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标题: 数字的奇妙:素数 [打印本页]

作者: clanswer    时间: 2010-4-13 11:41
标题: 数字的奇妙:素数
本帖最后由 clanswer 于 2010-4-13 11:43 编辑 . [( S+ ]* a( u: c
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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.
2 c9 z; g" W. C8 V& z0 q/ e. Cabc conjecture. 7 J' U2 Z" d. T; U
abundant number.
4 ?; X! e1 {3 ~1 f* S$ LAKS algorithm for primality testing.
5 l3 P8 h+ Q/ z9 K$ n: e9 `; i) xaliquot sequences (sociable chains). : O5 N; d% S% S" \
almost-primes.
) _$ P4 [: ~7 B6 ^) qamicable numbers. , ^( d3 L4 O1 J
amicable curiosities.   U: y( [% ]! ?, ^* ^
Andrica’s conjecture.
4 U& o) N# o8 l: f6 marithmetic progressions, of primes.   b9 q' s& Z* o3 B; E# [& g% p8 m
Aurifeuillian factorization.
' n6 I- M  @4 G$ S2 I  r* m" S) saverage prime. ! \  t4 I1 N5 L( {) E3 ~  \. O
Bang’s theorem. 0 A& B% k7 r0 P6 g4 v# B  N, ~
Bateman’s conjecture.
1 o8 c1 v6 a! gBeal’s conjecture, and prize. ; q5 w7 P. @  j" |5 T4 z
Benford’s law. + ^/ `% s0 ~7 I; I, M6 h3 O
Bernoulli numbers. - H. ]9 H# f& _. y1 z
Bernoulli number curiosities.
" A% O/ E- N0 L/ TBertrand’s postulate.
4 K1 t3 \# }8 j. r' EBonse’s inequality. 8 b( t- G$ d) n! [1 o5 i
Brier numbers. ) f* ]$ c* n0 E3 I5 z
Brocard’s conjecture. 8 ]1 A  M3 f: v  N0 W
Brun’s constant. ! \6 m/ L$ n0 g3 G  N+ S
Buss’s function. * F( g7 C8 S% N
Carmichael numbers.
/ _+ A% R) A; ?Catalan’s conjecture.
" Q  D3 L7 D/ ]& S, s5 x, g+ ^Catalan’s Mersenne conjecture.
5 j9 q* R1 M1 q( X. UChampernowne’s constant. / F* n1 C/ D+ F: T
champion numbers. % t0 z6 P: D! h0 f
Chinese remainder theorem.   W# C+ a; f0 E% L
cicadas and prime periods.
3 j5 Q1 o* W* z9 A0 R4 o; gcircle, prime.
; d' V3 t- ]+ A9 tcircular prime.
, L" W; U+ U1 }) \  C/ a! I2 [Clay prizes, the. 5 Z4 v' r, [  H8 ?; e
compositorial.   G. i3 X9 N2 |
concatenation of primes. " e0 P/ w/ d! q! }
conjectures. ( C- ~4 g- y* I7 e7 v
consecutive integer sequence.
3 h0 r( O5 i5 K6 s8 ?consecutive numbers. ! ~# F9 D2 d0 q, R$ h/ r! G+ E3 j
consecutive primes, sums of. , T/ e1 P& N( ^, t1 b
Conway’s prime-producing machine. ! ~/ H) n( m( R7 u" R3 k1 M
cousin primes. 1 G! L8 N' e4 h% Z9 h
Cullen primes.
* d! f+ P! U5 j% v! tCunningham project. ' A' R' b+ Y4 G
Cunningham chains.
* T! N( n  S; l2 ^# m' {" Cdecimals, recurring (periodic). # g; Z% V$ ^' r8 [
the period of 1/13. 7 B: ~4 l0 R. Q* g' [" t
cyclic numbers. 9 {5 W1 g& C5 _8 L6 C4 `$ }
Artin’s conjecture. ! t( d3 i2 J# B" z
the repunit connection.
9 e( @" B7 c& ?! j2 v- Vmagic squares. 2 k# }) V1 }( o2 V4 H. {
deficient number.
1 u1 Z& W9 Q/ j7 b8 W+ i# C$ Qdeletable and truncatable primes.
1 v1 x7 W; E% E4 Y+ oDemlo numbers.
2 A: b" O7 x* I/ b% p( f$ H  b5 wdescriptive primes.
+ l- ?0 w7 N/ f: p& r$ g/ EDickson’s conjecture. " l& g* F4 T3 c" I1 r" c; ^2 b4 m  {
digit properties.
$ G; G5 e2 g/ o* D- h/ J  i- wDiophantus (c. AD 200; d. 284). . j6 q/ U8 A" ]& }8 u, Z4 V
Dirichlet’s theorem and primes in arithmetic series. ' x; p5 P6 G9 o0 [7 U8 v
primes in polynomials. & b  M' k& j% y
distributed computing.
! O7 w+ Y* U/ T7 D* S. [# M% _divisibility tests. * o$ ~" J( e, u$ J. u2 e4 {1 ~
divisors (factors).
- K. r# i3 A& u5 k& [how many divisors? how big is d(n)?
8 Q' W4 Q; ^# G) urecord number of divisors. 8 h" T/ ?, @# [$ K
curiosities of d(n). 3 Z/ e: V/ A( P! d
divisors and congruences. 7 \1 i1 C( n6 \0 B( ~
the sum of divisors function.
$ j, l! S  d( d! t$ L$ N6 fthe size of σ(n).
: B' d3 G- }* Z" o3 e2 e+ ma recursive formula.
  ]1 v- x* h) a5 z" j. l* Ydivisors and partitions.
  D+ N$ @" ^) v: z" V* e1 lcuriosities of σ(n).
& O7 [. e' s+ i( gprime factors.
. K+ n2 m$ ?$ w2 p1 g2 q* gdivisor curiosities. ) V- G; c9 T' L, b5 }
economical numbers. 2 P+ R* R" b) K1 {6 A+ ?1 t
Electronic Frontier Foundation.
5 t& w2 k5 V! ?$ C4 Celliptic curve primality proving. 0 m( G7 {$ b; f9 u6 f1 L
emirp.
" |" q9 M3 G# }/ o# iEratosthenes of Cyrene, the sieve of. + K# h) G6 J" W9 F/ n% V- T8 l
Erd?s, Paul (1913–1996).
3 }+ e# a6 z6 B$ r# `( j5 k9 q4 nhis collaborators and Erd?s numbers.
; J; y9 c3 G5 A6 Terrors. % U# a! {- J2 C: V; y% q
Euclid (c. 330–270 BC).
  ~( v+ K- s$ R( a0 {) j; Iunique factorization.
7 s- L) Q3 B6 b' L- A2 L: l&Radic;2 is irrational.
1 o5 ]. U4 f1 w3 M7 y: WEuclid and the infinity of primes.
, }& u1 I) v9 B/ p$ Z* R% tconsecutive composite numbers.
; ?& C. U' T+ ?, T/ Q: Eprimes of the form 4n +3. ' X9 v5 e" \4 P  S2 q
a recursive sequence.
; E; o! ~& z! z# {2 }Euclid and the first perfect number.
/ J/ c7 _' n8 |2 n4 a8 m: yEuclidean algorithm.
- [. `' S0 W0 W  @) J& E/ L+ IEuler, Leonhard (1707–1783).
6 Z; L0 c+ d* U/ g  M" g9 SEuler’s convenient numbers.
  l) j$ ]8 K1 Ythe Basel problem.
/ A; h9 w& e( ^2 X* M( g9 v7 s9 x; bEuler’s constant. $ b- i; y* p9 V. |# O
Euler and the reciprocals of the primes.
: Y4 I5 b( q. m+ p. vEuler’s totient (phi) function. 8 i: r$ O* e) l( S" Q
Carmichael’s totient function conjecture.
$ c: q( H' n1 G8 s# U4 Qcuriosities of φ(n). , v+ G6 s7 L% Z: Q$ e/ j% e% X
Euler’s quadratic.
# @" A. D( |  N( _/ S) y$ zthe Lucky Numbers of Euler. ' o. P% @2 F' X( j" w2 H) v8 z
factorial.
# {) r1 t5 t+ b, n' y# ?factors of factorials.
$ j  p' z9 u( }factorial primes.   e; ?; H( D' Q5 C5 U1 {& o( S+ ~5 C" u
factorial sums.
& b7 i3 D) \* T4 \# W$ Dfactorials, double, triple . . . .
. @5 `# F; k: X+ |factorization, methods of.
* N; e- w$ g; Tfactors of particular forms.
' U/ `3 |# p; c+ N% CFermat’s algorithm. & l5 \+ d! @3 X
Legendre’s method. 0 |9 D+ y8 s. F, x5 I) Q
congruences and factorization.
4 S5 Z9 C5 T; ^+ {7 s0 Rhow difficult is it to factor large numbers?
/ s8 k. l; J) ], O$ Tquantum computation. 9 |; d. H% a7 E  H4 Z
Feit-Thompson conjecture.
" K1 V  U  Z& i) G( A/ C9 P1 j# p! W$ aFermat, Pierre de (1607–1665). 0 J' o4 K3 Y: f9 }7 H5 b2 i
Fermat’s Little Theorem.
5 H1 v! S/ A" u5 Z: _Fermat quotient.
' J0 [1 J4 v* {- J' @" q- ZFermat and primes of the form x<sup>2</sup> + y<sup>2</sup>.
" ^+ h4 L/ g- N+ P8 D8 ~' |: o$ [Fermat’s conjecture, Fermat numbers, and Fermat primes. 2 g4 t* E5 O5 S
Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>.
) p& P- u$ Q( Q8 S8 \Generalized Fermat numbers.   W9 @8 b& u! V, D8 c
Fermat’s Last Theorem. 6 {, x$ ?6 a# R: L
the first case of Fermat’s Last Theorem. / F5 ?8 |0 J7 l1 D% b
Wall-Sun-Sun primes.
; O. x6 S; {# G+ {3 JFermat-Catalan equation and conjecture. 0 n4 h0 U: `) D" E
Fibonacci numbers.
; L8 s$ N4 O# z; vdivisibility properties. , p- x) m8 p+ F0 h- ~
Fibonacci curiosities. $ I! {2 V2 `! r8 R
édouard Lucas and the Fibonacci numbers.
1 J2 w9 }  J5 c- g# KFibonacci composite sequences. 1 C% B, P& _, k; O! v. _* d5 R+ R
formulae for primes. % X9 q1 X  c; \0 {
Fortunate numbers and Fortune’s conjecture. " n' k! J$ e4 Z1 Z9 _6 f: D4 ~( H6 [
gaps between primes and composite runs.
- u- |$ P, L1 u+ h/ q/ eGauss, Johann Carl Friedrich (1777–1855). 5 x" U8 J6 D+ m
Gauss and the distribution of primes.
- m# r0 U" r# n3 eGaussian primes.
" L' A: v5 @) y4 \Gauss’s circle problem.
9 S9 p, c- \, t" VGilbreath’s conjecture.
. N( [& p0 Z1 }7 OGIMPS—Great Internet Mersenne Prime Search.
- Q. X! b" H2 O/ hGiuga’s conjecture.
* c- _) r$ }& sGiuga numbers. - J/ H* }! a* c8 t' R
Goldbach’s conjecture. 7 R1 _: o+ f6 @( P! i
good primes.
$ ?0 l; \5 w9 @/ {Grimm’s problem.   {9 @- S5 L. {; t! ]1 O
Hardy, G. H. (1877–1947). ) _! Y& F  G2 J: t  E/ v9 W; B
Hardy-Littlewood conjectures. 1 K2 j+ s1 ~3 i
heuristic reasoning. : B$ h  t8 q& J& M3 O3 h" R
a heuristic argument by George Pólya. . Y0 V) Q) E* H
Hilbert’s 23 problems.
# G! J" T. F6 O4 |* K0 shome prime. 6 m! N" U2 ^6 ?" l7 y( X+ \6 r
hypothesis H.
( J- D/ r; W# l# H  i9 |4 `& `8 ^; tillegal prime.
4 \! E: r7 D! E3 \: z! zinconsummate number.
" ~7 l$ A% N0 {# ninduction. 0 j' S; A* x/ l0 _& U% P: k* b$ ~
jumping champion.
/ _8 ~6 z6 k4 S6 y1 Nk-tuples conjecture, prime.
" o; d: b0 Z. B: c; ]knots, prime and composite.
4 ?, a* g( r, y( Q4 Z& \Landau, Edmund (1877–1938). 1 i( [' c+ Q+ g9 `. a" ]
left-truncatable prime. / s3 y+ ^- s3 u9 f* e/ c
Legendre, A. M. (1752–1833). # K7 B+ g8 u2 d& k, @
Lehmer, Derrick Norman (1867–1938).
, E& Z2 k5 k* i+ O) nLehmer, Derrick Henry (1905–1991).
8 D0 a& O8 \2 k# ^9 uLinnik’s constant.
6 S. m$ J$ J2 F( YLiouville, Joseph (1809–1882). ! K" ~6 k" {9 K& A% J) ^; ^; E  J
Littlewood’s theorem.
8 A8 H. j# O6 l4 v# p- {the prime numbers race.
( W+ }; F& x& I5 @2 z) cLucas, édouard (1842–1891).
* a/ E3 p3 x. `0 j6 ithe Lucas sequence.
! {" e3 ?$ Z# K9 e2 D* Pprimality testing.
, d  h! Q9 K3 s) K( j% x8 ZLucas’s game of calculation. , @: B. w% f' K! o- k! r
the Lucas-Lehmer test.
4 G  C6 }. V5 O' w/ a) S3 Alucky numbers. . o1 ^. m# ^9 N1 a* v
the number of lucky numbers and primes. ' X+ i' J- b& n- n* G
“random” primes.
4 u% M/ x( Z/ e* Z3 Z/ ?7 V7 p, wmagic squares.
) m# q# e6 @/ t/ o, m0 z5 ?  I/ dMatijasevic and Hilbert’s 10th problem. : I0 m8 V/ k# v1 K1 g. S0 q5 h
Mersenne numbers and Mersenne primes.   @  h2 T  H# F, e% n
Mersenne numbers.
9 D2 T& [) H3 J4 xhunting for Mersenne primes.
- [. S4 U# b; g4 d$ p6 A! H5 q& J) hthe coming of electronic computers.
6 h; ~# ^" ~/ A' E" \5 EMersenne prime conjectures. $ g* a) F# i' g6 [
the New Mersenne conjecture. % V5 K! P& i4 A- `: _6 o; r& v
how many Mersenne primes?
7 G, }* G6 M) h% j% KEberhart’s conjecture.
- p3 _7 w; K/ _  cfactors of Mersenne numbers.
% ^* [3 ~0 a& DLucas-Lehmer test for Mersenne primes.
: ~! v. P3 M, x0 @1 GMertens constant.
4 u7 x8 j/ N3 w* g" b  }( Q- r8 w7 XMertens theorem. + n( h: ^- b9 Q3 u1 r/ _0 e
Mills’ theorem. . ]7 c/ V8 b( Q( x
Wright’s theorem. 9 y( t9 Y7 u, I( W- i9 L
mixed bag. / }& c1 X9 I( ~8 k! B( O/ |
multiplication, fast. - U, y( A, A+ z3 y6 S! t% f0 Z
Niven numbers. $ Y& S: d* K+ O: x# {. `! ^% E7 I( z
odd numbers as p + 2a<sup>2</sup>.   u( g8 O& \8 z7 V
Opperman’s conjecture. # Q! O- E9 M+ h$ D( d4 R3 b
palindromic primes. / ]) V8 s& [) h' R$ M  N$ v: S
pandigital primes.
7 I" Y% }, L' ^' }Pascal’s ** and the binomial coefficients. 8 s  E+ U: t" |! ?* I! W
Pascal’s ** and Sierpinski’s gasket. * v1 @' v! J9 F, b4 h- ^' L. {
Pascal ** curiosities. 2 h! _) l2 w9 ^0 W8 Y
patents on prime numbers.
- J; U& I/ s  |9 }& A: _Pépin’s test for Fermat numbers.
  R" k( U  J8 lperfect numbers. 2 ~& {7 n: }& `- |
odd perfect numbers.
8 j+ A; S* B4 k! @" {7 ]perfect, multiply.
* J7 u" G4 X, Hpermutable primes.
% P* g8 q2 B/ t9 Z* bπ, primes in the decimal expansion of.
- \/ j4 [+ s8 yPocklington’s theorem.
! w) a) l. ]& ]# M& ]" U0 k' zPolignac’s conjectures. 5 p4 @3 r8 R* f& ?/ ?" r. l3 w+ D
Polignac or obstinate numbers. ' d5 ^2 F+ d9 ?( P2 x! x- o, c0 F
powerful numbers.
# G* {, o+ q! D. _4 b* I+ Oprimality testing.
$ Q% o- t9 }! c4 _. Jprobabilistic methods. 4 N5 L5 q" |' y/ u
prime number graph.
& u3 ?  \. Y& J$ ?) s, W$ F, x4 Wprime number theorem and the prime counting function. / J4 E3 T+ W% H# v
history.
. {; W9 M" P% J# E: B) B/ ^elementary proof. 3 j+ }8 }5 V4 l. G$ e- F- K
record calculations.
* B+ d. I/ M2 ]' Sestimating p(n).
0 i! X$ B8 c# D: P/ r" q% ^calculating p(n). : ]3 }' U# w8 k5 Y3 X* P' f8 u
a curiosity. " {9 G0 d6 P# q: `6 ]
prime pretender.
/ A$ h- b$ T" O6 lprimitive prime factor.
0 f; {# F8 a! |& uprimitive roots.
- ?9 i8 X9 w/ O0 M# [* p9 E! KArtin’s conjecture. $ X$ Y8 n7 h. }8 _) r1 E9 f
a curiosity. , x- `+ L( `& p
primordial.   z7 s9 r) P9 X1 N6 [! J
primorial primes. * H3 ~6 S3 A$ j& K8 _; a
Proth’s theorem. 2 y, s* P1 I2 Z8 Y& S
pseudoperfect numbers. / |% L; w2 |( k! Y  L
pseudoprimes.
, W3 m; s. m5 Pbases and pseudoprimes.
8 g. o! H" W( ?; gpseudoprimes, strong. 7 s9 D1 n) m; P2 o; p& `$ {
public key encryption.
: g7 A2 G- R/ r1 Mpyramid, prime.
. U: }8 R4 q7 A9 V" ?Pythagorean **s, prime.
- F' O* D; O( y! uquadratic residues.
0 y0 c: k: X/ q3 o9 y8 Eresidual curiosities.
3 Q( r+ ?* {8 N. L( Ypolynomial congruences.
5 o* a4 P/ y9 H. Y* ~quadratic reciprocity, law of. . s% u% t6 ~- _5 f4 p0 |) \/ o0 Q* Q
Euler’s criterion. * C- K2 b4 T0 ^0 n6 c
Ramanujan, Srinivasa (1887–1920). 7 B$ E6 X1 {9 S3 R. i
highly composite numbers. 9 `- }: [+ t# {" Z; K/ B3 C/ {
randomness, of primes. + T2 ~' U& x0 X
Von Sternach and a prime random walk. # z" U7 q. J7 G% D) v
record primes. 1 K' R/ N  P+ z" U7 W2 E. a) x
some records.
- l9 P" \( L/ Z% W) [: jrepunits, prime. : l2 b% l" |3 C) O/ e1 y
Rhonda numbers.
; t: ~1 {5 l5 V8 X8 YRiemann hypothesis.
, ]. D& Z0 W1 Z/ F& D  F7 t6 H4 zthe Farey sequence and the Riemann hypothesis.
0 u1 g( R- q8 E+ w4 a7 Nthe Riemann hypothesis and σ(n), the sum of divisors function. 8 h, Q3 I0 I4 p
squarefree and blue and red numbers.
* e8 S: @+ H3 h1 U! ithe Mertens conjecture.
! u+ E" E  b# o- uRiemann hypothesis curiosities. ; e1 B0 X1 @2 E
Riesel number.
: D% I8 Q" d7 R- E3 s3 pright-truncatable prime. + M. r0 {- v8 z8 ^
RSA algorithm.
/ t" U5 t) N- F3 |, Z7 Z. l; yMartin Gardner’s challenge. 2 w3 e: l, F/ R- V1 Z. V0 p
RSA Factoring Challenge, the New. # s# b. s/ Y$ p& u" r% ^
Ruth-Aaron numbers.
5 S$ ^- z! ?; t: v( i5 a6 j7 ~Scherk’s conjecture. ( {8 ~8 g' x& l; k- P# O# k. x4 j
semi-primes. 5 [, t: ?2 Q1 H5 c1 ?0 ]# D& d# ~
**y primes.   }* ]! u" N7 K4 P2 O. X) w
Shank’s conjecture. " _' O) I5 D' u$ _; I3 J* w! u
Siamese primes. * y) p/ S! ^  R+ j
Sierpinski numbers.
4 r# Z% x( ]; d# ^Sierpinski strings. ; D* T+ A1 H- B
Sierpinski’s quadratic.
4 r" R" [9 A: z+ q* CSierpinski’s φ(n) conjecture. 4 b0 w. g* l& ^7 C7 N: h: h$ G
Sloane’s On-Line Encyclopedia of Integer Sequences. 6 H2 f! @. p5 p1 h$ o) `
Smith numbers.
, v8 A6 [7 O* s+ m6 ?) h: WSmith brothers. ; `+ r6 d# U! e9 v5 R+ a
smooth numbers. : w7 R1 W6 r; W5 \$ P' v; @! a
Sophie Germain primes.
/ ?: T$ F9 p3 j* z2 D8 @safe primes. ( H: C, V* F4 @1 j* s9 h, i! B% J. ?" `
squarefree numbers.
2 N% \# A; K3 q% }  K6 uStern prime. * e( g" q& b% D" e- Q2 _$ I( ?, W
strong law of small numbers.
( e; ^% Z. V) Rtriangular numbers.
- ^5 h" e5 x) }& D9 `trivia. ) ]+ G; e( \/ e  P# Y
twin primes. : X1 h$ K9 X: S% L: n
twin curiosities. . }+ y; i; M" `* x, j0 g
Ulam spiral. , Q& ~) a3 e3 j1 c, t. L6 v
unitary divisors.
2 x1 c3 P( \, v' o4 r3 Qunitary perfect. ) t* m& n1 x. ]. z; F! X% H2 R
untouchable numbers. ( d: j1 z! c. }( s. |% `6 `
weird numbers. : v  q5 `% g/ U9 n  k# Q+ K
Wieferich primes.
, \  ?7 Z* s1 t4 w0 q0 wWilson’s theorem.
+ a9 E2 }) a/ E, F2 g& ntwin primes.
# x: \: Y2 p* s# W! d8 OWilson primes.
  p$ H+ p/ ?8 y0 zWolstenholme’s numbers, and theorems.
5 e+ v: [. e' f$ C6 C# u2 u) A6 U3 mmore factors of Wolstenholme numbers. + `% a7 L& F& U. q' B' i) y
Woodall primes. . D! |; o5 C+ y3 ^/ L
zeta mysteries: the quantum connection.

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2 h4 M. q9 S0 q* d& o5 o5 v, _8 N附件: 素数.rar (1.44 MB, 下载次数: 12)
作者: risiketu    时间: 2010-4-27 18:48
解压密码是什么啊?在哪里能找到解压密码呢?
作者: risiketu    时间: 2010-4-27 18:48
不好意思  我找到了解压密码了  谢谢大家
作者: mightyrock    时间: 2010-5-8 20:12
楼主强大,支持楼主,不过我就不下了吧~~~~~~~~~~~~
作者: clanswer    时间: 2010-5-8 20:18
回复 4# mightyrock
9 `  K, c" d2 J/ ^6 V) a0 ~' R9 V! h" ?8 V# C9 m$ Z; V2 r2 O

) R7 ~" M3 m* N% g# I" y    多谢支持
作者: 风痕    时间: 2010-5-14 22:39
似乎看不懂………………………………………………
作者: clanswer    时间: 2010-5-14 22:44
回复 6# 风痕
0 x6 v/ `3 ]3 h0 H2 P0 I
7 M" ^) J3 U3 ^1 n
/ Y" i& P3 l6 R  V  A( c# L    哦?是吗?呵呵




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