 S3 B( p
72254704797687083 3000000000000000000 0.958095338 e+ G/ \- j. z5 R( v" Y! W
95676260903887607 4000000000000000000 0.958208716
" X8 I; p3 v! @4 W100000000000000000 4185296581467695669 0.958226556
5 o' I* V. Z2 X* R1 G118959989688273472 5000000000000000000 0.9582965292 q- Z! f0 @0 n: q) l* s
142135049412622144 6000000000000000000 0.9583681581 z# e. r( t) ~' g6 b' ]
165220513980969424 7000000000000000000 0.9584286468 n$ L" `3 w+ W. s
188229829247429504 8000000000000000000 0.958480986
}, L# l4 f0 ]/ v# Z% {9 I211172979243258278 9000000000000000000 0.9585271
/ c% t# J7 X& n& }234057667276344607 10000000000000000000 0.9585683155 l( F J! q R( ~% i& J
460637655126005490 20000000000000000000 0.958838542, B* N. k* ^- M; h0 \& }3 l
684559920583084690 30000000000000000000 0.958995813
/ m: c# ~/ ^, C706849401776940275 31000000000000000000 0.959008504
( g9 L$ c6 c: L7 T5 @, W+ _7 D906790515105576571 40000000000000000000 0.959107022
) Y+ N& H; ^' O _! G1000000000000000000 44211790234832169331 0.959145642
8 E1 `9 [4 V# L* `% g1 Z% M1127779923790184543 50000000000000000000 0.959193055
/ U" k% N8 }1 i: N8 G2220819602560918840 100000000000000000000 0.959458995
% W9 o# G& z! D. x, g6 C3516585752930430595 160000000000000000000 0.959638155
/ ^* T. F. r& v8 U9 k8 m$ _ N3731397829842461168 170000000000000000000 0.959661194
9 A( w2 B+ h$ k2 M3945938652811699917 180000000000000000000 0.9596829
* r$ U n. T0 L! c' s! B- t9 G4374267703076959271 200000000000000000000 0.959722871
. g; z: \# V8 w* q R. Z4588082544160859769 210000000000000000000 0.9597413660 S2 n5 c+ A( U5 k: ?( B) o" [
5654086442526321042 260000000000000000000 0.959822191
; w, l7 J$ O0 p6 G, r5866733862193360875 270000000000000000000 0.959836454
) y+ k' M5 R' l9 Q6503696293016202398 300000000000000000000 0.95987623
5 L4 x4 e: C8 M4 f! J9 e5 b6715709842660010419 310000000000000000000 0.9598886
( @* T" a2 y7 ~4 o0 t; ~6927578466326617308 320000000000000000000 0.959900571& f' Y! m# Q( M M7 ?3 J. {& @
8617821096373621600 400000000000000000000 0.959984581
5 D, L9 _" o; _; F' N$ _& H10000000000000000000 465675465116607065549 0.960041680 M' k+ ]: c; j$ A0 K: _" n
10720710117789005897 500000000000000000000 0.960068355; B, b. \5 ]# H' V! I+ [
12814731195053369962 600000000000000000000 0.960136628
0 H7 j/ r) B, d9 }9 Q6 Z21127269486018731928 1000000000000000000000 0.960327059. ]; E' v1 h: c5 F
41644391885053857293 2000000000000000000000 0.960583407
4 v- T2 J2 h7 B x+ t3 T82103246362658124007 4000000000000000000000 0.96083734
% l8 G. r. V$ z$ C100000000000000000000 4892055594575155744537 0.960910633* b, X$ o, I0 D/ z! S9 o
201467286689315906290 10000000000000000000000 0.961169232! K! w- F. }; F! L' M
299751248358699805270 15000000000000000000000 0.961314699
- E) u6 d1 B6 ?& z( h1 \397382840070993192736 20000000000000000000000 0.961417385
( |; T# | h0 g& [783964159847056303858 40000000000000000000000 0.961662996" [7 G, d+ _2 D' H
1925320391606803968923 100000000000000000000000 0.96198374
. W% Y/ t) X- O& N4 i9 R# I7 f& l18435599767349200867866 1000000000000000000000000 0.962769828
+ @+ l5 ]: S' Q; x. p2 y- l. e% \176846309399143769411680 10000000000000000000000000 0.96352742281009973617214866335650
% @6 Q: k1 n% j" V1 ^1699246750872437141327603 100000000000000000000000000 0.964256911769038367410632552188605 f# N3 Z5 y A: z' W3 R9 V6 i* E
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
0 J* ~5 ?; N0 O$ m所以无穷大时p(n)≈n×(lnn+lnlnn-1)成立
+ S4 k3 y3 j8 Z. A/ @1 S" I5 r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?& z4 \ n$ `% F2 Z6 s: {
我坚持无穷大时p(n)≈n×(lnn+lnlnn-1) }; }6 q+ w9 v& D4 _# m( s
|
zan
|
IP卡
狗仔卡
发表于 2018-6-5 22:02
转播
淘帖
分享
收藏
支持
反对
微信
提升卡
置顶卡
沉默卡
喧嚣卡
变色卡
抢沙发
显身卡
