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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.- w8 ^+ w7 F6 R/ Q) C- z 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.( m# N- h8 X7 M- ^. k1 Z 0 ?; Q* K( ]* _8 q3 | 3 |1 l; U# }) f) i1 C+ G4 w9 R/ E n值 p(n)参考范围 计算的k值+ Z( T# R; P. q$ P7 _ . s* G: K5 k4 U' G; [ 10 29 0.236617538+ l7 ~: n, o7 ]& m) V. |) Y 24 90 0.584322837( S d% e7 R# |" D1 Q 25 100 0.3879080011 B7 q4 F) t# P8 D8 K3 ]5 c# ] " D: m; L* m+ C! \ % ~( W% B7 o4 K 9 f" F; @0 N% H" O! G$ G 6 h* {& e- U1 S; l2 a: }- |. U ) Z+ @1 Y# o" J3 t8 s3 t- P 9 P) i+ Q1 W7 x' \) l: z+ p0 a 0 s ?/ i. q2 T 0 Y0 ~# Y4 k4 j9 p6 ~& q 8713 90000 0.948434316' _- n& F3 K5 |1 M' I y 9592 100000 0.959124075& X2 t8 H$ ~, p4 A3 Z' b4 k % F3 B1 b! q; \ 4 s: v* {& Q* \8 i7 Z+ ? 30000 350377 0.962732035, \% g# m( l5 N! a! t0 j' P: C- u 50000 611953 0.962094066" t6 I4 S6 P! h: w ; q4 U5 @* ^) g# p j/ ^6 {# ^7 { 71274 900000 0.960576676) u( i+ q8 ^3 K. e5 l- q# i4 k 78498 999983 0.954084756! j. Q6 J/ W4 S$ ~8 p4 l5 n$ j2 K " e# _3 k( B$ o6 z $ B- _8 z. ^; P) f# L/ X4 ]1 `8 X , z0 F \# ^ B5 } 300000 4256233 0.95870651) I, Z1 \) i/ O% G+ i5 n 7 M% }* ]+ x" }- C K 7 ]" J; `1 U+ h: w4 m% a! G ( {2 V% A" r$ |/ { : V, j9 J. X; f; g4 h0 X1 h 664579 10000000 0.9555591541 P' l" Y" Y3 y6 J) x 0 F8 ^ V$ j X9 F# G 800000 12195257 0.957804142. F' P7 M2 U3 G- z4 F# H + i* C; E3 j; v# `6 s+ i 1000000 15485863 0.9554394723 T8 E6 c2 }7 C( V5 T2 h* E# R 4310144 73473859 0.956066856% F5 M, `$ I8 } / T! N$ F# t. ^1 c! w+ s( H & J9 D8 z' g1 h. l/ ~1 S0 r# S 10000000 179424673 0.955570945$ N- y& C, h; n , ~9 Q) @) i$ x7 d/ R: S) r- S 31255985 598608349 0.9541818837 O1 M& N% B. \ / X, V6 ~3 |0 ]9 ]- y8 l) ?6 O 2 W5 {# |; V0 x4 @3 |. n* Z 9 Y" y' Y6 _: b- Q" E* `* d 100000000 2038074743 0.953407301+ z+ w1 A" C) K) ?1 J% s) i3 A* A - B( C+ x0 X$ @ & o" X9 a/ l( _- f ) p' `1 [. J+ o : U& Q1 J* O) y3 K " \- v( A' N0 ?4 o1 \) [ - |$ y0 }' q5 N+ O 498388617 11000000000 0.952836503( I8 ^5 ?: d& y1 `& o) g* N3 a 541555851 12000000000 0.9527924382 C( _: g4 n6 s7 z5 @ 551987369 12242181113 0.952827232- D; ^3 R$ T3 L& ?' A 675522133 15125167433 0.952807270 _" l: A" J% l6 ?- U1 Y7 q5 v6 L6 d 1000000000 22801763489 0.952759371. ]- J& K S8 Q4 i- v/ ? " Z; c; `7 M: ?- Q3 Q 1234567890 28423087477 0.9526597976 } z! |& g4 K+ n. L 2031255985 47824232591 0.952633346% i0 e0 M! @0 a9 B! @ 3722428991 90000000000 0.9526328423 o4 P) i4 a) V9 G- c0 r 4 H6 X% G% F' S5 T& x R" n( V D 4512105232 110000000000 0.952609693! m! |" D' Z2 a1 ]; z 4904759399 120000000000 0.9526305762 L) Q, x/ g3 }' @0 Z6 V 8724310144 218695452037 0.952688936( l6 A) q# A# u5 w S5 n+ { 7 \# X4 |) `5 a A! X# V/ A( G1 y/ |' g* d1 @ 4 K$ W7 k0 Z% E! N- Z( ~ 7 X" Q; F$ o% j# M# F ! Z% ~) [( k1 v ! A' Q* {) d- |2 P 24188924259 632071564697 0.952803332. s# Z# n" e1 a. c9 Z3 g 33981987586 900000000000 0.9528566277 C& U2 p5 F* s1 R/ u 37607912018 1000000000000 0.952882443! f+ w @4 ^ r6 {6 Q$ _* S1 s' l 41220703418 1100000000000 0.952898557/ i1 C% e+ m$ u 44821651132 1200000000000 0.9529137499 j; w8 W5 X; ~2 Z. R! q + Q7 a: p' Y, a0 X4 ?+ x2 N9 j J4 A% b# u( n) L7 B 55563209929 1500000000000 0.9529598231 N, H1 e" \& t / f4 t: G; x8 S0 V+ H1 x 62680547806 1700000000000 0.952978131& h a; }/ l( u3 ~% X- a( ?% Y/ m 66227858344 1800000000000 0.952997051" l, r$ B) i$ D/ k7 | , H! C4 v: f0 o3 M+ r( M( g1 C. t K$ T' p6 D) _# l/ A 6 Y) \* g! ~; b: ^% T* L 80350940550 2200000000000 0.9530315769 p) C7 \8 j* B8 B5 j3 S" n3 c* q 83866890515 2300000000000 0.953043799; r1 @! _) m% {6 d4 h& x4 w$ G: U4 R 87377470252 2400000000000 0.953054856 J2 q$ T! h* k) L- k3 d) U: g . Y8 _; g( ], E* O$ t" {5 D 90882915772 2500000000000 0.953063852' ^- ?. Y |" U9 @1 J 94383447111 2600000000000 0.953071222 g. }; X6 I: |7 h+ q& R6 } A8 n7 w$ i& X, {& K 7 n5 c/ L0 Q) A5 ]! k 9 a& D* W# k9 y3 K; a1 E + }! s9 h# d7 ~: k7 I% m) W. A - X7 q0 Y( M4 k8 F7 u. O) g' e4 z 9 f% Y/ k$ J( d2 ]' Z# K 111819048275 3100000000000 0.9531138959 Y. Y0 u2 l* W* v/ L5 j0 _ . K( J L4 ~0 ^% N 118764942011 3300000000000 0.953129267. u3 `, P% v9 G9 g ( i1 q1 m, A% O' R0 V* z 125696244675 3500000000000 0.95314551 }7 b* C$ d, B $ \; K; _" q6 e8 G 2 ~: z- V5 _5 t: t 136067688083 3800000000000 0.953155352% d3 j" B2 k+ I. M( K: @4 d8 g. \4 P( l * I( \# H! _: ~; w7 Q4 H 142966208126 4000000000000 0.953175813, G( G& s' O! K 146410910264 4100000000000 0.953173082' s2 n% D5 f1 v9 I( K ) b1 Z- }0 ~* L0 r6 E4 F. C 153291810623 4300000000000 0.9531871377 U8 Q; H1 {1 p5 ~& D" E& | 156728136258 4400000000000 0.95320009- C7 M" ?1 P+ C* Q1 ]# D3 y 160161747327 4500000000000 0.9532066728 a% p7 S( p2 }1 [! ]) W0 g D 163592692077 4600000000000 0.953204523 Z2 |7 b: K& T, W. \7 c1 {. \ - q" J" [& C3 I6 M3 r9 t & T) v+ C; i6 }2 C" f. s6 W7 o 1 ^3 g9 U" J8 ~ e" k, a ! p+ y: |3 g/ q" T4 Y 180710431905 5100000000000 0.9532371571 V9 Y$ n& g% r& ` s, x) G) [: r 184126901158 5200000000000 0.953242428# T9 p3 f: }, u4 {4 n5 [ 0 D1 b+ X; e @# E% [ ; b% y- C+ ?- T6 A 194362990637 5500000000000 0.953252061) ]9 p q$ J x0 r# m$ e$ b/ ~ : c6 M. P+ I2 j0 c/ @ 201176428961 5700000000000 0.953260598/ ^% d$ ]* O0 \, X0 Q % f# j% o4 M, | 207981734215 5900000000000 0.953269379 i% O: w, K% [1 b+ X- O# N; H4 h 211381427039 6000000000000 0.953273465 Z( M+ F7 j J6 y4 {* e; r : m2 f- G) c- J3 Z: \) C! M + [( {0 u; f ]9 ^' w+ s5 S. e 221569102517 6300000000000 0.953287444+ n. R2 G2 Y B2 w7 \. W # B) W, M4 ^0 R1 @1 ^( }# r . D1 }7 X8 b) l0 t \. D 7 D' I$ Z6 x. }% w9 q 1 B' i n4 S- T# {) i4 c8 r5 \ 238512407609 6800000000000 0.953311095- u3 S5 _9 m1 b$ t( X* y% e! X 241895851648 6900000000000 0.953309053% o# v' S' ^; l3 j3 N # T, M2 B# a9 E 248657916582 7100000000000 0.953320369/ I. w; X5 k' s$ G! E9 ^5 Q" M ' A6 V9 P7 g+ M& w8 f 7 z+ N2 u+ D1 b8 p! v . k1 H& I" Z5 w; E n 6 c# e% B2 K+ n5 J6 M8 b6 q # Y# S5 w L, R9 H* h 265535241952 7600000000000 0.9533367: ^$ ? U# h* Z4 t" |8 u 268906152117 7700000000000 0.95334203; V$ B3 C/ n4 _. K" [0 `2 o9 F 272275559525 7800000000000 0.9533442613 _& L* i' K4 y7 G! V% g+ K 275643544693 7900000000000 0.9533500043 z' N6 }, C. j" t 9 b3 m. C) D8 @5 H0 B* y9 Z0 Q " Y1 P% a0 M2 E$ q4 L ) H7 X: d! f7 f' R8 D $ P2 U( X: J0 s4 Z6 F; r ) p& g1 q$ O5 Q 295821814466 8500000000000 0.9533671579 k4 t* ~3 c+ w * k+ l! t& l8 X# U" f' K4 n 7 V4 m4 B" J$ Z! y$ D8 ~' } 305892791866 8800000000000 0.953375381 g7 o6 k/ P5 C. }/ B, @; t 309247216816 8900000000000 0.953379226 ~( b+ \. o% j4 [ % ]0 ]7 ?) a7 F' f/ k1 w6 k) l 6 z' y' Y5 e6 M6 B& X$ J7 h 319302948414 9200000000000 0.9533886141 ^. I$ [$ R, m M2 f6 Z7 [: l * X6 O, D+ l! ^& L) Y: a. w' Q$ V 326000647688 9400000000000 0.953394916 w7 O4 }2 y" B6 J: u+ l2 O 329347709593 9500000000000 0.953398697) G; w1 R/ [$ E: ~2 w0 w; w8 _4 G ( _0 C v7 h ~ + f( T1 w6 E2 j; u% ]+ ^- m . `1 @6 u( @' S9 W6 P% C5 \ 7 D$ O$ Y2 ]. y6 w4 p 346065536839 10000000000000 0.9534119961 s5 ?" o) ~ G6 Q. P 379418886337 11000000000000 0.9534386216 g8 I5 a, p9 e8 k( ]5 C 511905471132 15000000000000 0.953527263- a; _; h& @7 w . |5 ~# L" c5 J/ G; t( M" _ 0 q' ~; }: i: g9 F 773621469799 23000000000000 0.953652834- I k$ {$ f9 `& b. f5 c3 @4 a, U6 \ 8 y6 t" \3 ?* d) T# [ 887114276903 26500000000000 0.9536963965 {) a5 m/ j6 ~ - j& J n; J I3 ^9 x3 H! D 932911185326 27916701633581 0.9537119169 M% y# _- j! y # R* g" {4 e: x, D, q' q % R. A4 g7 D3 s# { / N8 `' ~) A" S ^ z' r ^. B; ` 3204941750802 100000000000000 0.954126498, ^0 M) l9 J0 M) v$ o% y: ]4 T5 } 5 ~1 I4 V* i1 ?. n& n x 29844570422669 1000000000000000 0.954950335/ M% n* f5 m7 G0 J8 t # l" P( M6 e8 W7 X2 f' c % G' M1 Q$ y2 G/ A8 b 547863431950008 20000000000000000 0.956106462, D0 ~& s4 v/ `4 w( M- y 5 c/ u9 y) A7 `8 U 1075292778753150 40000000000000000 0.95638055! s6 e q' z. I) u' m" I 2623557157654233 100000000000000000 0.956744527, N# b2 H* U+ O ! c/ ?; h( @7 |+ { 10000000000000000 394906913903735329 0.957291265 V: w. J2 K' i4 J" B+ L1 G# H, Y 24739954287740860 1000000000000000000 0.957660554 b; r- @- y7 i6 l5 U/ |7 U + Z' R! @- `8 d$ O 72254704797687083 3000000000000000000 0.95809533- ]. N) J4 G' y( t4 {; P 95676260903887607 4000000000000000000 0.958208716. e- K, t3 X9 d7 b3 F6 Q 7 W y& v- c* |/ z' W . y1 T; m' g1 I% R% ~8 q 142135049412622144 6000000000000000000 0.958368158/ Y1 l0 _( e: H9 @ 165220513980969424 7000000000000000000 0.958428646. S6 R7 t$ p. I# B, o 188229829247429504 8000000000000000000 0.958480986' [3 `9 e: n7 S$ S& a/ L 211172979243258278 9000000000000000000 0.9585271+ H5 e/ D" l, [- P/ E 5 f1 V. n) |! ` 460637655126005490 20000000000000000000 0.958838542& W3 Y/ p, e8 N% e* X% x& D! b+ l & V" V) b% u' H( T% S- p : I2 F" d- I% k! J/ K6 {& X 906790515105576571 40000000000000000000 0.9591070226 v0 p: _4 z; @# C 1000000000000000000 44211790234832169331 0.9591456425 U. I( ]% [2 q/ k5 ^ 0 q$ P. o" D1 f: ^( e! T+ { v' m: n" c8 b$ o. _3 d$ ` 7 w* ~! e! `5 h, [ a& x( d8 r 3731397829842461168 170000000000000000000 0.959661194& f; e2 M; w: t 3945938652811699917 180000000000000000000 0.9596829( a+ K6 n0 \3 F4 C / U0 U- u4 ?# H2 C% ]) M 4588082544160859769 210000000000000000000 0.959741366! \7 O f& C+ M0 _ ( F# k) O8 l7 i6 } 9 f7 l1 I( {" P) y" ?8 B 6503696293016202398 300000000000000000000 0.959876232 d1 J- j! j3 F; u ; e% O7 V8 M5 ~& I- g" R 0 I7 ~6 q J" v2 B$ ] + b/ }: _2 D( X) C; { 10000000000000000000 465675465116607065549 0.96004168 R0 P. ^: w" G3 T& y v( G6 ^3 Y" m! k6 A 12814731195053369962 600000000000000000000 0.9601366288 \4 q* X( F, o5 {# @$ Z4 o+ p% V 21127269486018731928 1000000000000000000000 0.960327059* A9 q/ \: N0 Z' i h% ?) ]8 l, N7 Q8 ? - C3 W. K' |3 O4 Z7 W7 ?/ ~ 100000000000000000000 4892055594575155744537 0.960910633" Y j, P' l! D& M! R; \5 Y 201467286689315906290 10000000000000000000000 0.961169232" y, A7 G# ~, K* K7 F# o . J9 o4 a/ @3 z/ e: R# O* M/ e # D/ f+ W+ G! v9 \ . t1 _, g1 m5 U. x( B % d0 ?( x n8 j 18435599767349200867866 1000000000000000000000000 0.9627698280 b, @, p, ~# r5 T7 j: o2 A # J! Y8 p% o# G! t% I r* v 1699246750872437141327603 100000000000000000000000000 0.964256911769038367410632552188602 |+ [6 |4 u1 r+ N% L# z + X0 U/ M, U; U9 b) W 所以无穷大时p(n)≈n×(lnn+lnlnn-1)成立. k; Q" y# b$ ^/ N5 l/ e& q 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?/ t+ y o8 O& ~: L& g 我坚持无穷大时p(n)≈n×(lnn+lnlnn-1)7 ]* r& g5 u+ N" B* s; x
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发表于 2018-6-5 22:02
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