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数字的奇妙:素数

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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
    & U; p% }4 n9 V( @& _5 E! m
    . p" V2 a8 z! y0 C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.
    9 {9 ?* e3 d1 J  ]! \. wabc conjecture. # T' H' X" T1 e
    abundant number.
    " v7 D( i& h/ r2 A& K5 NAKS algorithm for primality testing.
    % R! Q6 G! e5 L/ O/ ~7 Maliquot sequences (sociable chains).
    % t1 H4 u0 P/ M5 Y  N2 Balmost-primes. # T- _/ Z# C( w" k& i% g$ x
    amicable numbers.
    0 P, i8 m2 l+ L6 Lamicable curiosities.
    / i" W3 j' G& l6 j; d" G" wAndrica’s conjecture. 5 |* E1 V* g3 I! x, B* |, h
    arithmetic progressions, of primes.
    % @. @7 i  i* X- C% f  tAurifeuillian factorization.
    , ?/ J1 i1 J9 e& @: }average prime. . C# A3 @, i  R/ I1 P
    Bang’s theorem.
    # i: ~) a5 w, m/ @Bateman’s conjecture.   n$ j2 G$ P: d+ T' v. [; q/ K8 R1 {
    Beal’s conjecture, and prize. , A) x1 s0 B2 s0 b3 d6 m
    Benford’s law.
    2 S' Y+ K1 w# d# ]- L9 pBernoulli numbers. - G# H1 `$ `/ c* p
    Bernoulli number curiosities.
    3 m! M- W4 K9 j7 }Bertrand’s postulate.
    0 l" @) }" a3 BBonse’s inequality. ( B* I0 E- Y# D% f
    Brier numbers. / U, s8 Q3 u, g7 J( |
    Brocard’s conjecture. ( q( M" K6 `6 _8 u
    Brun’s constant.
    7 ^! _. d1 j* b8 t2 w3 U# D  XBuss’s function. $ l9 P1 u) ~2 _' S0 o
    Carmichael numbers. % U  F7 M* H  ^  q2 K
    Catalan’s conjecture.
    . k' g$ x' G. {0 y: u8 f$ KCatalan’s Mersenne conjecture. 7 F1 s4 H/ b# y5 i+ q
    Champernowne’s constant.
    2 _; d! D$ |: S/ E' B/ ichampion numbers. 3 V2 R1 h5 ^. ]9 r, a6 U* f
    Chinese remainder theorem. ' |% L( E: v2 b4 q, N4 R
    cicadas and prime periods. 1 D, G9 |+ g* ?# g6 G& Z
    circle, prime.
    ; m& d$ @% T4 Icircular prime.
    / ~1 Q& L# ?7 B3 T( J, ^Clay prizes, the.
    9 P2 F( a( d6 I8 Ncompositorial. $ w6 L8 j: g" R+ R" J9 E: s$ o
    concatenation of primes.
    * `( j6 j7 O; z  dconjectures.
    0 I6 Q7 x' Y1 W+ y( ~' o) Wconsecutive integer sequence.
      N4 t5 b- M& \7 x( J4 oconsecutive numbers. + ~1 f: F! p. q  @
    consecutive primes, sums of.
    ! o* a; x' y3 d; r6 {2 ^7 `- YConway’s prime-producing machine.
    ; ?* _- r4 |3 R6 [- dcousin primes.
    ; J  v0 ?5 q( u( _) C  xCullen primes. / y# n" b6 e% h1 s
    Cunningham project. + }; r% W& ?) G% f/ x2 h4 }
    Cunningham chains. 6 F6 I& `, A* ~7 d
    decimals, recurring (periodic).
    , c3 Y9 y6 E4 p& pthe period of 1/13.
    , T0 l( i  A6 f% n+ P% c% Q  }" Acyclic numbers.
    & ]' ^. M# ?& }8 E9 b, uArtin’s conjecture.
    " O+ D- w3 ~( I' Q0 zthe repunit connection. ) _1 H7 q: j4 R5 i( P+ b
    magic squares. ! P4 ~" y6 g! B# ]' Q# u0 g
    deficient number. 3 A* a" K1 G* x* q# H) A
    deletable and truncatable primes. ; }- ]' Y5 x; T0 M4 L2 @
    Demlo numbers. - ?! h) B+ z3 l2 V
    descriptive primes.
    $ o) a3 h. G+ l/ O  t: z! ~$ TDickson’s conjecture. # n! W! p# d( o
    digit properties.
    4 V) E: U" I7 k; Z8 nDiophantus (c. AD 200; d. 284).
    3 t" ^& c# W+ p  m+ mDirichlet’s theorem and primes in arithmetic series. % c# K# g5 l2 [$ b
    primes in polynomials.
    5 S5 X& m8 J7 Z/ l  X, Ddistributed computing.
    3 k0 e' Z4 g2 @5 K, G- R) s; Adivisibility tests.
    8 q, |' O' T( b# Z: wdivisors (factors).
    ' h/ E% J' R6 u( w$ g# x% K+ Lhow many divisors? how big is d(n)?
    7 g2 V8 S& C, Trecord number of divisors.
    , O" a, K* {2 q% ]curiosities of d(n). ; u  I# V4 V* Y- I2 _1 Y  j3 I
    divisors and congruences. 4 K  T5 p( ~3 i9 u' ]7 m# ~
    the sum of divisors function.
    + z: d8 b* X7 X1 L( G( P! H1 Z: Ithe size of σ(n). . R; g# R  d) b0 k
    a recursive formula. 6 q. n( l. F. K% ~8 W
    divisors and partitions.
    0 E: |' F0 J9 d. U3 V) jcuriosities of σ(n). * D8 H" P% J& Z
    prime factors.
    ) M  T: D& q4 ~divisor curiosities.
    ( U  z3 P! Q4 b+ jeconomical numbers. & K% W1 R1 f* {* h
    Electronic Frontier Foundation. . M2 u" V. i* O& p! {7 b& \% }
    elliptic curve primality proving.
    ' S. L" v: c/ N8 l4 h$ s  Eemirp. 5 }: S9 U8 Q5 G! q" ]% f
    Eratosthenes of Cyrene, the sieve of.
    , D% ~( B0 h$ C  ~, PErd?s, Paul (1913–1996). $ s1 \* B, K$ K! i6 A# Y0 l* S( z7 O
    his collaborators and Erd?s numbers. + v  [% O% ]# n* V
    errors.
    % W6 ~) y& I1 J7 W- c5 {Euclid (c. 330–270 BC).
    0 ~) |# U  q/ I' E% x$ hunique factorization.
    / Y! f( q# C# \2 H) E' ]&Radic;2 is irrational.
    $ l- {5 m, K2 Y/ j: b" j* ]2 ?  fEuclid and the infinity of primes.
    9 A1 U5 v$ P# G, ]) w3 t  Iconsecutive composite numbers.   U' ^! o. [" O& D6 {
    primes of the form 4n +3.
    1 g& i5 O2 F3 L; ^a recursive sequence.
    % ~$ ~& A7 a* eEuclid and the first perfect number.
    , x- q3 D# ]; f* S- xEuclidean algorithm. , {. |& t6 d! |; j) O
    Euler, Leonhard (1707–1783).
    % k* D$ P3 r3 q; r6 B& I- [( |  JEuler’s convenient numbers. : b  M* W3 @0 |/ P1 T) d6 }
    the Basel problem.
    ! W. R3 n, |0 ^. E! Q# W: o# QEuler’s constant.
    : ~. G% \' O* QEuler and the reciprocals of the primes. ( w* ^# t+ P" {2 e1 F
    Euler’s totient (phi) function.
    % i/ y% |# n. Q# R5 @Carmichael’s totient function conjecture. ' U+ _5 z& w% z
    curiosities of φ(n).
    & p3 q  r1 o7 {( X$ p& F$ Z8 VEuler’s quadratic. & ^. Q1 c& G% B% W* U0 E* R
    the Lucky Numbers of Euler. . R, t( o: K/ ~; Y( Z  v
    factorial. 3 f% ^# Y% ^% J7 ]. v# q7 ^
    factors of factorials.
    $ G  t) G7 O$ Y2 vfactorial primes. 5 Y3 N# f! ?! x- u
    factorial sums.
    & n" n* A/ m  j; ofactorials, double, triple . . . .
    ' X  w4 H6 m2 V# E3 L  m8 c1 _factorization, methods of.
    2 e6 h7 A- ]2 T" z  _/ r( Gfactors of particular forms.
    ' T  X+ r: n( G% D" d+ bFermat’s algorithm. ' D( X0 o$ x/ g5 E5 m! T
    Legendre’s method. . a! D, D: `; c% W
    congruences and factorization.
    6 x2 N" s/ z9 q; r/ a, Uhow difficult is it to factor large numbers?
    9 z# A! @( P) {, ^quantum computation. : \2 k0 I  ]  v2 x% d6 }
    Feit-Thompson conjecture.
    / t, q% @+ A5 q5 L" eFermat, Pierre de (1607–1665).
    4 K7 m7 p7 R. ~4 mFermat’s Little Theorem.
    * w% C- v% c9 ]7 ^; W0 j2 P. eFermat quotient.
    8 C2 T8 J  N3 Z2 `9 X0 jFermat and primes of the form x<sup>2</sup> + y<sup>2</sup>.
    2 w5 G( U1 ]2 v1 J2 J2 S" }Fermat’s conjecture, Fermat numbers, and Fermat primes.
    8 l( Y. X, e, n, X; Z! O' [Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>.
    $ E. X. s7 u# Y/ T7 S+ wGeneralized Fermat numbers.
    & f% ]/ U4 J  N  p4 |- B4 `9 V* t, VFermat’s Last Theorem. 5 a4 p2 K# I# i4 D" [
    the first case of Fermat’s Last Theorem.
    6 U. d: s, y3 Q2 o3 Y) X9 ]$ c( G3 K" sWall-Sun-Sun primes.
      z; H& N1 i) p4 F  OFermat-Catalan equation and conjecture. & |- r* u! v+ r2 x
    Fibonacci numbers. 0 c4 y+ P$ e8 H4 I1 I/ w
    divisibility properties. ' n# T1 `2 _2 {7 z$ X
    Fibonacci curiosities. $ n8 ]7 N( p1 ?. F% V
    édouard Lucas and the Fibonacci numbers. ! T6 I+ N& f8 W2 s+ O6 A
    Fibonacci composite sequences.
    7 @6 X4 H. m: W/ m  z* i8 S3 mformulae for primes. ) |  @& c  O4 l+ ?& b4 B
    Fortunate numbers and Fortune’s conjecture.
    " e( f- L) L$ f3 v9 D5 q! T. ygaps between primes and composite runs.
    3 Z6 [  s; S+ r  P/ p7 s- cGauss, Johann Carl Friedrich (1777–1855). / y# h! R+ S/ W( l$ V
    Gauss and the distribution of primes. , B* g7 E2 R6 M9 V
    Gaussian primes. 3 T  x& R: m& |2 {9 }+ L( ^. e
    Gauss’s circle problem.
    " Q5 }, u3 V6 hGilbreath’s conjecture.
      Q! r4 b. ]- e- y- QGIMPS—Great Internet Mersenne Prime Search.
    ! c4 r$ e/ `) e- RGiuga’s conjecture.
    0 W8 s! k2 Q3 d! |* EGiuga numbers.
    7 S* K0 H/ w% B2 EGoldbach’s conjecture. - y$ l4 t+ X4 S7 k; P8 o# p
    good primes. ) G- A' P" t0 n& g
    Grimm’s problem. ( I  n+ j0 C. V( S2 e2 D
    Hardy, G. H. (1877–1947). 2 e9 [' ^' b; c% w0 x
    Hardy-Littlewood conjectures. 6 A; w3 f' ^/ Q5 E5 g
    heuristic reasoning.
    9 Y, a6 [  ~) q5 U) o0 U2 Ta heuristic argument by George Pólya. * S% k# y: H7 u% J; k. g/ ?/ N
    Hilbert’s 23 problems.
    " l4 W; D9 @& a: D. c$ R1 Whome prime.
    : G6 r7 l0 O% k/ @# mhypothesis H.
    . e8 n; B1 y. c8 Pillegal prime. - g( H: D" {0 [. V8 d- U0 x
    inconsummate number. 4 U3 r7 i. H0 _
    induction. + }. q! ]9 f- y- z0 Y, W0 @  ?
    jumping champion. 1 K: y6 d; p$ \+ X. o# S
    k-tuples conjecture, prime.
    9 ?1 W! _5 W' Y' R- U$ U9 m. jknots, prime and composite.
      A3 y2 b/ z8 O: d4 JLandau, Edmund (1877–1938). 5 {  d8 ^4 V! o! d( M. d5 a9 l$ A! B
    left-truncatable prime.
    1 O/ L' K4 A8 O% z2 }/ W% yLegendre, A. M. (1752–1833).
    ) F8 l% @8 p; Y2 \0 @9 j4 A+ cLehmer, Derrick Norman (1867–1938).
    7 q9 h* _$ W% w& G) `# VLehmer, Derrick Henry (1905–1991). ; P! F( ]! s3 r6 t  `( i
    Linnik’s constant.
    2 Q7 U, a$ C" R) u# G4 A+ _Liouville, Joseph (1809–1882). - M/ M8 m! ]/ U0 }+ ?. m$ O4 {2 m
    Littlewood’s theorem. # ]5 q5 F5 s& M  y
    the prime numbers race.
    ( S  x! D( e$ ]8 ^8 }Lucas, édouard (1842–1891).   w2 z6 ^1 I+ R) n$ x& r
    the Lucas sequence.
    . L2 s+ J* w  G& }" _1 |primality testing. & ]/ x  O4 j4 y" g8 z2 p
    Lucas’s game of calculation.
    ; Y- E2 t) T( H, @the Lucas-Lehmer test. 7 e' b- N2 @8 O
    lucky numbers.
    % X$ j" T; B( o4 a8 o  nthe number of lucky numbers and primes.
    ) w- Q& ]9 |+ w  c“random” primes. 1 j  k7 J8 P! n2 v
    magic squares.
    4 Q# A# U8 k0 j" J* E; fMatijasevic and Hilbert’s 10th problem.
    9 l3 _  _9 \' L2 c  KMersenne numbers and Mersenne primes. 5 E1 u. A6 j# A- C% f
    Mersenne numbers. : j3 e9 _/ ]6 S4 ^* [0 S$ f( A
    hunting for Mersenne primes. # a' R6 F7 {  {4 ~9 `
    the coming of electronic computers.   {' ]# q. c' Z& _( `, |
    Mersenne prime conjectures. ( B: y- ~% r8 k* n0 j2 h3 H
    the New Mersenne conjecture.
    3 z* ]9 f8 ^) @how many Mersenne primes? ; k7 v/ X0 w: [0 R$ q. V4 z+ V
    Eberhart’s conjecture.
    & ?6 q( |: \- w) xfactors of Mersenne numbers.
    8 J+ l8 g9 f! P0 z+ W- K! cLucas-Lehmer test for Mersenne primes. ! s! G* i) e! T1 `+ m8 G
    Mertens constant.
    : z- ?, Y* i3 V8 N$ wMertens theorem.
    8 B2 f' z* Z9 T$ [9 [7 jMills’ theorem. - K3 o" q( F: m. a3 R
    Wright’s theorem.
    ! z+ P7 N, Z$ Y  k; Jmixed bag.
    ; b8 W( p* }3 `, Amultiplication, fast. * M9 `% Y9 {. Z" Y! d
    Niven numbers.
    3 T! V/ U. |0 Y0 ~odd numbers as p + 2a<sup>2</sup>.
    + I/ ]9 }7 Z0 P4 |9 e/ |! s6 }( uOpperman’s conjecture. ; D; Q- F) A0 N+ R3 ~/ w
    palindromic primes.
    ! q4 d: s. {4 l; opandigital primes. & l" D, ?# n' O2 T( t
    Pascal’s ** and the binomial coefficients.
    5 G9 U3 L; n( T- P7 e6 f$ QPascal’s ** and Sierpinski’s gasket. $ J( M4 Y# z  R8 h
    Pascal ** curiosities. 0 }$ n. E' u, l5 y3 p
    patents on prime numbers. : i  ?+ \( b$ R0 A( W4 M$ s
    Pépin’s test for Fermat numbers.
    . F7 _/ ~' I- a8 b+ w3 kperfect numbers.
    3 G7 G$ t" d7 R6 o! J; T7 Uodd perfect numbers.
    . A2 T( c& P! A/ H- Rperfect, multiply.   d; w2 H  q5 u- r/ Z0 C
    permutable primes.
    1 c- c% ?* i, X. C$ d1 L2 Rπ, primes in the decimal expansion of.
    ! @6 y  o6 m/ i' ]- U2 j* RPocklington’s theorem. ! T( e2 U, O- N  @$ E; r. d
    Polignac’s conjectures.
    " @  v8 |' V, W+ _Polignac or obstinate numbers. ) N$ p3 G$ |6 Y0 H7 Z: [
    powerful numbers. 6 v; l  a9 z) f$ f( A' K
    primality testing. + a) G$ t1 W$ s7 v2 s7 v& {; _/ u
    probabilistic methods.
    ; n4 S$ S- X1 g2 o2 L0 Aprime number graph.
    9 w6 q4 v; r* [  Q" `prime number theorem and the prime counting function. 4 L# q" ?2 F4 ?: K
    history. 5 D0 a4 \8 a# {) m
    elementary proof.
    2 l& f  Z' o( ?  mrecord calculations. " N. N$ S+ _% s
    estimating p(n).
    0 F' F( j4 t2 o2 L4 Y% n/ k4 _8 }calculating p(n).
    " L/ P! B# |. U: @a curiosity.
      o* j7 s- A- G1 b) T( H6 Eprime pretender.
    1 f' F2 C2 T( y: [0 B( Nprimitive prime factor.
    0 P! L, J0 i8 F; ]2 V4 Fprimitive roots.
    ! {8 Y0 s) m$ S% KArtin’s conjecture. ' I/ e1 a" i9 g3 H. ^! t, c* h8 O
    a curiosity. . B. S) N+ K9 Q- e, F* t$ I: K
    primordial.
    6 c: u* T1 q" [6 s9 Rprimorial primes.
    2 k- X* y1 @5 b& \- j( kProth’s theorem.
    ; J' F7 b! |& @2 r" S. }) Gpseudoperfect numbers.
      o0 _$ F2 c% n& D* v' qpseudoprimes. 9 \  L" {% ?- i4 G
    bases and pseudoprimes.   j3 r) x2 U0 z. O" j8 J( q
    pseudoprimes, strong.
    $ {6 j1 W# w! e9 i3 |public key encryption. ( Y$ {2 T2 f- n' p; Z
    pyramid, prime.
    , m6 {, v6 j8 U6 h$ n8 S' W& TPythagorean **s, prime.
    4 t  z/ v' j( f* Z8 a: J" L" o4 vquadratic residues. ( f: n+ k" M# m
    residual curiosities.
    ' |  k; O* N# N0 Wpolynomial congruences.
    2 {, E# E8 ~) z/ \quadratic reciprocity, law of.
    ' U) L/ q2 h  w0 @/ bEuler’s criterion.
    3 k5 t- u$ I- L. l) |Ramanujan, Srinivasa (1887–1920). ; |2 p3 ^. \% _. Y! ~9 v" A
    highly composite numbers.
    % [% D/ a. \$ J7 T: prandomness, of primes. 2 c1 t' x" K" O
    Von Sternach and a prime random walk.
    + k0 R( v/ B6 f* @record primes. 1 x  h. @0 t* r; Z1 J/ f+ a
    some records.
    % _% E& w  J5 W. _6 Prepunits, prime.
    3 R* H: G6 _) P+ @6 jRhonda numbers. ; v) E, _# j% j/ ~8 S* ^! ?
    Riemann hypothesis.
    ( X+ `( d0 q7 e& l& h2 y6 Q# s& Ythe Farey sequence and the Riemann hypothesis.
    $ R. t: k& k6 K. V! `% b8 vthe Riemann hypothesis and σ(n), the sum of divisors function.
    + T# u4 f! t1 Csquarefree and blue and red numbers.   H6 L2 }6 z! U& @" X- W3 ]- N
    the Mertens conjecture.
      o% J; i4 [7 m" ARiemann hypothesis curiosities. 7 z" F# l+ x0 Z
    Riesel number.
    * u, B3 C8 ?/ _6 ~7 k  uright-truncatable prime.
    + M' u5 u8 n" b4 E7 T; DRSA algorithm.
    ' R+ a% A6 F' WMartin Gardner’s challenge. 0 Y3 q% \. O' O
    RSA Factoring Challenge, the New. ) w3 [  O/ Q& a
    Ruth-Aaron numbers. # b; k/ `6 [0 `
    Scherk’s conjecture.
    0 G# n* I! b! N0 O0 ksemi-primes.
    4 x) b7 C0 U! I9 l**y primes. 1 L) @% _2 m/ ]0 ]" l7 c
    Shank’s conjecture.
    9 I9 z8 {* s. ~1 r) ESiamese primes. ' V7 K9 A6 a& k' r+ k  \/ I
    Sierpinski numbers.
    ; f: o& N' ~; x1 kSierpinski strings. , ?& A' G4 t3 w* _4 @! h: v% E' R
    Sierpinski’s quadratic.
    ! {# E  r/ ~$ D! F* A8 R- OSierpinski’s φ(n) conjecture. 0 ]+ W5 o+ X+ `7 |) H! S% \
    Sloane’s On-Line Encyclopedia of Integer Sequences. + N* w: B" S8 ~8 O6 q7 q/ d: v
    Smith numbers. 9 i" }* S7 B& t  N7 v
    Smith brothers. " T4 `- s% m3 `2 u; @  U' v
    smooth numbers.
    / g0 f7 }# p- _7 H5 S& f0 ?Sophie Germain primes. ) r4 \5 ^, N* H0 D. s6 S- W" l
    safe primes.
    4 [; T6 t( K, Jsquarefree numbers.
    $ b3 V. R; H. x. H- j, QStern prime.
    9 P1 R+ _) Z# o0 Z# @strong law of small numbers. 7 t7 p: h' ?$ ?! w, X
    triangular numbers. 3 C' l- z2 L) t, Z+ [5 s- i$ {8 V2 l
    trivia. 7 ]0 u, }" b+ X: p: V; K0 m+ s# O
    twin primes. 2 c) q) P. |  P6 R2 K  p
    twin curiosities.
    2 ^9 f! ?9 |  U2 W# \Ulam spiral.
    ' s  w$ k; d- f' C! F% aunitary divisors. # x6 Z% I# {) X9 a' b7 k( _5 }
    unitary perfect. ) x0 r+ O" X$ n) Y/ K
    untouchable numbers. & z8 [5 r. h& I5 k
    weird numbers.
    3 q" M5 e. M4 G9 g* W0 J! b% IWieferich primes. 9 L7 h% S: k9 x, `
    Wilson’s theorem. 1 ?4 W% Z3 w' B$ e9 b0 Q1 f
    twin primes. - B) s$ F) R' l8 Y% N
    Wilson primes.
    , Y, i  y0 Y  ~! {* ~1 {5 t% @Wolstenholme’s numbers, and theorems.
      u4 z5 M! ~2 b# S2 v9 p' B; ymore factors of Wolstenholme numbers.
    1 R0 m6 o7 \/ a2 O! F6 n  \Woodall primes.
    $ E" z% n$ x, Z4 p' R2 u0 Q1 G2 xzeta mysteries: the quantum connection.
    5 o: `* l3 j. G( \* u- X' a6 l

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