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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.; M. L" r; q+ L5 A( |" Z5 ^$ E, z . J! t9 H3 L/ I3 l( x ( `# j! c2 A% ?, r& l- O A ( H: W+ ?, |' ]% ~ n值 p(n)参考范围 计算的k值+ l- @+ c+ }! m. P! R 4 10 -0.787071379/ J m. O2 |% X; k 0 p; F1 s: a( Q! O' K6 Q* Q6 D$ S8 R 24 90 0.584322837* |2 N& _! L. D5 L! h; x 8 b0 F- o: E% `, n, ?) m + @' p4 ]6 O; ?% E& v; E ( k+ C0 e" Q! S9 p * x9 c' k6 M( w$ T+ z 7 g2 F X2 ^8 P: _5 R + Z) W1 {- Z: M8 s+ N" t0 w y2 Z1 J: c+ y2 ? 1229 10000 0.939318112+ f+ r4 ^7 ^5 O6 I8 R 3 ~" D3 j* ]# _( K/ g. F, l % v) U* |- M" H, c ' V( o+ t2 Q0 c8 T0 B: j1 {1 H 9592 100000 0.959124075, O. p7 K: ^) ^ 10000 104729 0.957767178, {" I- i- g" W z % @3 a8 h4 W4 Q4 n! K6 S3 z 50000 611953 0.962094066 h" f/ x- u! v+ I& d 70000 882377 0.962864732# D' M5 w) n: M 71274 900000 0.9605766766 `! w, g- o" `, A; a 78498 999983 0.9540847561 H; g0 _: x- Z; Y: O # X) m9 s* c! |6 O( m: K$ `5 O! I+ l. V 100000 1299709 0.9593058231 z# q5 l* x- ?; c 200000 2750159 0.9572112317 L7 N9 I- A' o8 W- q* G5 i' n 0 k Q. i# p ^4 I 400000 5800079 0.956189157+ M5 _1 ]! a% p3 |+ } 500000 7368787 0.959107282 `$ V7 z- R0 y- _ 600000 8960453 0.958712825/ w. ^- P, L/ d1 t! N8 `2 U 5 r! o1 B; P3 `# ]& A* s 664579 10000000 0.955559154% k/ Q- K7 M6 c/ L0 [& b; {5 U8 M 8 i/ p8 d0 M \1 @2 O) c- l' t 800000 12195257 0.957804142" ?) T2 o- L) A2 d& L- `# e/ w3 O [ 900000 13834103 0.957060924" y F. {; k5 w) x 1000000 15485863 0.955439472" s7 r1 K5 o8 @; J 4310144 73473859 0.956066856$ c% m+ G9 G. Q( g ( y7 d- I; p4 \ 5761455 100000000 0.955107932, Q) N$ S/ G# E, Q6 z ; n I' K" v2 E% b0 A % l# ?* }8 A. h" n# ]/ n/ c: q8 x) d 31255985 598608349 0.9541818838 F. [9 k& N7 p1 o: k " y# U, J5 D5 T ) |2 `" ]/ i5 y& t 62106578 1234567890 0.9534237931 O7 i& C- q$ L! a: z+ _ 100000000 2038074743 0.953407301+ N/ Y6 v, R* d0 z 111111111 2276855641 0.953517847! Q, E3 B& j9 m7 k& j$ P( k1 i3 B' O9 H O- r6 [6 ]9 u3 r: I4 a 399487944 8724310144 0.95293163/ K, C3 V( T- m' S8 q2 J) @- \ . I% Z. v; u( g/ m ! N7 ]6 i$ u: C- J0 x' N Y 455052511 10000000000 0.952960865' |3 Q# {3 \. N' W7 i; L 498388617 11000000000 0.9528365035 J2 y% \& m) k- I5 b6 ~7 A7 A r" C5 H/ v0 f K0 n* H% \4 Y 551987369 12242181113 0.952827232' ~+ V7 m+ c0 q5 Q! k0 I # Y) q8 v1 |- Z+ |/ L 3 F/ O" a4 k+ _$ w G: Q4 `0 X* r: w& ?4 K' V ( l2 H/ C& g3 ]+ t* Z / p2 G+ \; @( V: f 3722428991 90000000000 0.952632842, `/ v& n% r/ _: e# c# J3 f) ` 4118054813 100000000000 0.952661953; p' |: W7 U* h/ ~ @! \; [# [ 4512105232 110000000000 0.952609693" m6 k( i* ]$ V: F, O- E& x$ \ 4904759399 120000000000 0.952630576& N7 l& j' O( ?- b% j9 U8 H2 V; [ 8724310144 218695452037 0.952688936% Q' E. z3 c- E: _ 9000000000 225898512559 0.952686974/ J* Z) A0 r5 ?" Q! K/ m: U 9876543210 248857367251 0.952697866) J( Z" z5 ]9 D! d 10000000000 252097800623 0.952688406" c4 ^4 h9 w3 o/ u& x9 d/ j6 m ! l/ x+ a1 l" b 5 F- M" R, q; I. }9 {& ? D 15125167433 387829275881 0.952732747" u( w$ k% D( S/ ~; m1 ? 24188924259 632071564697 0.952803332( N% o" k- _# G3 C) k& |8 M . @. C6 s4 m3 P% n3 U* D- t3 ? : z/ r' v9 i% J2 o$ c, c 41220703418 1100000000000 0.9528985578 b P L+ ~3 k% v$ `' v 44821651132 1200000000000 0.952913749$ [% U6 w: E& X _8 { 48411812843 1300000000000 0.952928255( F8 v1 @, ^2 W, P1 v3 b1 \% d8 _ + \/ j+ w$ Q0 n" @, ?; t. n I1 o% N 6 ^& g7 Q: s1 }/ k' S9 w3 F / O$ X) L0 Z! V9 q# n; |4 @ 62680547806 1700000000000 0.9529781310 z. a6 O3 v, B7 y" q( Y4 O7 y $ O/ S, \7 @# V! T! K$ {6 M! p ! {6 k/ g+ s+ V5 P4 F, i # l+ K' B/ h* q0 n) D 6 z9 e$ }" D- ]% N7 b6 _ I% _' d 3 c) }# r9 u$ _. a4 K! S 1 f/ D! K" F" V9 ~ ]* J 87377470252 2400000000000 0.95305485: n% |+ w& g6 s: e8 e+ c, ^ " ~+ w) @- ^5 d) v) L2 f1 o 90882915772 2500000000000 0.953063852$ j. R: C( _6 t1 O5 F 94383447111 2600000000000 0.953071228 B7 Y( W; L9 e. s7 H9 {) c 8 O8 n( w8 K- {2 g' t; c . \2 h0 J3 |' |# L) @$ D/ X 5 e) k' S+ N1 _( ]6 j! C 101370585277 2800000000000 0.953089006' n% V/ _4 ~* Q: K$ _ 104857545428 2900000000000 0.9530976523 P: M% y# u+ B; t 108340298703 3000000000000 0.9531011715 B7 L9 H0 L# d5 p! J0 H 111819048275 3100000000000 0.9531138954 \' A; f! B& o. d3 m% K# t 115293888086 3200000000000 0.9531236955 Q; W/ X) _2 R- @* m7 Y( x 118764942011 3300000000000 0.9531292678 C6 ?2 W8 y* S' o; K 0 l0 X8 A+ o' D 125696244675 3500000000000 0.953145516 A# W. h+ Q; f) i% r $ \- m8 ^0 }% k+ _* ]$ C6 P 132613795649 3700000000000 0.9531511376 `. Y) i7 n% I. p2 b) ]/ _+ m, @ 5 [2 L# D4 I, S7 U4 W& z3 t! j ) ]8 l+ J' U! i A h" ` 142966208126 4000000000000 0.9531758138 v( Y7 z$ N3 [0 u9 w0 l / L/ d" ]4 U8 W & i; h' Q4 i& o( @ 1 v& e' y, `" ~5 j 156728136258 4400000000000 0.95320009: V/ D3 R+ D0 J9 w" B% Q. L3 K7 Z ( C+ J0 m+ Z+ i5 ~7 q5 v 6 n" \" W7 Q9 ^/ o1 W 167021151370 4700000000000 0.953215136/ G: M6 ~ c5 G# F- D x - i; G$ @- O7 ] 173870573446 4900000000000 0.953226341; O$ T- x+ k! K0 j' S; s# W& I7 T 177291661649 5000000000000 0.9532300355 n+ ?" m/ M3 n7 l * K. {; t& l3 ?% i5 e& C5 J J* a( f E" g7 X2 q1 ]- ~; e$ d 187541119457 5300000000000 0.953246415+ E3 z' i/ W" I 6 U! H, }/ \7 E6 o: p 194362990637 5500000000000 0.9532520618 E$ X: s& Q1 N* R ; q% |% e0 M+ |& I6 N6 Q5 X5 @ 201176428961 5700000000000 0.9532605982 O4 d& E( ~+ H 204580066580 5800000000000 0.953263125+ I) G7 z! N' D; }& G " f; }% a. A5 i! R" R9 S+ _, ^ . K, ?* L5 U3 Q: Z5 X 214779167476 6100000000000 0.953273786* v* Z0 G0 c6 C: k' h0 ~, H 218175058254 6200000000000 0.9532798373 O8 u8 |1 h& C 0 w: v4 q# { p9 L # S5 v c# \( j" m) W8 ~* m 228351698532 6500000000000 0.953296988" N5 ?- ?) X+ p 231740339225 6600000000000 0.953302771/ E9 X1 P* ]3 b. c) A+ w$ u * d: X3 O& w/ v : ]6 A0 J; _8 f. d 9 t( X9 F# J; n' b- w 245277688804 7000000000000 0.9533133296 v, P9 x+ L" x+ p' k" d * k( p" ^6 |0 [$ C x 252036515078 7200000000000 0.9533248420 c# {3 W2 c& {. q( f * L2 f! O, f* r2 H6 Y + U, E5 E0 ?2 |1 ?$ a# C" c 4 {4 g" K& q. d- L6 ~6 L , q2 e( F& f% p& M/ ^6 I$ [# V% O 265535241952 7600000000000 0.9533367( U- {1 N% d& ]. t1 x ! J8 q" \1 Y8 x# `( `, C 272275559525 7800000000000 0.953344261- A1 _# p" G' B1 V% ~ 2 \+ t5 _# q4 T3 G/ L7 J; E 5 S$ D9 G; A4 r8 T/ p. f 9 i5 X9 I U: t - V9 ^ |$ n. S) Y: i 5 f* i3 G1 J6 H- U1 ?. m+ _5 O . @' p" q) k- B% Z; H# A 295821814466 8500000000000 0.953367157- j9 w# V8 O' W$ a7 X, J9 @$ \# P4 a 299180106058 8600000000000 0.9533692795 L/ w" |' A P' _! L ' h* I. i8 N- d $ v, q1 E: O* y6 E 309247216816 8900000000000 0.95337922( m9 V. A) d% ]0 P! `. B 312600354108 9000000000000 0.953380747 A6 Z) \0 ^7 n0 j9 s ' P8 d& B' I' v# w( g 7 m9 l0 b3 ]1 L# l w5 h " j1 |" A: ]1 s3 y4 @ 8 }1 ~8 f$ x, g d: g& x ( x+ c% F# B+ }. m$ x 332693561966 9600000000000 0.953399676" x5 ]. Y" d8 s2 P( }6 p2 a 2 u' _$ i9 r3 Y 339381817251 9800000000000 0.9534047474 }/ M9 ^& w0 V 6 R) N. ~0 L! o4 b# Z% c 346065536839 10000000000000 0.953411996# t. ~# s+ F( @: d8 U! E 379418886337 11000000000000 0.953438621$ Y- q7 p! b a2 v8 e" M 511905471132 15000000000000 0.953527263, _) @3 c# W) R4 v! Q 643217611048 19000000000000 0.953596753! _- z/ S8 [- {" t- ]7 D% c* G. {& M $ \+ J4 r9 `7 ~0 f H 773621469799 23000000000000 0.953652834- s9 K6 L& x/ H E! A 886674661126 26486412297029 0.953696348* z2 ^0 ` F! m 887114276903 26500000000000 0.9536963967 L B4 B* \" Q) K( w; J. [$ V 900000000000 26898370231697 0.9537012473 i2 c2 c# c) n7 _9 A$ ? , ^+ x& j0 ?1 X$ D- B/ b 967879555617 29000000000000 0.953724541) R9 E. @( D& l% G 1000000000000 29996224275833 0.9537359357 @, n/ ^. G i/ ?# y5 s3 M( ] 1000121668853 30000000000000 0.9537358975 U& ~ Z; y: b6 t4 u + i$ T: o% W5 _. m' E 10000000000000 323780508946331 0.9545371177 ~. w- W5 n! e/ t 29844570422669 1000000000000000 0.9549503350 k$ V5 Q) \$ B: S& w" X 3 r1 d& x) t6 z1 x 2 Q! W$ i* V! A; p $ U! \7 a# j) k7 J" I8 t' I 4 [. B% i( X9 O" U4 z 0 Z I8 Z( e8 {8 A 2623557157654233 100000000000000000 0.956744527. s; H- m5 k9 n F# K 3893882469583623 150000000000000000 0.956905884/ B+ O3 \# }% m9 O8 \ 7 N4 {9 ^9 ~" o. O 24739954287740860 1000000000000000000 0.9576605541 v0 R$ |" [' V 1 n9 C: e- A7 L$ | 72254704797687083 3000000000000000000 0.958095338 X ]9 B5 B, Z7 j! z+ n 95676260903887607 4000000000000000000 0.958208716, d6 G" k# D C 100000000000000000 4185296581467695669 0.958226556) Q: ~3 |% I; u- ^ " [) _! J- \( h 142135049412622144 6000000000000000000 0.9583681583 C1 l; h- _- \& q6 I: {7 K. S . X v* D% O& l* ~2 K5 i6 j ( e$ h( u7 G& C9 f& b, i0 n + p- e* f- N2 Y0 ~$ B ' j+ f# }' H6 Y4 r/ a: U% ]3 O 460637655126005490 20000000000000000000 0.958838542- x; G+ N9 |% [' N. o 6 |+ Q) i8 X( A0 z 706849401776940275 31000000000000000000 0.959008504# S' T" C2 c1 W$ a6 d, B- E ( F: F$ n3 ?5 X2 |) u/ A U" y( w/ n& H& I 1127779923790184543 50000000000000000000 0.959193055 F- V5 j3 S* K6 s/ F4 n, v 9 U( L# z# k* x 3516585752930430595 160000000000000000000 0.959638155# y9 f# n4 J! Z 3731397829842461168 170000000000000000000 0.9596611940 P9 q, l/ h; o7 l } L# B % ]6 H0 {4 P N 8 Z( ]" s' p0 a4 q8 }: a1 z 4588082544160859769 210000000000000000000 0.9597413666 x* V3 p3 }' t 5654086442526321042 260000000000000000000 0.959822191" Z! Q/ O) O' v9 v0 Q - E5 {/ L+ M9 C6 Q 6503696293016202398 300000000000000000000 0.959876230 Z( r6 J, m' p" ^% | " F) G: a9 J" l4 s4 O 1 o" j5 W' _! n5 R * p# j& n5 c5 X' Z% j3 w+ g* G 10000000000000000000 465675465116607065549 0.96004168; L @" Y3 ^+ a& A 10720710117789005897 500000000000000000000 0.9600683553 r% z5 m- R, A& I8 R9 B & N3 t; N5 N J1 a5 \1 f% w 21127269486018731928 1000000000000000000000 0.960327059- H, a5 G) A7 W5 C6 h& x. B5 R 41644391885053857293 2000000000000000000000 0.960583407# ?8 o1 ]. k8 F. t5 F9 H) t. o 82103246362658124007 4000000000000000000000 0.96083734- k& ^$ [5 ~! s* L( ^- a j/ ^ 100000000000000000000 4892055594575155744537 0.960910633) i4 p4 g: n( ]- K" Y3 m + n3 S5 [) `: f/ D 299751248358699805270 15000000000000000000000 0.961314699+ n7 w6 F4 j; p2 y) J" x6 a. J 3 d. A: c8 {/ u9 r- F9 L 783964159847056303858 40000000000000000000000 0.961662996' |8 `0 e1 ]- Y8 c @ 1925320391606803968923 100000000000000000000000 0.96198374& v4 P! |, }* Z3 n8 N : o4 { y# \0 g2 l/ g# f " ~# M7 D4 Y r# l Y0 x 1699246750872437141327603 100000000000000000000000000 0.96425691176903836741063255218860$ g a: R* Y) d0 s ; t6 _2 [/ Z0 l- N& V# u 所以无穷大时p(n)≈n×(lnn+lnlnn-1)成立) r7 v) u/ u: c8 V 3 L# \* r$ @ H. h% D 9 F* |0 V3 J$ ~ p8 i5 ^3 n/ P
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