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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
    9 _  s! I: k) b" Y9 _& l- J: m
    ( i3 H2 R, \% i0 B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. / I, v6 I& S: i; d1 d' i: V
    abc conjecture. 0 @4 e' K, M; g. N6 G9 _$ L1 `- ~
    abundant number. ( u, K- n$ J& \6 T. U2 t( i  V" J
    AKS algorithm for primality testing.
    : S( G" N4 y  B* h$ y- Waliquot sequences (sociable chains).
    ) {4 u  o, a- Talmost-primes.
    " m* ^* F: `. j. M  namicable numbers. ) a5 u/ G6 i8 C
    amicable curiosities. ( u* ^8 l" ~4 u
    Andrica’s conjecture. ( G# `  f; d% ^; w9 ?. |- T
    arithmetic progressions, of primes.
    9 Z* g3 o! C6 w% b& JAurifeuillian factorization.
    6 d; M0 X6 @+ V& F$ {* ]  J6 ]average prime. * ]3 o8 I6 G4 ~3 S6 X* p" ?1 A8 M
    Bang’s theorem.
    6 J8 ~. z5 N$ b1 F3 j5 KBateman’s conjecture.
    # g7 v( w* L& r: f, t/ d6 mBeal’s conjecture, and prize.
    * G& z4 H+ e, r% b8 ~Benford’s law. + v5 D) A8 u3 g6 D
    Bernoulli numbers.
    % q' y) |# [0 b% f  eBernoulli number curiosities.
    8 X5 D+ f2 f7 M: x- h, W; }) c8 xBertrand’s postulate.
    5 ?+ K  {4 l! l* t! y6 wBonse’s inequality. 0 ?$ d2 Q0 t  u+ c' j
    Brier numbers.
    1 m& w4 m" @/ I$ z+ Z5 IBrocard’s conjecture. 3 K0 y/ P3 N& i, D3 f
    Brun’s constant.
    ' }, ~& Y; [, vBuss’s function. - _0 H- y$ Z' u% F0 w
    Carmichael numbers. ) k- P5 z( x2 ?% }2 @0 F8 e# m
    Catalan’s conjecture.
    * T! [; a+ n% L* C; B7 ACatalan’s Mersenne conjecture. ! T. e* c! v, U9 ^+ o
    Champernowne’s constant. 1 y% \9 ^7 N9 J' F3 `7 {; J
    champion numbers.
    / R! D* `4 I8 g# D+ d4 `Chinese remainder theorem.
    7 e. `  j; d# ?+ Z6 f6 t2 K) ~cicadas and prime periods.
    . }. b9 c  p8 j3 j' Bcircle, prime.
    , b6 {/ o1 s5 Dcircular prime. 7 Z: O1 J: Y/ z/ W  _
    Clay prizes, the.
    5 t* J4 O' T) C# I) t& W) |compositorial.
      h2 C8 p" S  L& ?- |concatenation of primes. ( l% Y7 F& R7 p' \* C3 _* ]+ G
    conjectures.
    3 |3 n+ \& o( x* ^. Yconsecutive integer sequence.
    - j: j( v; |* x! m; Z% N9 ~0 V! Kconsecutive numbers. ! I5 \6 }! f- U: e
    consecutive primes, sums of. ! `* W- O5 S6 i; k/ \
    Conway’s prime-producing machine.
    ) j. P( L* v" ]: p. L/ ecousin primes.
    & Y" P- ]* U+ R+ X1 u: A1 UCullen primes.
    , X6 |/ O7 c' XCunningham project.
    + c! z! C* ~7 \1 E4 }Cunningham chains. ! T: W# H; R$ t9 S
    decimals, recurring (periodic).
    , a) ~! w/ g& hthe period of 1/13.
    0 `( j, v# ~0 k6 c# p8 Fcyclic numbers. : E' i3 }; s7 w7 @4 r0 [
    Artin’s conjecture.
    ) l6 P/ ^  A" G5 o' Pthe repunit connection.
    " D$ v2 l% F% K. j  Umagic squares. - B. F: W* o- U/ w6 T; `
    deficient number.
    ( U1 `' d+ _! A, t/ m# `) mdeletable and truncatable primes. ( a1 }) A1 m: `! R2 r1 x* \
    Demlo numbers. 6 A$ ?, ^+ y6 ^/ t1 b5 R7 ^( D
    descriptive primes. / @$ x* F. S1 a$ d
    Dickson’s conjecture. # q5 V- d! O" n, U+ n$ s1 B
    digit properties.
    3 D3 Z& I) ?' \Diophantus (c. AD 200; d. 284). 6 O$ F0 S9 Q; c( ?
    Dirichlet’s theorem and primes in arithmetic series.
    9 s  B7 ~0 C. l% Yprimes in polynomials.
    0 k4 w$ g  \) k/ r0 @distributed computing. 7 A8 @8 G, [' h3 w$ r+ Z
    divisibility tests. 1 Q/ y' {2 c! X" Y. I
    divisors (factors).
    8 z/ `; U  i% U2 U2 d. C8 Q. Rhow many divisors? how big is d(n)?
    6 e: E% J8 a) c# e7 I/ crecord number of divisors. 5 N) H+ `! O3 I7 ?
    curiosities of d(n).
    ; ^  T" {; ]6 a' g1 vdivisors and congruences. 3 V9 h" b9 @$ M" Y% |
    the sum of divisors function. ' ]/ X  r+ p8 W2 F" V) I. J5 ~
    the size of σ(n).
    . g  A2 Y* D7 q* D, v/ ba recursive formula.
    0 m) d6 I' N$ {+ G6 ~1 ndivisors and partitions.
    9 f# v5 H* ^( ocuriosities of σ(n). * h/ k- `; k9 L
    prime factors.
    ! Z& Q' `7 x$ |7 e( Fdivisor curiosities. ! `# `/ Q9 I. i- O/ v& e
    economical numbers. ' Z- X2 d* l/ Q+ U
    Electronic Frontier Foundation.
    . E) z8 }( g: W, ^% \elliptic curve primality proving. 3 T( Q/ a6 h7 K# T/ P2 L: u
    emirp. & m$ W: o8 w1 r" c0 J/ @' g: J
    Eratosthenes of Cyrene, the sieve of.
    - }- Y2 P6 o3 f4 I4 eErd?s, Paul (1913–1996).
    ( ~9 ^  m" w! b- ~his collaborators and Erd?s numbers.
    3 F, V! n. l3 S9 s( Z8 m% Merrors.
    * l1 i1 O' A# J9 z& o7 p# k1 C5 FEuclid (c. 330–270 BC). $ }* D2 f4 i; A' q4 U* N$ y
    unique factorization. : o0 k. P0 Z; @# ]& h
    &Radic;2 is irrational. # A+ r0 b! P8 P# \- w
    Euclid and the infinity of primes.
    % d) s  ]2 k; b. Pconsecutive composite numbers.
    4 N) d5 ?  Q; W( d8 y% n  wprimes of the form 4n +3. ) @* F1 r& M- G3 M- G
    a recursive sequence.
    1 C. M5 ^1 U. m. ~; W, |, s5 N8 sEuclid and the first perfect number. 5 `8 z4 Y# b6 R1 y; o" B7 E
    Euclidean algorithm.
    ; C6 ~$ F5 Z5 ]+ AEuler, Leonhard (1707–1783).
    0 ^* v5 W+ J4 L( Z# s2 VEuler’s convenient numbers.
    6 b1 v3 g! h( m$ \" Athe Basel problem.
    $ ~% |/ y& y' {. B% `0 PEuler’s constant.
    8 A1 y1 ]# K1 b7 ^Euler and the reciprocals of the primes.
    $ a$ M) t0 d  V- [+ k; v: }7 bEuler’s totient (phi) function.
    7 g2 U3 L  F+ {+ n+ ?! Y4 lCarmichael’s totient function conjecture. , B* m) Z' v! }: @
    curiosities of φ(n).
    ( L0 W6 V' u# D& J# K( T' v. tEuler’s quadratic. 6 N1 ~. |" {3 C7 h6 D
    the Lucky Numbers of Euler.
    0 _4 B6 x" ^% Wfactorial.
    1 P# g; ^/ W$ cfactors of factorials. ' g& b* o, @( @
    factorial primes.
    + N7 Q' u2 x; A! ?; Sfactorial sums. 6 U  b, v/ h* ^7 v2 |+ {0 {
    factorials, double, triple . . . .
    8 {& \. h" [3 }- M$ `9 P5 }  d. xfactorization, methods of. 0 S5 B" n; J, G# t0 U+ U
    factors of particular forms.
    % v4 A& h" b! H: M( zFermat’s algorithm.
      a0 O1 c' r/ `6 sLegendre’s method.
    5 u1 `9 x/ j  T1 b# G& C4 k0 w; Lcongruences and factorization. 6 m& u2 j- I& n4 W% U, M
    how difficult is it to factor large numbers?
    2 r1 U8 x# t2 kquantum computation. 3 a3 V6 G+ f8 O  o- L% S
    Feit-Thompson conjecture. ; v( e9 K1 I) T1 _+ C) e; y
    Fermat, Pierre de (1607–1665).
    ! J# Y. c4 [/ D) QFermat’s Little Theorem.
    ( w/ b# a" n# w6 ?7 P) NFermat quotient. 0 |$ U! ?( F& m- r* O- J" h1 K
    Fermat and primes of the form x<sup>2</sup> + y<sup>2</sup>. + e$ Y. w$ W& |" A, I" h8 @
    Fermat’s conjecture, Fermat numbers, and Fermat primes. 5 h+ B( G5 [' v+ H7 O
    Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>. ! E1 X1 Q8 z- I7 k8 C; l4 @' `# C2 w
    Generalized Fermat numbers. " C* q; E/ w( ^
    Fermat’s Last Theorem.
    + J2 D: z; W0 q+ tthe first case of Fermat’s Last Theorem. ; A$ y% d3 l# l
    Wall-Sun-Sun primes. 6 s. c7 m1 S: r7 ^1 W, s  F0 w
    Fermat-Catalan equation and conjecture.
    : d3 j# A1 a( y2 Y* `4 B$ m8 dFibonacci numbers.
    * F* w) L- |& q1 ]divisibility properties.
    % W) T, G9 e0 x# u3 i2 QFibonacci curiosities. ( o* M- V6 |$ R; U# Y" t& g# p, Z
    édouard Lucas and the Fibonacci numbers. ) l, m7 i# \4 U- U% x* b
    Fibonacci composite sequences.
      h2 Z8 ?4 E3 j; J- zformulae for primes. + R  B9 a6 G7 _& ~
    Fortunate numbers and Fortune’s conjecture.
    + Q8 I6 u5 ^, R4 y( [% V: A2 Cgaps between primes and composite runs. : ?( ^% d( f% l) L- e# i& _+ |
    Gauss, Johann Carl Friedrich (1777–1855). % w5 ]4 |. t8 J1 q+ ?$ I
    Gauss and the distribution of primes. # t! u4 O) n( y$ p
    Gaussian primes. 6 M+ O- ?0 J5 p  T' h1 G6 x: V
    Gauss’s circle problem. ( m4 z7 w$ j2 ~2 _& o! Q; u. L% X
    Gilbreath’s conjecture.
    5 B: W; M. r) P, CGIMPS—Great Internet Mersenne Prime Search.
    $ m) T) z! L: v# U1 xGiuga’s conjecture. - y! E0 G1 T* Q. B3 u4 ]* h# i. n
    Giuga numbers.
    " }: k8 B7 `: n1 R# P' `Goldbach’s conjecture. ) e+ C* O5 E& X1 V- J$ o, V, x6 R
    good primes. : E. V, Z& y8 E9 J1 K2 Y; J
    Grimm’s problem. ! j2 ]5 a, }2 d% |% j7 D" l: z3 N
    Hardy, G. H. (1877–1947).
    + {  |3 o+ R- J+ P3 f' gHardy-Littlewood conjectures.
    4 |) V! q$ m+ K; n3 e% Iheuristic reasoning. 1 p. S% [# m. u) j/ t0 O+ X
    a heuristic argument by George Pólya.
    ! [7 x3 ~9 y; }: _* u0 H; cHilbert’s 23 problems. 8 d: R9 J9 K8 y) m6 J
    home prime. ' S, L2 i# [7 B" C
    hypothesis H.
    9 V! Y" O6 v1 Hillegal prime.
    / C/ f) e1 C$ V1 |8 m9 A7 Oinconsummate number. 1 }  X1 ?" y; i( O) }. ~' J
    induction. : K7 L& m( j) W- V
    jumping champion.
    9 P: C' p" F$ Kk-tuples conjecture, prime. : ?9 U! Q' z. a/ x6 m
    knots, prime and composite. % H/ O+ J' W8 }& |: L
    Landau, Edmund (1877–1938).
    $ i+ M( V) R+ Dleft-truncatable prime.
    + W; M; |( {! RLegendre, A. M. (1752–1833).
    $ V  h- j6 E, a  C3 W# t4 `Lehmer, Derrick Norman (1867–1938).
    & D; C5 A" T; x" x0 I; ELehmer, Derrick Henry (1905–1991). , g3 ?2 i; ?. R
    Linnik’s constant.
    . h& ]" X% a* |; i- i1 F3 JLiouville, Joseph (1809–1882). . S1 r7 a0 A( @; J1 m, n7 R
    Littlewood’s theorem. / [! X. x4 ~) f# U5 P8 B  H
    the prime numbers race. $ t7 h! m/ ?1 {/ f; f
    Lucas, édouard (1842–1891). ' K" z7 C" C4 h8 i$ r' I, \3 H! Q
    the Lucas sequence.
    & Z8 G2 L6 n3 L; n1 P/ M' ]+ j2 Sprimality testing.
    + L8 p" ^6 r. p4 @3 A7 aLucas’s game of calculation.
    ; [" j. \3 b$ f) \% C1 O7 `( M) ythe Lucas-Lehmer test.
    ' j2 n  r. T/ P- K* N# tlucky numbers.
    ; ~, L. Y# d& `' j0 d  V! S3 h. A: lthe number of lucky numbers and primes.
    % v- n8 I+ b$ }# M“random” primes.
    1 {  ~: ]% H4 T# M) t4 V: {( kmagic squares. 8 Q' m! B; T2 d4 d0 B
    Matijasevic and Hilbert’s 10th problem. 0 x+ T  y, s9 k5 N( h
    Mersenne numbers and Mersenne primes. 3 V/ @3 t% u) m, {9 t& b
    Mersenne numbers. 1 Y  n4 }- B( z5 R( A) f
    hunting for Mersenne primes.
    ' X" r3 g6 x3 R( w+ I1 z/ Mthe coming of electronic computers.
    3 V. O- j4 n: M$ N2 b) ~Mersenne prime conjectures. 1 z6 E: u8 a, \- A9 Y
    the New Mersenne conjecture.
    " N4 i% h. g/ l; I0 X) vhow many Mersenne primes? ( b2 i  ^; @7 M
    Eberhart’s conjecture. ( N# \3 a! j- l8 T$ C( g* O" B
    factors of Mersenne numbers.
    3 U/ j2 ]! M  M$ q* T5 h) f0 QLucas-Lehmer test for Mersenne primes.
    8 |* w' n! M& D/ s; h0 `Mertens constant.
    ' T2 r) }$ [9 U! S1 p' tMertens theorem. , `+ e5 \+ j' A2 v6 u
    Mills’ theorem.
    % m% i1 T6 A: [; h2 B" hWright’s theorem.
    6 C. ~& [* }$ i% f3 U) Cmixed bag.
    1 A" [1 N! F! f6 s9 d) A% omultiplication, fast.
      i& [. o/ N) P' O% xNiven numbers. 1 {  b+ X2 C7 V  A7 E9 G8 v
    odd numbers as p + 2a<sup>2</sup>. , c4 |- f" Q% l0 a: Y! o
    Opperman’s conjecture.
    % N% k0 C4 n4 W# q/ B& mpalindromic primes. . P. W0 b0 r0 e/ Y( ]
    pandigital primes.
    & A/ H6 n, c3 J$ }0 k6 Q: O; ]Pascal’s ** and the binomial coefficients.
    3 Y" X* o! A1 P. _  \: Q$ t7 Y; KPascal’s ** and Sierpinski’s gasket.
    & H( t- k5 i  k0 v1 q; tPascal ** curiosities.
    2 H3 b( T% i: B" x( \- \- Spatents on prime numbers.
    9 n- L% Q$ G( s; i  GPépin’s test for Fermat numbers. , ~  b7 U7 G0 w% t& x+ a
    perfect numbers.
    # c8 D. ~% V3 x5 x8 r6 @! Godd perfect numbers. 4 i+ z( L6 x  N+ Z9 g: V0 N
    perfect, multiply.
    4 a! X" z) P1 O% Q; X0 j! q8 f8 spermutable primes. 4 G; p# A! @  M* l4 y) R3 c
    π, primes in the decimal expansion of. ' S6 e, `% X& c& x, C8 G0 @* K
    Pocklington’s theorem. + d" R  j; R' l$ l  r4 T$ l
    Polignac’s conjectures.
    ( |! j. `9 Y" p3 P. v# YPolignac or obstinate numbers. $ e# o1 M" V6 ~0 {8 a! q
    powerful numbers.
    % ^0 ^. v- h" C9 Gprimality testing.
    : z) y, C- _" {' j# e( vprobabilistic methods. . H9 s# n" ]& y5 x* `. }5 Z; z
    prime number graph. # k* V/ _$ y! `
    prime number theorem and the prime counting function. ! U4 p( Q. E5 g/ N
    history. 8 N8 `: g% h( k
    elementary proof. 7 u( e1 G+ O( N5 y6 \
    record calculations.
    7 G$ T' E) R7 m; X* H( p% B# nestimating p(n). 6 T) `; l, R) o0 p& a! a" R
    calculating p(n). / A1 _$ Z4 ^% q
    a curiosity. 5 p' B" x' o' [7 _6 h# ^4 Q4 u
    prime pretender.
    8 B& G9 C2 [3 _8 m0 \$ p% t% yprimitive prime factor.
      C6 P9 |' ?# v/ D5 S( Kprimitive roots.
    6 a4 s; ~8 S8 W% s! EArtin’s conjecture.
    1 S" @- W. ~, D5 Q- b* T+ p2 U8 J1 ha curiosity. ) F9 g# O) ^/ J+ J- H* R
    primordial. , e$ f! M; B* d- M$ y6 Z
    primorial primes.
    , U1 k/ o& U  rProth’s theorem. 0 W% E- T$ k; \' ]
    pseudoperfect numbers. * F, a# ?* b" Y  L0 q, n7 z, k0 D
    pseudoprimes.
    ! O. w0 @8 J- g2 W; L0 j. Ebases and pseudoprimes. 7 m4 Y+ b% q3 N
    pseudoprimes, strong.
    6 }& E0 v# A9 m4 ^6 k6 Bpublic key encryption.
    ! \+ `+ ]  a7 w/ D6 dpyramid, prime.
    ) n: D8 G( N% X# |% _# \" \Pythagorean **s, prime.
    6 }/ j) }7 E" q/ D2 g% B! {% Lquadratic residues. ( F# Z( E# H, ^+ z; V% ^' |2 |5 J
    residual curiosities.   J& a2 U3 w% I$ @% w/ [, f! \: _. x
    polynomial congruences. 3 S+ t2 K& d8 e! Z& I0 ^
    quadratic reciprocity, law of.
    . ?8 u8 Q' `, H( w* ^4 e% j+ [Euler’s criterion.
    9 N; C$ g8 C' ]Ramanujan, Srinivasa (1887–1920).
    . ~9 p; j9 c! fhighly composite numbers. $ F2 D4 Z1 M0 }5 k
    randomness, of primes.
    8 n, Q5 l2 g: t& N) [Von Sternach and a prime random walk. 7 x  A5 z; ~. `' n& e. ?2 s
    record primes.
    & b/ w" [& v4 u. k, K' y! t+ |" Zsome records. " S6 x3 f7 H  e& s! n6 T0 {8 h
    repunits, prime.
    6 G5 z' |, I# `2 U4 ~3 z* CRhonda numbers.
    / J+ m( c3 y+ h0 x) _' m5 E; a* vRiemann hypothesis.
    # h# a( i7 a$ T5 v- xthe Farey sequence and the Riemann hypothesis. . S* B$ Y4 g9 w- m; \3 l9 Y8 R
    the Riemann hypothesis and σ(n), the sum of divisors function. 5 T* C( e. }5 p2 @
    squarefree and blue and red numbers.
    $ W( S- T, W: Mthe Mertens conjecture. 8 m. C; s" c: H! C) Y7 [
    Riemann hypothesis curiosities. # O( v/ M# Z& n
    Riesel number.
    ; |0 b- r: s1 v6 Q, _6 D/ M, S$ D. `right-truncatable prime. ' ~& d: g7 @. [- p; M* ]+ c
    RSA algorithm. , x/ @4 j* K- ]
    Martin Gardner’s challenge.
    ; n& f' D- f8 h) Z% Y9 MRSA Factoring Challenge, the New. 2 s2 o$ H- z, f
    Ruth-Aaron numbers.
    & j2 T7 y4 o4 B, f. e/ W: O, ]Scherk’s conjecture.
    " f9 K9 C: f3 g3 u4 v1 q4 I$ jsemi-primes. ) P% a+ j7 y5 [& R; C# P
    **y primes. 6 w3 J; f: r3 D/ z+ P9 P* s. B
    Shank’s conjecture.
    4 e9 P- c: ]7 \; l$ BSiamese primes. / _7 C9 w% A) T3 ^
    Sierpinski numbers.
    ) E* I6 k1 t2 L& N) q' I% MSierpinski strings.
    3 W3 i+ ~2 w$ B  {8 CSierpinski’s quadratic. 7 m% W1 g0 d% l9 q2 B- W: I+ A( [6 A
    Sierpinski’s φ(n) conjecture.   i/ t* W" R( i2 ?) j, E, N# ]
    Sloane’s On-Line Encyclopedia of Integer Sequences. 6 L7 }& p3 N. g, o9 r, P
    Smith numbers. + D9 N) {  Z' E5 }$ y' o& W- w
    Smith brothers.   d" D6 T9 U$ k( [' P
    smooth numbers. 9 g8 e0 ~3 S: r' m' N3 D
    Sophie Germain primes. 9 v% m0 M. s/ H4 @" V, b; e
    safe primes. 0 a, S% D5 Y6 @
    squarefree numbers. ! Y, E  \6 ^$ f: o
    Stern prime. * m2 h- _; V4 O9 i' C3 ]
    strong law of small numbers.
    5 z1 w8 |* i, B' @: g) _# ?triangular numbers.
    * p8 p. r4 q; E* |9 Otrivia. 8 z3 f& K- `6 U- p0 ~$ Y7 H
    twin primes. 9 _7 `/ E8 k6 Q
    twin curiosities.
    & E+ P$ {+ E" K# @- _Ulam spiral. ' ~" B4 I5 v6 u  E8 `
    unitary divisors. 6 Y; D# m1 B7 j" K7 j' J" [
    unitary perfect.
    2 Y) x5 [; I* Runtouchable numbers. , ~, a5 W" f: Z: \- Y& A% f
    weird numbers.
    ) r  S( {! P- ^3 i- MWieferich primes.
    % W9 j* E+ ^# {5 m) i1 C- sWilson’s theorem.
    3 H9 S4 l3 f5 N, m. N. Htwin primes. * u  f, `: P5 @/ K
    Wilson primes.
    0 b' [. l) \6 r8 ^- Q( q- gWolstenholme’s numbers, and theorems.
    * k4 ?, g5 S* e" ]/ umore factors of Wolstenholme numbers.
    + }# p9 J. g! l6 CWoodall primes.
    * A0 i9 q! m6 F% J  q# T7 S# Bzeta mysteries: the quantum connection.
    * H- Q; o7 U! l$ T6 B& y/ |
    9 }4 b8 Q1 S; \1 m8 o
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