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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.) A+ D- N" ?* ]+ E. B' e8 t 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.3 z* O7 S! z* S4 z - }! E, l! s% G& I8 h) w. e 5 M: D- ~. d% s. a* n& r C ) N. _& M* O, U# q , b& f2 [1 Y/ `( c! D( D / ~4 h) W6 u: @. A4 T 24 90 0.584322837: x& G) j+ h# Y# j $ Y% |7 ^% ?; y 100 541 0.722349812" v% W) m/ Y$ h( @; c9 F 5 ^; {- A; h$ Q 168 1000 0.8055113818 v6 Z; F& ^# V( ^ 500 3571 0.899510764$ R' h) t% k' P& G' E9 _ 1000 7919 0.9214000136 f$ I; A6 x& x6 V& Y! r. a 1117 9000 0.909640998- F j& M6 K8 _5 b3 ^$ K, o 1229 10000 0.939318112' _. Y h$ V& L. r! w) J% ?) B; l 0 j# D2 T8 c4 r5 [ 9 D% ?7 R8 ^* Q 9592 100000 0.959124075* x; d' n* B& q 9592 100000 0.9591240758 w0 @ m6 L8 e" C 10000 104729 0.957767178; A) v+ m5 S% q% R* ] r9 J' n 2 y& R3 M' _( m7 }3 ]9 R V0 g 0 b: }) V* \# O, m 70000 882377 0.9628647326 a& l \ d( @, o5 @& m! q 71274 900000 0.960576676! ^. ?, w' h" Z6 }: l 78498 999983 0.9540847561 H" n* x3 d# }9 ? 1 G. A9 L% w |& [! f 100000 1299709 0.9593058237 {" B2 ~* p! P- [5 v. Y 200000 2750159 0.957211231. y. F ^* n0 K1 _- V3 f5 a , ~8 V6 B0 z: W+ y 400000 5800079 0.956189157& I# A% y$ G9 {* u3 r % m' @: s3 m7 \% } * D7 ]0 P6 b$ r( u7 N/ C ! P3 \2 C$ B* C2 I0 H& p# X 7 ?, i& q6 c; U. v6 } 700000 10570841 0.957269999 ?5 k) t" T3 I) S+ N! b 800000 12195257 0.9578041421 Z) A6 v3 W) V1 S z* a 900000 13834103 0.9570609240 h# g- i2 I& T9 ]0 ]+ a6 O, D! L F* T6 Q8 U/ J 4310144 73473859 0.9560668567 K- X: D7 E, Z% G! ^/ y ( P0 m' H6 F( @, A- c! B. t/ O % i7 t( O& o$ J$ i1 I # Z2 Z4 R' x! I4 E# Z+ Y 28944316 551987369 0.9540162839 q5 \. s' b% a 31255985 598608349 0.954181883/ ~+ k% |' q: B! g! B9 g 46009215 900000000 0.9534692557 F. t! Q6 h6 p2 G1 s* U7 E" P 9 g4 o! j1 i6 f" K7 z& L! Y, W 6 Z% w3 v" m1 M" }) K/ l0 u 100000000 2038074743 0.953407301) I$ B, y8 `' E* G7 ?1 Y 111111111 2276855641 0.953517847& m: A+ |) t9 F+ F- V 3 U, ?! l8 _2 b5 q# T3 H 399487944 8724310144 0.952931634 U/ Y# l# w$ x, H. i 411523195 9000000000 0.9528727788 D) ?& L$ ] t7 e* C9 Y x/ V) U / E( @/ @( O9 `2 \# S1 J6 o 455052511 10000000000 0.952960865# }0 W3 k/ d, S! e 498388617 11000000000 0.9528365031 w8 _/ {1 h$ ?6 e U! h- C d- f' K+ o( U v % e: t! k. Z7 G6 p1 J0 S 675522133 15125167433 0.95280727( m; v8 e+ a- v# _ 8 V3 B; Y8 `; ^' H 2 F6 y5 \5 ]' E; L9 g4 k; x2 j & t. ~9 Y% c& e1 R% G ( r8 B$ g* ~. X' u1 [: i 3722428991 90000000000 0.9526328421 D4 g' F' q% d9 o h; F, H8 N; |0 k 4512105232 110000000000 0.9526096938 \! O) l, i# o, l: [ T 4904759399 120000000000 0.9526305763 Z9 i9 S/ U9 \9 q8 T2 x 8724310144 218695452037 0.9526889366 e& j; a2 c s % Y1 W B( s3 O, O 9876543210 248857367251 0.9526978669 c! a: x' L" _3 I/ x. F3 W+ f 4 l+ S$ M7 C7 I$ b+ U0 _ 6 |6 t m! V" U- B 8 l1 I E) Q7 B: b ! }9 W8 R! P$ P9 [6 `- E2 s$ T 4 f& S& N- X, h% m6 L6 K0 k P7 H % j7 R1 B+ J* L: t9 r2 y% B/ C2 L * n6 E- t0 y$ n; W ) s! k: v g' j 44821651132 1200000000000 0.952913749. M8 w% h5 P) J1 ]0 b o" u7 Z ' x' t' G9 ^: W) C6 t ( P8 g) e( y0 U - X# E2 g3 H6 e$ j+ |* I+ ^ 59125832286 1600000000000 0.952965853 L% ]9 e1 O4 C" }- l! D 6 U' @ X1 Y5 I( V . T+ }1 t1 E* L1 ~/ ^: V# a 3 t! L& V3 B) k m" O- h 73301896139 2000000000000 0.953018171: h- T# u6 @. p" Z4 A* l M 76829404177 2100000000000 0.953034877: t2 M" x9 y( c$ | 80350940550 2200000000000 0.953031576: F( h' B+ D2 S! p. c$ O . G1 x- N! d$ F9 \ j: v8 V 6 h9 E6 u3 ~8 W5 S; X 90000000000 2474799787573 0.953059364 e8 B; D2 O- P u8 x M 4 q+ |" m6 d0 a$ l) W. O1 R 94383447111 2600000000000 0.95307122. \: m4 F& r. n: }! r3 ^( C+ ]! g 97879280182 2700000000000 0.9530812131 ~/ C, [3 z9 k2 [0 w 3 K" m: ?7 o5 i7 W ; x) X3 n8 j- s8 a6 z 4 l* c1 Y$ T- b. s1 g # u4 u5 t" L9 B9 R% b! |' }2 C7 T 108340298703 3000000000000 0.9531011719 D ~8 I) V& W+ e5 L6 ? \8 |1 A, A3 X. Q5 W5 _ 115293888086 3200000000000 0.953123695% Q( e7 K! T6 e( q5 A0 o 118764942011 3300000000000 0.953129267, Y! e1 o1 `- P- M4 _ ( ?2 Y) B/ d+ X 125696244675 3500000000000 0.953145515 ~" e- y4 m7 W. f, L5 i4 L. O 1 U3 Y. ?+ Z7 R7 | h8 M % ]9 s m4 p+ ^3 C& e: L$ r- n 1 T0 [: r# q; O/ U: @7 m' q ! y2 A4 D& w" x* k- |: T 142966208126 4000000000000 0.9531758133 l9 j4 y) ]# k 146410910264 4100000000000 0.9531730820 [7 \" r8 B: t+ L 149852773964 4200000000000 0.953181021+ J% I( e0 M; [: b9 C9 S! ~ $ e6 J- m# B- o2 F9 [2 Q 2 x2 ~' J2 A# T+ ` 160161747327 4500000000000 0.9532066729 q% E8 \" i9 s$ @9 |0 J+ V+ z / m* A4 w7 p# ?6 ~ 167021151370 4700000000000 0.953215136' j' b" l4 a6 Z1 e7 x8 ~7 P6 u 6 h+ T" O' a& n5 H% p- I 173870573446 4900000000000 0.953226341# h( E, H# [6 S 177291661649 5000000000000 0.953230035( l, X( n7 z/ S* x 180710431905 5100000000000 0.9532371579 L1 z' e `6 r( P9 W + J# N- E1 V3 F - s" r- P* N- _ t% X; c% d( H9 s 2 s8 O% j- {/ B 194362990637 5500000000000 0.953252061" J' Y7 r0 h; \: P( Y/ n9 N& } 197770743547 5600000000000 0.953255983. ]4 M/ }0 h0 _$ ~, W 201176428961 5700000000000 0.9532605980 f p( K% f; \8 X$ Y: X 204580066580 5800000000000 0.953263125; V6 [/ \' _" F0 d - l: Z( R9 B. l + Y; F X; `" c+ I+ q+ j 214779167476 6100000000000 0.953273786, Y& ^, E" a7 \5 y6 Y 218175058254 6200000000000 0.953279837# D& r- d2 M$ X 9 U& ^( ?2 \5 r( B1 b * v, p1 P. Z! O o% E \ 228351698532 6500000000000 0.953296988 R# G6 Q: S d 231740339225 6600000000000 0.953302771; Z& k. l- i7 y9 d/ u' ~ 235127223891 6700000000000 0.9533063126 {' D, E e0 T# I7 `+ {9 q 238512407609 6800000000000 0.953311095% n3 {9 R- {; Y0 i M+ k0 B# L& F; T 245277688804 7000000000000 0.953313329* f; G& S! U2 q" n* s 248657916582 7100000000000 0.953320369! K( S, \+ H; k7 q* g n0 I 252036515078 7200000000000 0.953324842, P0 m4 j, a9 P, @+ E( \1 T8 ^ 255413505374 7300000000000 0.953326527: [* t. N' K" F 3 l, L$ }5 |0 f: F* ^& v/ c 2 G% l, Y& p( Y) V . a. j6 G6 H/ i 7 Y W) v6 N) w9 R! g0 | 6 C6 K# L4 A8 | ; r) v" }+ n; d 275643544693 7900000000000 0.9533500041 e( y2 ^# V& j 279010070811 8000000000000 0.9533531242 e3 U& B8 q( G- R& Y$ `! o9 V 282375171661 8100000000000 0.953355251& l% `: v5 p% f7 J( s: I7 s8 s - f {5 ?' @* x# Q 289101209285 8300000000000 0.953360526$ S0 I, ?& c; n$ ?/ \/ M) F 292462199848 8400000000000 0.9533654711 R! G Z3 V) Y! G. K1 X 4 _& [& k* @1 I; M2 A5 _3 {% Q0 {8 z ( o5 ?% J# d0 E8 ~: R7 b8 l3 r 7 m7 O. t) _& x0 y + T e* P1 K# T& M, g ; k8 q" r2 c" k8 C, I " P( k% S. c$ l3 Q5 @4 {4 k3 a A2 R- j _; J. k0 S! B ; W' P0 ~( @; d; l9 h ' j X; A' W% n# ^5 d: O 326000647688 9400000000000 0.9533949169 ]9 V3 e! p1 d- A ( J) H( ]0 o9 O9 Q a' w) J6 j 332693561966 9600000000000 0.953399676$ G( e; ^# p5 D* H 336038264769 9700000000000 0.953402105, X! X, p# G4 _8 }. P! ~ 339381817251 9800000000000 0.953404747 Y$ C% W$ U5 n9 b, L4 d, Y7 f t9 `: y7 E& X- I 346065536839 10000000000000 0.9534119962 o6 y+ `% q, \, J8 K 379418886337 11000000000000 0.9534386216 f) ]8 M' ?9 E3 u 1 `! s8 M% g, J$ a: M! m1 w 643217611048 19000000000000 0.9535967539 _% N3 [' B, k6 J8 W" q' N0 a 1 W k" p) j* F" F . C s- q) ^$ A4 m3 G* d* G- ^ 0 e/ T+ O$ ?: e2 h q$ a. A - a! c7 p6 [* z4 q0 x+ E1 `; [5 r 0 p2 P% o" }) d8 o+ |( o+ b 932911185326 27916701633581 0.953711916) ^! { j U+ g/ t, |$ e% ? 967879555617 29000000000000 0.953724541, j3 P ^; c- P$ { 1000000000000 29996224275833 0.953735935 ]) J+ b& b$ z1 z2 O3 f3 T 1000121668853 30000000000000 0.953735897* T: R% K0 s+ h, Q : [' t ?; z: K+ t0 A 10000000000000 323780508946331 0.9545371174 o F K6 X. c " \. x7 _3 T9 Z/ ^" Y& H# a! R 8 _# {4 B" d* b# J) O' Y( Z+ v 279238341033925 10000000000000000 0.955833997! }6 I9 ~' z$ \1 j; r - V' `% s7 {; R- e/ I x . `' z' |! l6 j$ a4 p' m! O 1075292778753150 40000000000000000 0.95638055' Y- r' C* w# I( E, I9 G ( c: z( ?: a; e" s( y- o0 E) } 3893882469583623 150000000000000000 0.956905884, j" [* q9 F, i& l; B& v- R/ r ' T V/ p, Z) R' @+ B+ T& s0 d7 y% q 7 s+ F% e, p* P/ z' M1 }' ?7 l / |" R, s/ L! n- H; L0 L6 r- X3 J! c / m0 Q! m6 D; {, \ 1 V9 w8 O: g. L 5 g' [+ H" A" ^% w ' A& J1 E: Y* q$ s8 ^: a " |: O3 M, {8 O4 T 165220513980969424 7000000000000000000 0.9584286469 k, [1 M W8 ~+ i% e) M, S3 | 188229829247429504 8000000000000000000 0.9584809869 [6 W) C' R3 _% W6 ^( j6 K& c2 l 211172979243258278 9000000000000000000 0.9585271# S3 |9 f* |) v 234057667276344607 10000000000000000000 0.958568315 I8 n, W8 _$ _- Y; G& j # y G: C+ b0 L( q; x 684559920583084690 30000000000000000000 0.958995813, Y, O' L& o9 b8 r8 P& F4 n; [ 706849401776940275 31000000000000000000 0.9590085041 i" t9 H" x) z! }& D; x1 g! {4 o. {/ X 1 J1 z6 n( m; `5 J & }' d# r; B+ k. K9 N: c# ^& z! M! ` 1127779923790184543 50000000000000000000 0.9591930558 \" ^6 W/ F1 R/ D % Z0 G; Y0 d" J9 B6 C9 V 3516585752930430595 160000000000000000000 0.9596381552 L# p& T2 i5 b" R$ _2 G 6 ]9 G6 \8 d) ] ' R* d1 B( [- x2 T4 y0 @9 I 4374267703076959271 200000000000000000000 0.9597228713 a% A# M6 T: `; s1 {2 g 4588082544160859769 210000000000000000000 0.959741366( s! {' d0 t$ d! f# }6 |9 q4 {1 l9 ? . C8 f( a9 r& a& b 5866733862193360875 270000000000000000000 0.9598364543 ~4 ~2 {$ l, j: z3 c" K+ Q4 l0 s 6503696293016202398 300000000000000000000 0.95987623' m4 v5 [) d- s/ N , V$ i1 ~- R$ w) _, {8 f$ e1 k 6927578466326617308 320000000000000000000 0.959900571& L9 K: w+ L. x3 A) g 8617821096373621600 400000000000000000000 0.959984581; u6 W2 F& D2 K. `% s+ r 10000000000000000000 465675465116607065549 0.96004168" X. Q6 e! i% G 10720710117789005897 500000000000000000000 0.9600683551 B$ Q" J6 q5 a; E" C9 H/ ^! c 6 N) q' R1 G: m, ^# i$ c 21127269486018731928 1000000000000000000000 0.960327059( V5 F! W; A( U0 ` % @; h/ r, @- r( [ 82103246362658124007 4000000000000000000000 0.960837349 K) ^" M0 K- z2 \0 M - r0 }5 ^, d$ M( l 201467286689315906290 10000000000000000000000 0.961169232) B1 q( ?1 Y$ M$ B. [- t - u) n0 o" H, T9 r5 v 397382840070993192736 20000000000000000000000 0.9614173853 t5 x) y& I' t& G7 ^7 T2 c" N' ?6 Z, U 783964159847056303858 40000000000000000000000 0.961662996' v- H+ X. E, C# A, V/ D" }9 s 1925320391606803968923 100000000000000000000000 0.96198374/ t; U0 i1 a# |8 R( t6 M 18435599767349200867866 1000000000000000000000000 0.9627698282 X5 U z3 P( D; Q1 a 176846309399143769411680 10000000000000000000000000 0.96352742281009973617214866335650. l3 D& ]$ ?; s7 {! ^ o 1699246750872437141327603 100000000000000000000000000 0.964256911769038367410632552188604 B' p s1 m. [ U# j ( `& K8 ^ e( U, r$ I8 @. \2 l! X7 m 3 U; } }* g2 m, l' l9 A- A3 x 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?9 ~) u; g Q% o" k % O% N$ p8 d1 b
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发表于 2018-6-5 22:02
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