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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. m3 Q" z4 r- F9 m$ |) s 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.% I v+ F1 U9 t& B l ' t. W! y4 P0 Q9 i k=lnn+lnlnn-p(n)/n0 ^, r# y* H1 Z' u7 _, A " l+ |" y4 k( N- e 3 Q. z& g3 r4 f1 ?$ B9 m6 }! W7 \- [/ s 10 29 0.236617538% Z* ?; o1 f$ y6 F) Q/ P. x 7 P7 b. o/ z! w4 T& n 5 |0 \( d: E0 ^1 j2 m8 ] * r: o6 h: N' o 154 900 0.8095980155 Q) C# r5 f, P5 g% H6 Z) R+ U" n6 n . y* X" `: i6 |* W; k/ L : t5 `; T! _: k& |7 T9 N 2 e c7 [, H# o' B/ X; @ 1117 9000 0.9096409980 y" a- N3 J4 ^0 v$ G$ }- } 1229 10000 0.939318112; Q6 b) Z: K0 _- {3 [ ; v$ g! {1 s5 l5 ?" Z 8713 90000 0.948434316) x4 `! m/ t7 s. M t4 r. X , J& u1 g( U8 T8 c 9592 100000 0.959124075( G# _, B8 G F; v. L: \ 10000 104729 0.957767178# a# X1 _$ R& s/ y1 y1 c6 }' N, K0 J " O/ K$ |: h4 j# d * u& W, s1 ]! L - { A5 g2 M! w" z8 z3 D " L& B* p/ y. i* Q, \ & h7 ~' Q" c7 f; j , t0 X1 u4 ^- U 100000 1299709 0.959305823% Y l! A( }1 {& {. D 200000 2750159 0.957211231% i! M+ a/ U+ E9 M 300000 4256233 0.95870651" G- G, D, w2 s2 q* A; O1 f 400000 5800079 0.956189157. c; N8 w1 o! Q4 b V5 ~ 3 Y4 h; p3 v1 Z- F! ?& P8 n4 |, p% C 0 T! V W1 {) h0 G! E4 ?1 O8 f k 602489 9000000 0.959219949) ~+ o( Q) I& ^* d9 q" s8 y6 D# c 2 u' ~* L# Q, y' p0 D1 v" X) w# S 700000 10570841 0.9572699992 c; _. n- V5 B2 N 800000 12195257 0.957804142( z- i/ D! I; {5 J% W0 I 900000 13834103 0.9570609247 a3 m0 h: \+ Q; {( P 1000000 15485863 0.9554394721 F* F8 F ?5 ^: f( Q 4310144 73473859 0.9560668567 q# {3 I" F' k! v, E: C' G: y; | 5216954 90000000 0.954714458$ d9 E$ u$ U- ~2 V4 d# a0 f 5761455 100000000 0.955107932- J3 F. A9 ?3 \ X* l! _) r5 ^8 x' q4 [ 0 I0 x- C$ T F 5 w! ?$ K+ ]* d# w9 I0 A 2 L2 V2 U @; K; P9 ]2 f- X 7 z! ] I. f! m; N 50847534 1000000000 0.9537717712 Y. o7 j' s. w, w2 A 62106578 1234567890 0.9534237934 v2 W1 i# N; S4 z9 C 100000000 2038074743 0.9534073012 k l! B2 Z3 V% E1 |& S" T $ Z$ f/ k+ T- P( U- [1 j- N 0 q# Y, r/ R' Z 8 t# }" Z8 Y" W% P% f $ ?% y4 `4 I2 o& F & f9 \% Q0 M, E; c! G( j* Z 455052511 10000000000 0.952960865 C: c# U) d. l" R1 e 498388617 11000000000 0.952836503- L# [! P" v7 ^$ Z, k 541555851 12000000000 0.952792438) G+ O" U. f: V: k% O/ g! U, U0 T 551987369 12242181113 0.952827232+ M7 O# W" s! B4 g) ` 7 g Z b2 p- O" | 1000000000 22801763489 0.952759371& q6 z2 k. N# N3 D( o! P ( A2 Z" ]: X& Z1 P 3 y8 P7 z/ Y- g' s- u, w$ b+ C : @! h, g5 L+ i, E* k5 ?7 c ) \ _4 P" M+ q: i3 E* f 4118054813 100000000000 0.9526619537 ^' I# x `1 y' G 8 ]% A: P; A( x" X v* Z/ E, k! ] 8724310144 218695452037 0.952688936) @/ q( a9 ^ f) h; d0 Y: y - b3 y& O* B9 |, A, W) ^, d 9876543210 248857367251 0.952697866& |3 S4 Y5 Z6 y 10000000000 252097800623 0.952688406+ }% `" j7 o( N) p" H6 d 11111111111 281329920307 0.9527014688 f! g5 o5 M5 V. ] ' S" M7 c4 v Y2 V% q' Y6 b. w8 b9 R 3 ]2 r; l( h) E# I! D6 Y7 K5 n 24188924259 632071564697 0.9528033321 e' n3 C; R+ o$ L: ?0 l 33981987586 900000000000 0.9528566277 n* T6 D$ R4 t 37607912018 1000000000000 0.952882443! S0 B3 p7 d2 i7 _1 |4 Z 41220703418 1100000000000 0.952898557; Y4 M9 a) \+ x3 Q/ ] G' p# I" _% D h5 {8 p* p, S ]1 j% B' A# u, `/ E0 z 51992079337 1400000000000 0.952943276; ^+ h3 y7 r4 g" `+ h 55563209929 1500000000000 0.952959823& p' C5 H, I, [& o( h 59125832286 1600000000000 0.952965859 U/ p8 n# i+ |9 F+ l* z! t ; q) H8 M% G0 k5 \8 t3 r + B# c! X Q8 L9 M! J) o * X& g' w; G( b8 k! L) V! ] % z ?) x" K. j: l 9 b" o5 f$ v- @7 c# @* i; r ! o9 {6 S2 t- m; U K3 D 7 J0 W, ]: H1 y% N5 V: u 87377470252 2400000000000 0.95305485, M# K4 g& G6 K; ~- k$ M; i$ w9 s " [' d1 G3 m, [9 j5 C; Z : o8 n* S1 x( z, I2 {: r 94383447111 2600000000000 0.95307122; G* i+ y- r& P9 _: `% L7 I. k 97879280182 2700000000000 0.9530812138 {3 s6 _6 ]( h: R* h( { " d/ }- ]6 ]. K 6 T6 o$ Q& L6 T/ ~% Q0 U % O- a( ?( s( ] 0 I8 Q3 E( p4 u% o1 Q5 F* C 108340298703 3000000000000 0.953101171, C7 v9 ?0 D+ F 8 t+ ?: C" k! _0 K 115293888086 3200000000000 0.953123695 n H4 K3 t5 x) H% k4 g6 u 118764942011 3300000000000 0.953129267, O# K: `# k; G; ]8 n9 C 3 B2 Q& B+ R, G( {& F" ~3 p1 N $ a( \% r7 N9 Q 129156678096 3600000000000 0.95314744 W4 k, x& Q+ l7 U6 { 132613795649 3700000000000 0.9531511376 S; l: o* {. D- Z 136067688083 3800000000000 0.9531553522 w$ \4 d- A% _ 139518461664 3900000000000 0.9531632733 @* Q8 w: M' _4 n6 x6 @ 6 X$ T) ~: E3 D. m a 146410910264 4100000000000 0.953173082, v; y( k3 F+ h4 y) U8 [ R 149852773964 4200000000000 0.953181021/ b: {, B; v1 ]" _& `7 P2 j$ ~ 153291810623 4300000000000 0.953187137 z3 _+ Z9 y6 ^& x; y# y& {# E 156728136258 4400000000000 0.95320009) e1 f' j9 Y. P: W, a- W 160161747327 4500000000000 0.953206672* T7 m! [' H3 y' w 7 B! D; G _9 T- A 167021151370 4700000000000 0.9532151364 J V1 [! v, t; _ k 170447066694 4800000000000 0.9532177888 J! Y9 G* U* ]/ I7 {" u; T , x2 r; n8 Q, X3 c/ g5 f: W$ I& E8 u 177291661649 5000000000000 0.9532300351 K, F0 Q# ?) C, {! R0 K. K8 v 6 w) z* l# }. L9 w. z. z1 P 184126901158 5200000000000 0.9532424287 s; v" \2 C9 P' v+ k- _( T$ A , n6 S9 h+ |. q! k ' _1 {- `8 v6 z1 a$ E' Y 194362990637 5500000000000 0.9532520613 D- L! Q1 u. g" w: x- t7 f1 Y& ^2 w 197770743547 5600000000000 0.9532559837 p9 w1 |7 J' ~4 o + N- a8 H) l$ h( W5 W- Z7 | 204580066580 5800000000000 0.953263125" \, K$ R* d8 ~5 X 5 n( \8 C9 ]+ Y3 s% ^( E 211381427039 6000000000000 0.953273461 V! ~( i0 B3 u: J8 `8 A8 f; c 3 B/ `/ o2 i; K- x1 R& |9 S 218175058254 6200000000000 0.9532798379 P; F+ v% y8 I# U . ~3 B" c( ^( Q& ] ( A9 i$ [4 e9 O; @. w + Z; O S7 {7 e5 L* i+ I: x/ t: W 231740339225 6600000000000 0.953302771- W% N/ [( ~: O! l 235127223891 6700000000000 0.9533063127 \0 r& [8 b, A+ D. A2 c3 l 238512407609 6800000000000 0.953311095 L+ y# Y _6 @1 r- F 8 J4 M" a+ H: C: R; @0 `& M 7 D0 _: }- U. J# F4 T5 L6 P- Q 248657916582 7100000000000 0.953320369; f& \3 [! e% d7 Z 7 G* j* ^9 Z; T8 O 255413505374 7300000000000 0.953326527+ W+ ^' _0 [! M 258788925595 7400000000000 0.953327242* u% T9 U, `6 Z) Z4 J* K& K 259656817434 7425719040829 0.953329238" Q' h8 l3 @/ ]# B4 a2 d 262162841215 7500000000000 0.9533318794 _: L( |# `0 d4 C& Q 265535241952 7600000000000 0.9533367& I* ?7 b) L4 d& B# J 268906152117 7700000000000 0.953342031 K8 }& s% ]! B" |4 e 272275559525 7800000000000 0.9533442615 o7 m1 g1 U/ K 275643544693 7900000000000 0.9533500042 s4 i) P/ M* z * H7 c9 m- w: e6 T: J 282375171661 8100000000000 0.953355251! C. H2 `3 L. l$ i5 W0 B1 p. ^# x 285738881494 8200000000000 0.953358042- C f* M1 J: m, ^5 j 289101209285 8300000000000 0.953360526 Y L: j- T3 M- r: O: l, e 292462199848 8400000000000 0.9533654717 @* Y, J6 e. |% k1 n r : x9 S" R( s, V4 S2 o4 x 299180106058 8600000000000 0.953369279& F: N7 W3 A6 G: K% A3 G3 W 302537108851 8700000000000 0.953373572! r, V6 [- x7 m6 j9 l; w8 w% h " l, i1 Z( j6 w2 y. [5 u 309247216816 8900000000000 0.953379223 o/ t. n9 L2 }& B# @1 k 312600354108 9000000000000 0.953380742 l* _+ ]1 U# q- F( B3 O j }" U 3 n/ ^) F3 L1 P+ |% F+ f! n 319302948414 9200000000000 0.9533886141 |. ]( a$ y2 O `& H' a9 g2 x 322652410741 9300000000000 0.9533926822 v+ f) n1 F8 |8 d% s9 C8 {+ B Z; ^4 U' U( V9 O- K$ z$ [ 329347709593 9500000000000 0.9533986976 G3 g& C1 s5 I ~2 a, U3 q$ f1 T 6 g8 j7 b g$ u6 X8 m 3 v/ \4 w6 Z. S, r. g$ n " Y; ]6 X$ v( G. k ! {/ E' ?: m; D' n* U0 K! C# | + V- l* w5 ?" o9 S& Y6 r9 f# h; \2 T 1 s) w9 ]4 M4 R5 S8 o( M" c9 F 511905471132 15000000000000 0.953527263; z% l+ e8 x+ _' u( b 643217611048 19000000000000 0.953596753: e# _+ b- }) |5 l x 675895909271 20000000000000 0.953610735% K, ^6 Z/ g" ] 773621469799 23000000000000 0.953652834( a% T1 C- `5 B0 q 886674661126 26486412297029 0.953696348' m, ? e8 v" U4 |2 b 887114276903 26500000000000 0.953696396& ]6 L$ d% _% A/ \# ]+ `, h+ L( _ 0 _% p0 ]- O# j3 w: I( a ; p' u3 ^; O" N+ ^* u! u- Y / i7 W7 t, i& e# H: m% p 1000000000000 29996224275833 0.953735935+ m& [7 V* y& `2 r9 B5 L6 c( u 1000121668853 30000000000000 0.953735897+ k9 k2 t S7 q# c6 G" G3 W% o# v$ q* c0 v 3204941750802 100000000000000 0.954126498% ^- q, W: G& y9 ~- S% S1 L: Y/ S% Y* b: g 0 F% U# W0 o( c 29844570422669 1000000000000000 0.954950335/ r, e* |! P1 L1 X% M5 |+ Q / p. P8 v, W! H: D q $ [' ]3 C0 t* f, o: z# ]' u, X8 [0 t 547863431950008 20000000000000000 0.956106462: N+ M! e- w! H4 b 1000000000000000 37124508045065437 0.956350996" x0 J9 V% W/ R 1 J x$ W9 H+ b: C " y, b( [, ^* m! v9 m: G 3893882469583623 150000000000000000 0.9569058844 C) d2 f$ _" L5 `- m6 o/ c 10000000000000000 394906913903735329 0.957291265- B' h2 R9 B7 K6 [ 1 t. S- [! s0 Q / B: ]% p7 L. ~ 6 ^' Z2 i2 _* F% `" [6 P9 v 95676260903887607 4000000000000000000 0.958208716: o% ^/ ~! x* v' W8 F* g f - ~& V: n' |9 f& F9 @3 P 118959989688273472 5000000000000000000 0.9582965291 B! {1 N8 Z/ @/ w/ \ 142135049412622144 6000000000000000000 0.9583681589 O3 w( e' l: e8 ? 165220513980969424 7000000000000000000 0.958428646* F, Z8 M" H- K) Q7 B, [- q 188229829247429504 8000000000000000000 0.9584809861 r ~/ x2 Z0 j" [( ]* e: Q 211172979243258278 9000000000000000000 0.9585271% W3 a& b, ]2 H2 L6 u. I ) z: `1 m6 n5 U: I" _, x* ? 460637655126005490 20000000000000000000 0.958838542# R8 J7 V* e9 N2 S5 m' ~% y9 D 684559920583084690 30000000000000000000 0.9589958130 G8 c- E3 j! i3 l9 u 706849401776940275 31000000000000000000 0.959008504* Y# c& ^: ~( |; ^+ F- g 2 i; @ ~; E+ t+ O4 P 1000000000000000000 44211790234832169331 0.9591456426 y- y- q) R% Z5 } 1127779923790184543 50000000000000000000 0.959193055% { a# j, }* X: A1 {& q" l 2220819602560918840 100000000000000000000 0.959458995! {- s7 {7 {$ i 3516585752930430595 160000000000000000000 0.959638155" ~+ r; A( @. V3 l 3 ?. d, p* _" \5 m9 T9 s0 Y: _ Q& \0 x. k7 ]$ }- b4 C2 C. I G6 H3 Z: _5 w' l + c! g9 l. f1 L8 h) Y# z1 @ 5654086442526321042 260000000000000000000 0.9598221917 ^- h! u, o$ }0 ~, B! E* X' F$ j # U7 m4 k) m. K: B$ \# O1 m ( n: ^. g9 [) e [6 h9 D 6715709842660010419 310000000000000000000 0.9598886" n7 [+ @& q, _2 U4 p* b5 q% O # W" g" s+ h+ T' f% s ' V9 t4 B3 @: W! i/ Y3 G' Q3 S 10000000000000000000 465675465116607065549 0.960041680 S6 X6 d1 ~. x ' J, Z2 y2 l# _ a& _ ' E: I: r4 R* N; z9 ~ 21127269486018731928 1000000000000000000000 0.960327059+ W j! X1 I; F, z7 E 41644391885053857293 2000000000000000000000 0.960583407% W8 A5 n( q, g0 X9 F' Z m2 E, C$ e$ G" V 100000000000000000000 4892055594575155744537 0.960910633: \8 y& y! w. {1 t 201467286689315906290 10000000000000000000000 0.9611692325 n% [6 L0 ? x' D: Q; N$ r 6 |1 T$ T2 [7 ]; P1 U, a: t 397382840070993192736 20000000000000000000000 0.961417385; t8 m6 w r. l' E# Z( U' S 2 c. l( y `* H 5 p2 n! X+ j1 @; w+ O$ u8 Y 18435599767349200867866 1000000000000000000000000 0.962769828# N& v6 n" [, e' ?1 @. J$ G7 @ 6 u) x: J* J- V! F% ~; O. z 9 Y' E) l) l4 ^. V- E / Y5 y# O+ r8 g9 Z* m8 _, ` . C1 i# n* o8 m7 R5 s3 w 1 Z" g( r6 }" e8 o. N3 { 0 f+ R% g, w" C+ a7 y) U, A( M
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发表于 2018-6-5 22:02
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