查看: 4684|回复: 6

数字的奇妙：素数

[复制链接]

字体大小: 正常放大

clanswer

39 主题	6 听众	5598 积分

TZB狙击手

升级 11.96%

TA的每日心情

	奋斗 2015-10-16 12:37

签到天数: 28 天

[LV.4]偶尔看看III

自我介绍: 香茗一壶，斟满了心田，溢过了心坎，茗香遍体……涛声一片，传遍了脑海，浸湿了耳畔，涛溅全身……

群组: 东北三省联盟

群组: Matlab讨论组

群组: 数学建模

群组: LINGO

群组: 数学建模保研联盟

电梯直达

1^#

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

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. 7 R5 T9 D8 J( m: ?2 a3 @; W0 s6 t! j
abc conjecture. 2 j( ]9 G4 q- x8 `; L* S- G1 b. R; U; F
abundant number. . F4 c6 i; F; q8 O
AKS algorithm for primality testing. 4 C+ I2 C1 Z1 g: v1 n5 }: p
aliquot sequences (sociable chains).
6 F0 P, ]4 h# D2 \almost-primes. 7 z5 M, r" y! U1 g
amicable numbers.
2 K4 @7 D0 i( v/ h; Eamicable curiosities. 3 A$ i0 c* L" Q
Andrica’s conjecture.
 J: ~4 P- _0 a$ {arithmetic progressions, of primes. 6 S- f# o( b# }: [( l, c+ E6 S. e
Aurifeuillian factorization. , l" K# W' z. g8 V2 ^ i$ J
average prime.
- P& u! q& K6 u+ u7 A4 k! r5 MBang’s theorem.
& n! H O* x5 ]1 \4 DBateman’s conjecture.
( A# M0 I/ Q, v5 JBeal’s conjecture, and prize.
2 p! T5 {' |% ]* ^1 z, ?# Q9 L! @Benford’s law.
7 U9 u9 d8 P9 \5 X9 u2 hBernoulli numbers.
$ {+ y$ O- k( L% S7 c+ GBernoulli number curiosities.
0 P* k. t$ c/ E, f1 \$ EBertrand’s postulate.
' s3 ?: n9 G7 m2 |) RBonse’s inequality.
/ l. d4 J1 _6 p, z8 [% W) z0 tBrier numbers.
; j! \. ^( [/ z8 o0 F& gBrocard’s conjecture.
- p/ v2 \, z9 X1 Y1 G+ u- y5 \8 P8 dBrun’s constant. $ S4 u% V! r6 b% J- H
Buss’s function.
9 D5 N7 P' `! q- D' i$ I- W2 {3 SCarmichael numbers. 7 W9 X4 E& l8 i
Catalan’s conjecture.
8 V/ L$ s$ G8 H; g0 P! L) H. o: vCatalan’s Mersenne conjecture.
( Q- Q& d0 X( VChampernowne’s constant. - H) y5 _- c8 i5 w
champion numbers. ! P9 v: M* _) o! O: ]
Chinese remainder theorem. : x% y9 G% A. K! ]$ {1 u# t- @
cicadas and prime periods.
7 ]6 e& M% O3 l& Ocircle, prime.
8 j) k, J/ J7 y* \% C. U3 n/ wcircular prime. 5 g: i7 m- f, j: y- K5 ^' k: j2 R) K
Clay prizes, the.
+ c# R# ^" S& T& A- Mcompositorial.
4 _9 P/ J3 r# j& R) T6 G* pconcatenation of primes.
) \; n7 l6 I, T$ }' m( Y& A! Nconjectures. 0 Q" _5 Z+ K1 d; S1 @
consecutive integer sequence.
. Y: m4 c% e" x" u/ Mconsecutive numbers. ( `0 g8 \; _4 y: o. r" B X
consecutive primes, sums of. 3 n3 t8 K3 ?- G9 |3 \
Conway’s prime-producing machine. 9 b6 q# s: C( ?% q2 s
cousin primes.
8 F; w9 ^2 ^9 g) s- aCullen primes.
9 D! Y9 n) W, g* ^4 v E/ l5 B2 m8 RCunningham project.
# w: o; |2 k3 u" y; X7 C- gCunningham chains.
 u! f0 m) d9 q( ~/ K& tdecimals, recurring (periodic).
. O4 r" W; b% U$ f X$ Xthe period of 1/13. 6 w) c2 n, j* J
cyclic numbers. * m2 b: ^& D' _& N2 N% E
Artin’s conjecture. " h6 z/ u2 X5 }
the repunit connection. 5 @- d3 O- N+ U5 q0 [4 N4 S1 {
magic squares.
* v2 G& G% }3 Y: O+ q! e' M2 |deficient number.
; U6 j5 z7 f$ j6 Tdeletable and truncatable primes. # a: F) R Q/ g) ?- I/ k
Demlo numbers. : A Z2 ^4 y7 r% Y h
descriptive primes.
6 }9 b1 U+ J0 l7 @Dickson’s conjecture.
 [' T# @- g# Xdigit properties.
0 `: b; o. V$ R2 Q" B! C- TDiophantus (c. AD 200; d. 284). * E$ H: L2 i5 u! r% J
Dirichlet’s theorem and primes in arithmetic series. + |9 R& J! e) ?. U9 Q2 Z u
primes in polynomials. 2 p1 T6 B; k8 K) s7 c
distributed computing.
- ~4 i. s. d: e2 gdivisibility tests. 1 F# w% m* A3 y0 l7 \
divisors (factors).
% [5 @9 n0 O" C6 F' S+ Nhow many divisors? how big is d(n)?
/ |* Z3 Q; L e, w# n" w3 ~& b) qrecord number of divisors. 9 g8 z/ `) m9 I- s/ I
curiosities of d(n). ) e, S* w. @- \8 p2 {+ D
divisors and congruences.
5 e, Y Y) p/ Y D( R+ y" cthe sum of divisors function. # ~/ o! X) c+ }0 j
the size of σ(n). & h3 u5 w& h% K
a recursive formula. 1 P Q' c; W6 l& e$ _
divisors and partitions.
2 X' p- l4 F$ m$ {) A, z. F4 ocuriosities of σ(n).
0 I0 D, I4 _' |* V6 q! Fprime factors.
* r- @$ o7 I0 D2 Jdivisor curiosities.
 ~' }" G0 l1 W* Y Feconomical numbers. ! w/ L$ g$ A+ y
Electronic Frontier Foundation.
9 L. w! x- f3 P7 I: \3 M$ xelliptic curve primality proving. . o! E" t9 N, V* p! ?+ Z
emirp. * S* v- \! Y" f2 E
Eratosthenes of Cyrene, the sieve of. c Q |1 r4 r- D1 x$ L1 I0 x
Erd?s, Paul (1913–1996).
9 @8 M3 E4 W$ V2 H9 `+ Nhis collaborators and Erd?s numbers. / C2 }1 n% R- U% N' Q/ S: y
errors.
7 H2 G3 N3 }7 N% e# Y+ mEuclid (c. 330–270 BC). % ~: n$ K# ~" R& N$ [
unique factorization.
/ Z( @2 p8 o8 r- m# u4 P! T% H&Radic;2 is irrational. 8 b/ J0 z2 o! b- M% J; a; K3 W
Euclid and the infinity of primes. , y8 V# s' ~; Q5 r+ c
consecutive composite numbers.
& T; i9 c7 J. F" ~5 V0 o- @primes of the form 4n +3.
" X3 r, A% J/ H1 N3 @. va recursive sequence.
) w4 _9 @( j \. H' h5 P" I% wEuclid and the first perfect number.
+ m% l/ [8 T/ P6 j- Q& n- ZEuclidean algorithm. W4 _8 G m# i
Euler, Leonhard (1707–1783).
4 e. O A* u* J7 y( U3 }Euler’s convenient numbers. . T9 ^- x! p5 l
the Basel problem. 1 ? }. [0 L6 W ?' [5 _5 i( S
Euler’s constant.
/ w! j: a; g1 j3 I) V5 {Euler and the reciprocals of the primes. 4 q" {( j6 P( p' a$ K
Euler’s totient (phi) function.
$ ^4 P$ D' b, D/ U8 N: I; R2 P- JCarmichael’s totient function conjecture. . o" O7 m2 q( F6 |
curiosities of φ(n). # z* Z2 J# i% ^6 H: `
Euler’s quadratic.
/ [4 e3 d) a7 o2 u& U3 ]* cthe Lucky Numbers of Euler.
) o# s- @% s1 Y- a, c1 Rfactorial.
+ E0 _* c8 k$ [- D4 ~+ K3 x( ^factors of factorials. ' ~' C5 w0 |( }2 ] O" T: @
factorial primes. $ b3 Q$ {) H& {+ F' A* K) W% J) m
factorial sums.
: | N0 I$ l5 l0 W! P& b' T( Bfactorials, double, triple . . . . 2 I+ j2 H6 J% R r
factorization, methods of. + x" @: b( ?: L6 G# z1 l, j3 O( v' B
factors of particular forms.
 }1 R' k' v5 A$ l! EFermat’s algorithm. * W3 }3 T; v5 v, W3 r4 ?6 `
Legendre’s method. 8 ]6 C0 U: W7 m" \
congruences and factorization. 2 n$ G/ V) e% W( V! e
how difficult is it to factor large numbers?
6 w% w% ~5 R H/ u* `4 N4 Jquantum computation.
$ [; J" w& M* j% U. tFeit-Thompson conjecture. 0 y S4 \! F- Y( g
Fermat, Pierre de (1607–1665).
, d! o" K% u- a1 IFermat’s Little Theorem.
8 r4 s; n% t1 h0 O3 m. CFermat quotient.
- Y2 O" {5 `( O) b# FFermat and primes of the form x2 + y2.
9 w0 e6 r2 @2 z" k# h4 LFermat’s conjecture, Fermat numbers, and Fermat primes. 7 W5 n7 ?+ c. u& I3 `7 {
Fermat factorization, from F5 to F30. 2 }7 V* `" J4 d6 ?' {
Generalized Fermat numbers. 9 b; z5 G) n6 K
Fermat’s Last Theorem.
9 |8 t& `* s: H* O8 bthe first case of Fermat’s Last Theorem.
( Y: X! {7 e( A8 c# c% N' @Wall-Sun-Sun primes. : }, Q# z. }+ G) i6 o; V' n/ d
Fermat-Catalan equation and conjecture.
* P1 S. x: ^9 R7 R0 f* W+ ?Fibonacci numbers. ) s5 ^+ r% ` b7 ~- V, c# x6 }4 i. B
divisibility properties.
8 t. C1 |1 X9 A# @Fibonacci curiosities. , b, A7 G5 K" L2 t
édouard Lucas and the Fibonacci numbers.
5 R! X; S5 C1 MFibonacci composite sequences. 2 B5 [8 w7 B7 G$ A
formulae for primes. 1 X$ O" E9 `7 _5 F5 U9 E% o
Fortunate numbers and Fortune’s conjecture.
5 E4 j9 `1 o: cgaps between primes and composite runs. 1 p! q) ^& u& q* y5 q F; |
Gauss, Johann Carl Friedrich (1777–1855). ) g( Q5 X( a* S4 m6 C [7 j
Gauss and the distribution of primes. ' A; W8 W) l% O% n1 F
Gaussian primes. ! a" @% O5 w1 q" h8 j- K
Gauss’s circle problem.
- E. y, T2 t1 }2 a! {3 ?6 WGilbreath’s conjecture.
: I/ s2 k! v1 ^1 jGIMPS—Great Internet Mersenne Prime Search.
& J+ A- X5 z7 S' V- G8 mGiuga’s conjecture. ; @8 A/ V" D! P7 C- Q7 S
Giuga numbers. % ~4 V3 B0 P, n, p
Goldbach’s conjecture. $ h9 I8 c. |3 P
good primes. 4 m$ F: o# V3 m$ U8 D
Grimm’s problem.
0 Y: |. _6 H/ H5 HHardy, G. H. (1877–1947). ! i$ c: a' t1 D, S) u, X: d
Hardy-Littlewood conjectures.
* Y9 [7 q4 o: ? d+ Gheuristic reasoning.
+ I* m! s$ q+ @5 ~5 {# q2 m1 Da heuristic argument by George Pólya.
; V& ?5 ~& V# N8 P. F- `( w* NHilbert’s 23 problems.
 d- J$ R; J$ \2 H* [6 M6 l- ?% ehome prime.
) C5 m" F2 `. Whypothesis H.
 |( u- R+ Q/ i4 A! f$ h0 Dillegal prime. 8 A& o' }! T3 i1 a, B
inconsummate number. 0 @' I# e$ f# z
induction.
0 h9 c a# Q. D* Z0 ^jumping champion. ; Y1 }8 F& ~5 N" u. D6 S
k-tuples conjecture, prime.
$ O/ x" i" D4 j; I5 jknots, prime and composite. ; l; ~; u+ R4 U' c0 d
Landau, Edmund (1877–1938). ( s6 c8 n/ l; H( b/ H2 Q$ g
left-truncatable prime.
3 b- d" P- `! s; p! rLegendre, A. M. (1752–1833). * I8 k) |3 W: p" z1 I- x n
Lehmer, Derrick Norman (1867–1938). : ?- V& G* v# B6 r* m
Lehmer, Derrick Henry (1905–1991).
+ r" s& o5 N r$ w* q1 N" A7 r, K. yLinnik’s constant. - C8 |5 N2 ], Z7 _
Liouville, Joseph (1809–1882).
; n# O' l: t# y# Z/ e& gLittlewood’s theorem.
. w: j4 q1 }( x1 C( e* D. Qthe prime numbers race. l- _+ n" i* \0 \
Lucas, édouard (1842–1891). 8 Q9 n& n$ Z2 I) i; L5 g
the Lucas sequence.
( V5 e5 k& Q* B9 @# ~! ^, W. Oprimality testing. " {. f9 l0 H, u( t' G. H
Lucas’s game of calculation. 2 J- p1 z& z- g1 j' E G g' M$ O
the Lucas-Lehmer test. ( w/ E1 T/ z% D0 c8 v& Y
lucky numbers. " q ]2 J7 ^, S- C& k2 k( p
the number of lucky numbers and primes. $ F9 M. f. l" i4 c: @; g/ R
“random” primes. 5 O6 c7 j2 F+ |# z' f) ?' E
magic squares. 4 l! {' l, d+ s5 S A- n+ ^
Matijasevic and Hilbert’s 10th problem.
) j! m7 `- w0 W+ N" ?% e0 ^0 h; XMersenne numbers and Mersenne primes. + P% t3 l E: T$ F3 {! b
Mersenne numbers.
5 A' b& [ c1 c1 Thunting for Mersenne primes.
' ?/ `- ?) W1 H8 g Kthe coming of electronic computers. ' J* L" e1 i. i: Y
Mersenne prime conjectures.
/ Q! u2 M3 ^% e3 }" Q! M( @the New Mersenne conjecture.
' E+ C* Q7 Z" d: _- @; L8 G( Hhow many Mersenne primes? 8 ^/ s6 p; \ {9 P) a
Eberhart’s conjecture.
( P3 h- ~) |% u- ^* ]0 E$ Xfactors of Mersenne numbers. ] T; z; W. `* R( _
Lucas-Lehmer test for Mersenne primes.
8 A# ^6 v7 o% P/ E. gMertens constant.
5 w2 m8 ]# W( _! ^" C- gMertens theorem.
1 @& X8 ~+ M; xMills’ theorem. 0 _+ F. [7 Y/ N+ g1 k8 J
Wright’s theorem. # U7 h( j7 ~: D7 R
mixed bag.
! V" f4 s1 X9 _( H4 n1 }multiplication, fast. ' ~) B2 ]. M. }
Niven numbers. : @' c2 Y$ a8 |9 ^, v6 q" Z
odd numbers as p + 2a2.
6 y9 x" E7 l2 g- X; y9 x8 ^Opperman’s conjecture. % l- G# V; h0 j1 f3 i1 B
palindromic primes. 9 ~8 S$ X+ ]. P" f$ P% D9 \
pandigital primes.
$ |2 P/ A) X1 _, {4 j8 GPascal’s ** and the binomial coefficients. # S: E8 L8 Q: H9 ?. @
Pascal’s ** and Sierpinski’s gasket.
8 G$ ?; h8 V' r' f% z0 A7 TPascal ** curiosities. ) z1 o1 z6 s, l$ S* |0 P
patents on prime numbers. 4 y4 { c$ u0 f6 w/ p% L' G
Pépin’s test for Fermat numbers. 6 z! y9 R' ~* y7 s
perfect numbers. 6 I$ `. W0 n; k9 ?9 h& G8 @
odd perfect numbers. 8 w) X9 w# B$ _ v1 |* k
perfect, multiply. 7 p' R6 `1 a' o, r$ V" Q
permutable primes. + \, s; i5 y: K( U% a5 {$ |
π, primes in the decimal expansion of.
1 J1 T. C( h, E' H8 |* [, T/ fPocklington’s theorem. 7 q0 @) o% j3 o& b; m" g
Polignac’s conjectures.
Polignac or obstinate numbers.
1 ?8 B$ P9 t2 c; ^powerful numbers.
4 Q' u; L1 h2 q- H5 zprimality testing. # y. E" d3 N3 @3 U' O2 R
probabilistic methods.
+ K; X* ?' O/ Q# U" \prime number graph.
$ m O$ @; d3 L5 _% ?1 Nprime number theorem and the prime counting function.
" X% c( G9 O. }: dhistory. $ }2 ~/ }* f: n
elementary proof. 3 ~ R1 f( l l
record calculations.
& x. J; i: }: k" s" Yestimating p(n). - T; }, t* a' X8 e2 t1 F8 i
calculating p(n). ( G& I. G: o: i( _
a curiosity. - x: E$ m- F1 ~" L" t% R! D3 j5 c! Y
prime pretender. 7 o6 @' S' f9 M) {6 Z9 Q, R
primitive prime factor.
: D1 J2 y) e4 h3 f, ?; }primitive roots. 9 L* [7 n) _! y6 E
Artin’s conjecture.
$ G; C) K1 m% G% a' ]a curiosity. 9 {6 ]. T# W6 m; w' j# H
primordial. Z) D5 y5 \: q9 R
primorial primes. ( |! A) F. ~% ]% S* c
Proth’s theorem.
' J3 \' |+ |6 M$ x: V. z# W' h5 jpseudoperfect numbers.
* r; i* A- [; T# |0 i# zpseudoprimes. / O1 l7 N; Z6 w" n
bases and pseudoprimes.
! m% x2 @# Y( t/ m7 r( H5 `pseudoprimes, strong. + l# z. ] \, B! @, h4 b* F
public key encryption.
4 U* m/ B9 {% w+ R- z% bpyramid, prime. 7 n8 \' E0 d7 v5 i
Pythagorean **s, prime.
8 @9 I C1 f8 e# Q' \4 |quadratic residues. 5 k& f) ^) T/ f0 D
residual curiosities.
; }3 X% U& ^( F A0 \$ b3 X/ p+ tpolynomial congruences. ' `, m$ X2 y" u
quadratic reciprocity, law of. ; b4 r7 M2 k3 B, w0 k% @9 F0 }
Euler’s criterion.
% v I' _& \, R7 N3 m7 C% a3 LRamanujan, Srinivasa (1887–1920). 3 V- a/ t' g) w) g
highly composite numbers.
5 w5 K& Q( ?' erandomness, of primes.
 M- N( W( N( x; J: CVon Sternach and a prime random walk.
/ S0 u* [, o5 S' M) h' m' F, G' g/ |record primes.
- S9 t, m# E5 A# W5 zsome records.
3 V: H0 c' b: _9 Z* K% Rrepunits, prime. 5 Z/ D/ k( M6 p' u* M; e3 a
Rhonda numbers.
, M$ r& P3 {& L' f: y6 wRiemann hypothesis.
! w6 z: k4 h8 s c# d ythe Farey sequence and the Riemann hypothesis.
+ L* W% ~" i; o0 g! V8 Ythe Riemann hypothesis and σ(n), the sum of divisors function. ) B8 p; c3 e, J p. C, D3 O
squarefree and blue and red numbers. ; t! L# W- z- l; x
the Mertens conjecture. l& c# C5 {6 {
Riemann hypothesis curiosities.
. [0 p' O0 L* X* l( y; Z2 T+ F( ERiesel number. . r8 F5 }4 _( r& ?1 y& _9 }+ {
right-truncatable prime.
% R& `- C# }4 aRSA algorithm.
+ K) f E" d, C# \/ G! \Martin Gardner’s challenge. . I4 a8 N% a' s/ C4 `$ F: [
RSA Factoring Challenge, the New.
! d* L- g4 E* U# qRuth-Aaron numbers. 2 a: l7 V( Z6 G8 W1 n }( j
Scherk’s conjecture. 1 w. S' Z; |4 [3 ]% v* S
semi-primes. " ]4 S Z# S$ b. t
**y primes.
Shank’s conjecture. E1 R k4 f! Z/ i: X8 M( D
Siamese primes.
. y& N0 `6 V7 [4 kSierpinski numbers. " O! U3 W/ r6 V4 b
Sierpinski strings. 0 {' n" ]) x/ A( d6 e4 Z
Sierpinski’s quadratic.
8 i4 d5 S; u* K9 g7 ^( zSierpinski’s φ(n) conjecture.
+ I" k# v8 _' |; S4 S) }Sloane’s On-Line Encyclopedia of Integer Sequences.
. E$ y" x# M+ V' ]Smith numbers.
5 [/ _* P8 w+ u7 \Smith brothers. 1 t# T2 ?* Z* ]
smooth numbers. * x$ Z& b @9 Y9 S
Sophie Germain primes. . u' c2 M( L0 ~" R" [* U* J
safe primes. 0 O( ?' ?, ^* d
squarefree numbers. 4 a1 J( w' W/ S
Stern prime. " ^0 \# I5 P# C
strong law of small numbers.
7 x, ^0 m$ H J+ \- O4 V6 vtriangular numbers. 8 M5 m* i/ N; f1 [5 {, j
trivia.
8 g; |% v0 P7 w! A8 @+ m- R7 ~twin primes.
% O1 l# v/ Z; r3 [twin curiosities. # s, i7 W( `2 J" l3 ?
Ulam spiral. - D$ W, w! c% Y ^% A$ {$ v
unitary divisors. ' R. ~+ F- o( B: h
unitary perfect. 3 D4 ~/ K3 @# i a: @! e4 y- B, z
untouchable numbers.
. X! \% u" Q% M$ l3 Y! R; b6 L8 ^/ Wweird numbers.
( E3 l1 l, N, i. S9 |* U$ DWieferich primes.
$ c, s. J7 {; n% k' O) FWilson’s theorem. 7 g& K3 }2 u& _
twin primes. 9 M @0 O% I7 s9 @
Wilson primes.
/ N7 _/ L' X' ], zWolstenholme’s numbers, and theorems. 3 z. N) U! F8 ^0 v! F* ?
more factors of Wolstenholme numbers. 1 ?6 \5 Y7 r# C. x1 I
Woodall primes.
1 l. }! ~1 R# w3 gzeta mysteries: the quantum connection.