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数字的奇妙:素数

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    2015-10-16 12:37
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    发表于 2010-4-13 11:41 |只看该作者 |倒序浏览
    |招呼Ta 关注Ta |邮箱已经成功绑定
    本帖最后由 clanswer 于 2010-4-13 11:43 编辑
    % k: [' r" W  f9 d) }2 T  m& q% j. l) f- k
    以下是目录,如果觉得合你胃口,可以在后面直接下载附件。
    Entries A to Z.
    8 t/ a; G* l! U- ?- y2 W9 I' pabc conjecture. ' ~0 _0 L* u" @8 l8 ^
    abundant number.
    - x4 r/ ^) V7 t  ~, e8 i% Y5 |AKS algorithm for primality testing. ( l5 L% r, x6 N7 W" C8 Y- t+ Y) i
    aliquot sequences (sociable chains). 2 o# e6 ~1 h% g+ W
    almost-primes. , w9 l4 O* E) R* Q
    amicable numbers.
    7 h  ~0 Q# z5 A" e5 T% Wamicable curiosities.
    ( r3 p' r" U5 q9 _; k9 {Andrica’s conjecture. . D$ F9 h3 I  A8 w2 F% g! q3 `
    arithmetic progressions, of primes.
      v4 {2 J' _" }: ^* oAurifeuillian factorization.
    # h# V( ]# R0 S/ k5 w: D6 Faverage prime.
    6 |* g" E: T" Q: K' B' |8 JBang’s theorem. ; H' p* ]$ w9 z% C" _/ y$ ?/ q' {
    Bateman’s conjecture.
    ! e! e/ ?$ `1 J' VBeal’s conjecture, and prize.
    # w  d! N0 z: t  f  p  J, IBenford’s law. 3 h" O# R# i, L* m1 G  y
    Bernoulli numbers. , ^. L. G9 c) c  a2 {
    Bernoulli number curiosities.
    3 Z# G6 m) s' \' o/ fBertrand’s postulate.   u  E- U( `  c+ A5 X
    Bonse’s inequality.
    8 [' i7 i8 `( Y! f/ d/ u; ~, r4 GBrier numbers.
    & r( O6 J* A, L4 a# K1 U0 aBrocard’s conjecture.
    ) ^) c& v* D4 VBrun’s constant.
    7 `4 k/ x; T( G% l. \Buss’s function.
    & j$ E) n. u/ r6 oCarmichael numbers.
    + p8 A4 d1 r* jCatalan’s conjecture. ) p& W# h3 U+ S/ C1 l, ~
    Catalan’s Mersenne conjecture. 2 o) G1 t8 k8 v9 ~! H- O
    Champernowne’s constant.
    6 B4 {5 H/ c3 K. ~# ?; nchampion numbers.
    ) @# p3 m" k! eChinese remainder theorem. % G8 K. f/ T$ r  y0 t
    cicadas and prime periods. 2 T. I5 b$ N+ X* V
    circle, prime.
    9 ^0 X5 B0 q/ |  Q- Ccircular prime.
    1 a/ g  s" L; E  i0 kClay prizes, the.
    / O% C9 t+ |2 d) Mcompositorial. ' ?, \; K3 Q0 b' i
    concatenation of primes.
    - c* V2 z. F* j9 B0 L4 |conjectures.
    % a  ~+ f, v% B6 rconsecutive integer sequence.
    8 k$ }5 q, Z( L1 |  V. ]3 `consecutive numbers. * J% r9 R9 S; h1 Z- Q) n- V
    consecutive primes, sums of.   i' u4 Z: r& q9 r" p
    Conway’s prime-producing machine. / s( ?" f/ E# T6 [
    cousin primes. / z  F  W2 a* s" Z( K% }2 k
    Cullen primes.
    # A$ V( u) X- h) J; dCunningham project. ( B! b2 o, I. |/ ]6 N
    Cunningham chains.
    : T8 ]1 ^, }5 h; d( Ydecimals, recurring (periodic).
    3 u3 o2 @( W0 W, y: F) Y  I" Zthe period of 1/13. 1 |( R  G9 P5 m8 Z1 ]% T) e
    cyclic numbers. 1 x1 N8 M& s7 `* d7 ?6 q
    Artin’s conjecture.   s! J' M- R9 [: I. G1 L
    the repunit connection. / x) L0 G/ \3 ?
    magic squares.
    # Z0 F6 H: k7 m$ d' P7 Cdeficient number.
    . E$ P" @! v8 W$ F, K' U# tdeletable and truncatable primes. 6 `6 I, s5 g! R1 _& X) i' Z$ i8 w( g3 K
    Demlo numbers. 9 c% [; R6 @0 f) i
    descriptive primes.
    % g) T! J  L' t( VDickson’s conjecture.
      H5 O3 i8 t6 [' G+ D( w7 Bdigit properties.
    6 W* y8 w& H  h- O+ c: kDiophantus (c. AD 200; d. 284).
    9 y  J: {5 s1 Y4 C$ J+ F- jDirichlet’s theorem and primes in arithmetic series. / E" c  e) t6 r% G- t2 R
    primes in polynomials. 3 |/ Y- m& H( a9 r$ P3 _  ^
    distributed computing.
    0 W) H; Y0 Z* ~' w- L  W- X4 Sdivisibility tests. ; ^9 p; q) u- U
    divisors (factors).
    ! P1 K- ?. s/ f: c3 U8 {9 _4 ahow many divisors? how big is d(n)? ; r; E6 E7 n  V8 n
    record number of divisors. . ]5 a/ W1 M, K
    curiosities of d(n). & |: v) E3 K& y# V! Z
    divisors and congruences.
    6 n, d8 F' K4 W% T3 y& zthe sum of divisors function.
    , G6 m1 U- v, p4 `' ^3 T/ \; tthe size of σ(n). ' o- c7 K2 `% T# S
    a recursive formula.
    + ?, }& s2 }# j9 i9 f% sdivisors and partitions. 1 x% }& J  f( [/ ]0 `5 A7 d
    curiosities of σ(n).
    ) V- @* N0 A) s5 t  fprime factors. 5 s0 q( u6 }2 b+ S- ^
    divisor curiosities.
    , c& p6 @& Z5 veconomical numbers. 2 Z! @2 S) q0 P! M- R
    Electronic Frontier Foundation. 4 f5 G# S4 o. c) R( e
    elliptic curve primality proving.
      e# |1 o" C% `' B  M( w( j5 |# ^& Kemirp. ! y1 d- p* c1 r. W
    Eratosthenes of Cyrene, the sieve of.
    0 ?. B0 c) M) L8 Y  ]# dErd?s, Paul (1913–1996).
    8 ~9 l+ R% f1 this collaborators and Erd?s numbers.
    ; @. ^+ P* O' b" X. w9 d4 Xerrors.
    9 j0 ]" F& }; I* }5 `6 ^7 ~Euclid (c. 330–270 BC).
    1 ^' ^: C8 J4 Z9 X" p( Hunique factorization. 4 u$ d- R. z" y! M' D2 P
    &Radic;2 is irrational.
    9 O" |- L. S* p! K8 g) e2 b) hEuclid and the infinity of primes.
    0 V3 g3 E0 y5 O! t, Nconsecutive composite numbers.
    : n; ^- v% W& n& N: t+ }  Y& Nprimes of the form 4n +3.   L" K9 p/ w9 D# q# T* f
    a recursive sequence.
    7 K( ~, k: _/ J6 N" ZEuclid and the first perfect number.
    / t0 C- c# L" s. `) x% I4 MEuclidean algorithm.
    . A1 e% E- T7 I! j0 i1 c* JEuler, Leonhard (1707–1783). ) u: c9 ~* }$ l( Q! S8 ?
    Euler’s convenient numbers.
    9 R5 F; M: E0 q- ythe Basel problem.
    - ]% G7 @! ^# iEuler’s constant. 7 _3 u8 L) J6 ]& ?( h( ~
    Euler and the reciprocals of the primes. 0 \0 q. G- J1 H4 q% F* E5 v
    Euler’s totient (phi) function.
    3 e/ R8 t6 m0 ^$ xCarmichael’s totient function conjecture. 9 ?! _* b+ U" i: G& n) x
    curiosities of φ(n). ( u8 e0 g4 u% S
    Euler’s quadratic. 2 {: o% J) m" p+ q  t  V4 o
    the Lucky Numbers of Euler. 9 B! l( m3 ^  {3 B
    factorial. 3 F5 y4 E' D& ?8 U9 G* G3 i
    factors of factorials.
    0 i) o& O7 P% zfactorial primes.
    . O1 X8 u9 d3 N1 C% A$ _factorial sums. ( K4 c' L7 c4 G  g. k
    factorials, double, triple . . . . ' |! Z& M$ o+ T4 ]8 R. V" u+ b9 V* o
    factorization, methods of.
    ( B. E* F* C6 F3 Q1 D" z  ~factors of particular forms.
    : p5 d2 }1 _; F! C1 qFermat’s algorithm.
    1 K9 H( ]% F8 [* X4 S7 E% wLegendre’s method.
    9 d$ v9 C6 M5 N2 Wcongruences and factorization. : a  g: O7 ]' H8 r# o
    how difficult is it to factor large numbers?
    0 j3 o1 v8 n% r' I+ w* C# lquantum computation.
    7 \- V+ L( \" M* f# `Feit-Thompson conjecture.
    5 Y; k& |5 k: Z5 \Fermat, Pierre de (1607–1665). , @7 T4 g) W. L' K. H1 `
    Fermat’s Little Theorem. 3 c8 \# ~+ ^" [4 x
    Fermat quotient. . K$ L9 r' S8 g, O0 y6 I
    Fermat and primes of the form x<sup>2</sup> + y<sup>2</sup>.
    : R4 m! H* Y( Q' W. |Fermat’s conjecture, Fermat numbers, and Fermat primes.
    3 ~+ ^- E1 @0 S. ]Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>.
    # Y: R. {& `" AGeneralized Fermat numbers.
    , p7 {6 X2 C. b, }/ q2 sFermat’s Last Theorem. 3 I, _% e5 P, E4 d! s# H
    the first case of Fermat’s Last Theorem.
    7 h9 E7 Q$ l; m- F2 x+ pWall-Sun-Sun primes. + h7 X% }0 N+ b9 l. g; y- ^
    Fermat-Catalan equation and conjecture.
    , ?& V+ z1 A+ b7 KFibonacci numbers.
    0 `2 A7 L% n' Q7 A* U4 R6 }divisibility properties. 2 t% x$ W+ i* M- y) O( e. f
    Fibonacci curiosities.
    ( D8 X9 l! S" `6 N4 [édouard Lucas and the Fibonacci numbers.
    : Y/ P! R9 r9 _/ n+ C$ k- x6 \Fibonacci composite sequences. - P3 @' q1 \5 W) Y1 Z. N
    formulae for primes.
      I5 v8 ]! y( {7 [) }( f" zFortunate numbers and Fortune’s conjecture. & K# P+ u: m! P
    gaps between primes and composite runs. 4 u$ a3 `6 V: Q3 |2 R- i
    Gauss, Johann Carl Friedrich (1777–1855).
    * e- _3 h& }5 {, f7 LGauss and the distribution of primes.
    ( M3 N3 u9 e& {8 cGaussian primes.
    7 i4 r0 Y7 @9 ]Gauss’s circle problem.
    - x" o3 J7 j* c, f5 F* SGilbreath’s conjecture. 7 c1 q6 |1 ~4 A/ q
    GIMPS—Great Internet Mersenne Prime Search.
    ( H/ J( r# ?, v% T  qGiuga’s conjecture.
    9 L+ c5 v! N% J4 s5 ]Giuga numbers. # P* ^) T+ v$ x: W2 P
    Goldbach’s conjecture.
    7 L, L3 J/ a' o: Qgood primes. 9 x3 g3 e  ?: w) C5 ~6 |: G
    Grimm’s problem.
    0 X/ T5 r* v7 JHardy, G. H. (1877–1947).
    # g* g# }% x) M; u0 Q# q& S7 X' Q7 UHardy-Littlewood conjectures.
    + `- p1 f0 O7 m% F& vheuristic reasoning. / y3 h* l& s, m* I: ^1 _
    a heuristic argument by George Pólya.
    & }' }& C  n$ E* u; B% e- uHilbert’s 23 problems.
    # a: A. `7 }* U& A" s% \5 e1 _home prime.
    : i( y- ]8 C% m+ Bhypothesis H. 4 t& U. |2 O' W! ?7 R7 t0 u5 Q
    illegal prime.
    * c& K; s: E; L+ S3 I+ o$ ?$ yinconsummate number.
    3 e/ N  S. y. o* `. F- ?4 o9 Oinduction. , _$ W" T. m& Y% W1 Z
    jumping champion.
    8 \. N5 W4 \1 I' c8 yk-tuples conjecture, prime.
    " _/ E7 Q7 W4 W" g- k3 @' {5 Eknots, prime and composite. : k' O3 H1 @3 U: L) M; Z; t
    Landau, Edmund (1877–1938).
    ' x3 W4 D1 ~* v9 E; eleft-truncatable prime.
    6 V+ Z; O% e7 K4 X5 q4 ULegendre, A. M. (1752–1833). ! N* o1 W1 R' `& F/ ?  R4 d4 y
    Lehmer, Derrick Norman (1867–1938).
    $ K/ }( B4 ?( r' Z" p! e! R) bLehmer, Derrick Henry (1905–1991). 1 o3 a/ R, [1 {! z
    Linnik’s constant.
    / |7 i  w$ o, u1 T6 WLiouville, Joseph (1809–1882). " b2 b5 E) e0 _
    Littlewood’s theorem. - b, C- }/ r% D
    the prime numbers race. 4 D( L& p" F! v! `2 T
    Lucas, édouard (1842–1891).
    ; e5 z3 E# c3 m  d7 cthe Lucas sequence. 6 P) [, K- }  M3 w
    primality testing.
    / R! o  V  D: [5 l+ p8 K' fLucas’s game of calculation.
    5 h( b9 w6 g' x7 S: Bthe Lucas-Lehmer test.
      m! P* L& {; ?9 B: f5 @8 }: vlucky numbers. / s! ~: e' d# h' h3 h5 L
    the number of lucky numbers and primes.
    6 c- I- N! N& i“random” primes. 0 h* V; P* E, o! e- W7 Q
    magic squares. 5 H8 F4 B9 B1 }- M
    Matijasevic and Hilbert’s 10th problem.
    : w) V( ]+ r% H' t+ h: h3 S0 IMersenne numbers and Mersenne primes.
    ( c% x- W7 P0 B+ xMersenne numbers.
      K8 t3 Z( u+ e$ G6 ]hunting for Mersenne primes. 0 l7 W( }: ?0 Y/ P* a9 n
    the coming of electronic computers.
    , @' Z4 f7 N0 {, d) h# eMersenne prime conjectures. 8 X6 E( @) |) E  }# _, J- _
    the New Mersenne conjecture.
    + g( \8 B8 O0 N4 n1 |how many Mersenne primes?
    : c$ o4 \, e, ~& F3 kEberhart’s conjecture. 3 P" `' t# m( B8 @" j* l: p: G
    factors of Mersenne numbers.
    5 _- L; H+ d8 c! a9 c; iLucas-Lehmer test for Mersenne primes.
    , n9 T3 f  t* H# e9 R4 G$ TMertens constant.
    . M$ v7 x9 Z) l: l# Z' WMertens theorem.
    " u2 ?+ {9 d: c4 i. m* CMills’ theorem.
    4 J. f# a) ?0 N9 h. N% rWright’s theorem. 1 T9 X' a: \6 H: P0 o
    mixed bag. : o; s, s0 P  t1 b, ~8 N% R3 Z
    multiplication, fast.
    . w4 I; [2 O8 H. z9 k+ |+ mNiven numbers. & ~: X; H* I( \0 L* W; U+ M
    odd numbers as p + 2a<sup>2</sup>. 8 c2 M. M2 z1 r' A7 `3 `
    Opperman’s conjecture.
    ' D& G& f, w1 |& s+ i) Vpalindromic primes.
    5 C' M( y/ @/ L, v4 g$ Lpandigital primes.
    * t/ Q5 k/ Z6 f0 e# \Pascal’s ** and the binomial coefficients. 7 I3 E/ v7 ]' R/ w( h& l/ c
    Pascal’s ** and Sierpinski’s gasket.
    * T) k; Z, L6 y; k0 G5 N5 ZPascal ** curiosities. ( p+ m5 ]5 B+ ]4 @/ c6 s- |
    patents on prime numbers. 8 M1 q* u/ d) ^+ D  c- Q. q* t
    Pépin’s test for Fermat numbers.
    7 R* s" X' q! k! F" Uperfect numbers. 3 [: u# O& b2 w. K  {
    odd perfect numbers.
    0 [$ _2 D! f- h1 Kperfect, multiply.
    3 V2 h& y) s# }" A/ C: D! hpermutable primes. ( b. g8 ]; E( I% q4 F
    π, primes in the decimal expansion of.
    % f  Y( m: W- ]! U5 ^  I4 hPocklington’s theorem. 2 M$ [& [2 E- @% a( V
    Polignac’s conjectures. " Q( Z  f; ^, S. h
    Polignac or obstinate numbers. & f* Z3 q3 @1 g5 ~
    powerful numbers.
      e, _: h% f0 jprimality testing.
    4 ^  n) _, t0 O' a& ?/ y+ d7 A& x  ]probabilistic methods.
    1 h7 r' W/ G% G/ @3 G  V) @prime number graph. 2 S, S& s( C- `* |
    prime number theorem and the prime counting function. 6 r" s6 O4 @" n/ d
    history. 8 e/ r+ S2 F! X6 E
    elementary proof. " y! F) P6 h9 I- L: O* ^
    record calculations.
    - ^: A8 e/ S( g% D, R+ f3 gestimating p(n). 4 ^" }- ]1 @- G# h/ f- j" o
    calculating p(n).
    + \" B$ w9 Z/ X$ }a curiosity.
    + D8 d8 n: N3 Q8 d& \. {prime pretender.
    6 }: F( y+ X8 Dprimitive prime factor.
    ! g0 M. I$ U4 A8 s/ W- z' sprimitive roots. " \! N- }4 d1 C+ _0 T/ J# b3 {! ~2 P- m
    Artin’s conjecture.
    9 B; o, d( t- ?) h9 r. wa curiosity. . {2 C% \) R# V$ N5 S
    primordial.
    . m, K+ a0 M% jprimorial primes. / W4 c9 }0 p6 \, q6 U4 A
    Proth’s theorem. ( V. E2 O. d9 F. M8 b
    pseudoperfect numbers. 1 b2 `0 W8 g5 i8 C1 o
    pseudoprimes.
    & B. L% l: T- K1 U7 _6 Fbases and pseudoprimes. $ D0 w* @' D. @( t0 Z2 K& h
    pseudoprimes, strong.
    8 e1 r7 o) ]5 x4 L4 x( U) Kpublic key encryption.
    + B0 _- S2 ~/ H, i2 [pyramid, prime.
    ) A3 r% P+ N1 t8 J/ @Pythagorean **s, prime.
    - E% c& Y2 w5 m$ l/ dquadratic residues. ' [+ d% z. O* p( Q8 m
    residual curiosities.
    ) O8 B3 u( `- Q# O; Y9 ~polynomial congruences. ; v: A. Q9 W% }5 Z6 T/ G- q! ^' F
    quadratic reciprocity, law of. + u+ a& U3 Q+ g1 L# e9 R  _0 }
    Euler’s criterion.
    6 N  f, ^& s" o1 ]/ wRamanujan, Srinivasa (1887–1920).
    8 I" C2 _# c  p0 {/ t& O( Yhighly composite numbers. 9 j; Z- ]2 I1 r+ Y' Z
    randomness, of primes.
    $ C8 _, Q5 H" [8 x; x* p5 }Von Sternach and a prime random walk. ) ?/ l. j) X5 L, K" q, F! V( s) s9 V
    record primes.
    3 ~6 a2 Q) `0 i# E6 |some records.
    : T- W7 v6 `- _repunits, prime. 8 F; N7 U! f' ]! H7 F
    Rhonda numbers.
    : T" P  |. P0 ]2 r* PRiemann hypothesis.
    : ]! X2 M9 s$ b. W; i, I9 ^  l! Ethe Farey sequence and the Riemann hypothesis.
    ) }$ ~/ F, ^0 d  J$ z5 mthe Riemann hypothesis and σ(n), the sum of divisors function. 7 t2 B% {1 B, y# f- S  `3 E
    squarefree and blue and red numbers.
    4 [0 A7 W5 ?' e' r% sthe Mertens conjecture.
    " E+ D0 n! F& f" h" ERiemann hypothesis curiosities. " P$ S0 D6 f" f; [3 G
    Riesel number.
    & b  e' Z; D* Y( N  A7 jright-truncatable prime.
    " C0 @2 |9 F: x0 yRSA algorithm. / H! ]# z( @+ X1 P# Z
    Martin Gardner’s challenge.
    ( A- @, k) M( Z+ XRSA Factoring Challenge, the New. 6 i0 J5 O8 Z3 D3 e! |+ U( m# c  B
    Ruth-Aaron numbers.
    3 V8 O# s4 \0 o9 a# y0 VScherk’s conjecture.
    . L* {+ l: J/ m- wsemi-primes. ! m/ O) e% T2 E& P! [
    **y primes. & {, q* s2 }$ _+ Q- m0 g
    Shank’s conjecture. ( k; q  t! J& q
    Siamese primes. 7 l" L$ y, w) {
    Sierpinski numbers.   G% T, j& m% @9 Z  H+ m: [
    Sierpinski strings. 4 X  w) Q# A- L$ T& f
    Sierpinski’s quadratic.
    . g. z6 m: p  I  k( MSierpinski’s φ(n) conjecture.
    2 |3 N" R* Q/ Q1 K* p" M3 K1 g* rSloane’s On-Line Encyclopedia of Integer Sequences. . G8 z5 L/ G/ \4 w1 C: P0 Z6 l6 \
    Smith numbers. . \8 C' ?7 b$ ^8 I( u1 p: v
    Smith brothers.
    5 @0 A" z. v1 ~' T" z, l: O) I8 J* ksmooth numbers. + G$ _# R  k2 @- _; I5 v
    Sophie Germain primes. ( ]" j7 O; W1 k
    safe primes. ! P& X$ a- N+ U7 d" a2 g5 i( n
    squarefree numbers. % N$ k6 @2 a& d8 r3 [! b% u$ s
    Stern prime.
    ' H" c/ u2 O9 f! J2 {strong law of small numbers.
    : s* o) N8 a7 N& y5 T. _triangular numbers.
    . Z  U& ^$ p; h) Etrivia.
    2 O7 f1 m* g2 g/ Itwin primes. / M  r8 _& S! E* ^1 k
    twin curiosities.
    3 G0 |% r: V4 v2 a5 ?. ZUlam spiral.
    2 I/ f7 w3 m3 C0 q4 }unitary divisors. 4 d% g. ]7 O) R/ O3 J; i
    unitary perfect.
    & Z% m: t1 l7 X$ u4 D: {' x3 Duntouchable numbers.
    ! R6 V( i6 [0 y+ u0 b2 Dweird numbers. . b8 f/ l5 D: I+ ?. I( C8 j
    Wieferich primes. 4 ]7 q1 m9 T$ f, h2 m2 e
    Wilson’s theorem.
    " @. R2 a# ^- q+ S0 |6 y: u7 ~  \twin primes. ; A9 B5 E+ g2 P* C
    Wilson primes.
    $ v2 I4 W/ ~: T' L& D7 N# ?1 a8 RWolstenholme’s numbers, and theorems. 0 w8 ]5 O; H. w* D
    more factors of Wolstenholme numbers. " s/ ~! x! ~/ J# U- H* I* J
    Woodall primes. ' K" n+ D7 t) o$ h4 d
    zeta mysteries: the quantum connection.

    ; o9 U8 R/ p4 ~$ _' X& h; `+ U, r4 E# G
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