查看: 4612|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 |正序浏览

|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. . U6 `. I( v F& C) H7 _$ V
abc conjecture.
: T1 {2 b, x3 t" A2 wabundant number.
) h& _$ K+ M8 Q+ D0 w' a( ~1 X$ kAKS algorithm for primality testing. 6 M" e0 q J; R, |2 y- V
aliquot sequences (sociable chains).
9 c, W" n5 M2 d! f" Malmost-primes.
+ D6 f. {* b# P$ Hamicable numbers.
) e! w" s, P- C5 m- Y* y, xamicable curiosities. * U$ \- a5 X: W' K8 o9 d
Andrica’s conjecture.
) a" a$ u: ?6 y+ `arithmetic progressions, of primes. ( u) V$ l6 o. S# k- O, J( t3 E ?: t
Aurifeuillian factorization.
% H; R: }3 e+ V: S0 paverage prime. " G* s# I% O& n j
Bang’s theorem.
# S( t* k% i1 ?: Z, l' p+ NBateman’s conjecture.
9 r) R$ D8 R# c/ {" e8 Z! vBeal’s conjecture, and prize.
 r U2 R) m% L) D- n, OBenford’s law. / Y) B5 t6 X% d' L2 ~5 @
Bernoulli numbers.
5 r+ `9 @$ q# @. s& M6 t2 QBernoulli number curiosities. 5 ~2 X- L! y! Q8 x- b
Bertrand’s postulate. - ^5 b+ i# T1 @) z8 ^) E) Q
Bonse’s inequality.
9 \. }+ ]4 \. J! b5 p oBrier numbers. % T' ? S! C7 c$ S4 j! Y
Brocard’s conjecture.
: b/ s3 b% Q5 }6 U) @Brun’s constant. + R. [! s3 ^ b. b2 w: S
Buss’s function. , y- Q- u7 \, q, ?+ Y' Q( @; e. P6 c
Carmichael numbers. * b3 e& w# @0 c4 o' w1 Z3 [
Catalan’s conjecture.
" R# w; A) k; b' U. Q. M3 Z: [Catalan’s Mersenne conjecture.
 z S4 s' h0 X9 ~, b; \9 _& SChampernowne’s constant.
* G% n) e! U* r0 V3 I$ ~champion numbers.
+ h" p Z' ~* @! X$ q: JChinese remainder theorem.
7 Z* S- b L' i* c% z7 m2 S7 @2 Bcicadas and prime periods.
! R; o( p9 F3 C0 ^& h1 [+ Pcircle, prime. 9 d3 ^$ _! e- v' R# D0 w% m
circular prime.
( y& Y' i4 b" j+ [& L$ Q8 LClay prizes, the.
. A, b7 o% h9 u) Hcompositorial.
# T7 E/ [5 A2 [concatenation of primes.
) F9 Q; N. G& g1 f* B+ t+ mconjectures.
% Q$ z. M0 H5 Q# Pconsecutive integer sequence. 8 ^" u. w- |+ ~5 C- A
consecutive numbers. & G, z8 g; P& B& c
consecutive primes, sums of.
0 e0 F5 \, J& @% P, }3 X9 [- ^/ fConway’s prime-producing machine.
' `3 S! Q0 ~! R- ? T0 ~( Qcousin primes.
; r: J" o- X4 T tCullen primes.
" U* `, }1 ]' E0 D; a5 }3 ACunningham project. . F2 ]4 Y+ ^; ^! m# f
Cunningham chains.
" W' i5 S; @2 _ ?( zdecimals, recurring (periodic). : n: t6 ^% x& R4 v8 T6 k
the period of 1/13.
" `8 P, P: `+ E% Gcyclic numbers. # |+ p( i9 h/ r
Artin’s conjecture. " j, h/ G" t, M0 f, p* F7 _
the repunit connection. 4 L w" k% z6 ^5 }
magic squares. 4 X, S( C# x8 U6 L4 Z, o7 v
deficient number.
3 L1 {- S7 }- u. tdeletable and truncatable primes. & `% A5 @( E( y7 ^3 q2 c
Demlo numbers. 1 g, z' [" ~8 J% e
descriptive primes.
3 O, Z q+ i0 G4 ~& ]6 }Dickson’s conjecture. 5 A$ K$ |5 {6 Y; U8 f* }3 S' x
digit properties. 8 ?* N8 X: u2 Y! R4 X4 ^
Diophantus (c. AD 200; d. 284). 8 N$ w3 s& b0 q' I: G0 @( b" R0 |
Dirichlet’s theorem and primes in arithmetic series.
- A+ F% C1 Z; m) B, F' X3 Xprimes in polynomials.
, g+ g+ L5 m: F; K" i! ^! xdistributed computing. 8 L% @, `" j0 d# q+ j2 N
divisibility tests. ( }! K# }) S4 a6 G: I- A& I9 o7 h
divisors (factors).
8 |6 [* t+ R }- X8 Bhow many divisors? how big is d(n)? 2 K% \3 M4 ?7 @
record number of divisors.
# j! U: f' |' p4 K( Y" x/ gcuriosities of d(n). 6 c! u8 ~9 X" ^, v* I# X! D& S
divisors and congruences. , a6 H8 U% h$ q) A6 x) e" F1 @
the sum of divisors function.
! C* L+ _5 k& G4 Z ]. ^the size of σ(n). : D. J7 r- h O) J5 H( W; d9 z
a recursive formula. - p- d7 \1 s7 T6 q
divisors and partitions.
! c, f0 i4 N4 ^+ h# e* Q, |3 ^curiosities of σ(n).
! {. ?2 |( J5 u! p; aprime factors.
- e! Q4 Q; d! j: }' ddivisor curiosities. 6 D. n4 B& f+ t5 E. L+ a
economical numbers.
: ^/ E/ D/ i+ }$ A4 l1 |5 ~Electronic Frontier Foundation.
6 j2 }% J8 \' K$ B1 r \elliptic curve primality proving. * n& o& f% a2 F7 j
emirp. . V. `7 Y F5 u5 q/ k7 A) C6 w- F, s
Eratosthenes of Cyrene, the sieve of. ! o& _( K- \+ A6 D8 Q) u8 `1 D. Q* \
Erd?s, Paul (1913–1996).
" U# t4 p# _, R2 T; ehis collaborators and Erd?s numbers. ) x, y) z4 M/ ^# x8 h0 {
errors.
3 |% }5 I" R$ t# N. dEuclid (c. 330–270 BC). + @! ?4 S1 G4 M7 q. q
unique factorization.
' `9 I& G! q6 I9 L L% b) o&Radic;2 is irrational.
2 N6 O! A$ B( E/ REuclid and the infinity of primes.
* G$ l/ `7 E8 B Mconsecutive composite numbers.
9 M4 g6 H+ X$ X7 g6 |primes of the form 4n +3. 1 Z: _1 \4 i( B/ p* O9 a; k
a recursive sequence. d7 o4 J8 W; I) Z" z3 b8 I% H
Euclid and the first perfect number. - J* h, I8 D( E
Euclidean algorithm. - q* G' S S4 t) e1 n- c
Euler, Leonhard (1707–1783). $ L4 z7 h! |& X) `" }" h
Euler’s convenient numbers. / r; t* b$ s( X) U b
the Basel problem.
, G: A# R* G" }Euler’s constant.
; ^6 g2 w$ N: X: ^6 u) DEuler and the reciprocals of the primes. 0 }9 U4 c" d8 Z0 l. y5 A0 [
Euler’s totient (phi) function. 0 S" O! F) ~8 P8 f
Carmichael’s totient function conjecture. 7 n& e$ b7 O- {4 H
curiosities of φ(n).
$ p5 ?6 d( `7 XEuler’s quadratic.
+ P' \5 E5 I' J1 s% p! |1 sthe Lucky Numbers of Euler. * }" h- M2 F1 O V1 u
factorial. ; U, M* h P' J! j% s
factors of factorials. / y& S2 M8 b5 @1 B1 Q+ T0 _
factorial primes. " j8 g" n4 _) j* p( ^. @- Y
factorial sums. 2 `4 R! j% l0 \# `8 m
factorials, double, triple . . . .
2 e; J; T4 n; Z% g8 L) o$ \1 [factorization, methods of.
. P6 _7 J' `( V3 X( Tfactors of particular forms.
$ E( C4 K$ J5 _+ L1 kFermat’s algorithm. - F6 Y, f t9 _& R; D- z' L; i
Legendre’s method. # \. r. H& ^7 X1 n f4 ]; ^% A
congruences and factorization. % j' ?7 R0 Q/ {8 {- [- p6 L& W: L
how difficult is it to factor large numbers?
0 p f) t$ b; nquantum computation. : F ~! s* I3 H- K/ |
Feit-Thompson conjecture.
* f% r$ T: N: f4 GFermat, Pierre de (1607–1665). % W+ V9 Q# U1 p) ~
Fermat’s Little Theorem.
; }9 _! p0 n0 q4 ~* ?' v* x0 P( [Fermat quotient. ; R4 H* M3 b* R! T/ ]
Fermat and primes of the form x2 + y2.
- l5 ~" k& _0 MFermat’s conjecture, Fermat numbers, and Fermat primes.
- V/ Z7 B0 ?" y0 v) p; F& w1 U0 ZFermat factorization, from F5 to F30. ; x8 A1 u" v* j4 m
Generalized Fermat numbers.
# g# _& A0 y6 s3 N4 @. `* \5 wFermat’s Last Theorem. 0 [$ S8 S4 `! y/ K0 Q
the first case of Fermat’s Last Theorem.
% A \) x$ c- E8 v1 yWall-Sun-Sun primes.
; u3 ]5 K- U/ m' I6 WFermat-Catalan equation and conjecture.
& [: e2 i4 e" i1 ]+ n" {- c( QFibonacci numbers. " k8 K1 D9 a/ l' z4 a6 [$ s
divisibility properties. : e2 O; x9 m5 l. h; I
Fibonacci curiosities. 2 U ]6 f1 Z+ h$ W' X0 U8 Q
édouard Lucas and the Fibonacci numbers.
/ j6 z6 W, e3 Q0 g' L9 k' e- CFibonacci composite sequences. " s: A1 a4 x6 g- g# m
formulae for primes.
1 }# t# E1 t# l( @Fortunate numbers and Fortune’s conjecture.
2 C1 e1 O% @. J4 b! |; Y2 pgaps between primes and composite runs. 3 {" p8 o4 d& ^ i' j' t
Gauss, Johann Carl Friedrich (1777–1855).
1 v" Z/ s7 u4 [# Z+ s& O% k9 D" mGauss and the distribution of primes.
: P6 X x4 @$ }% dGaussian primes.
, u' ]1 P& u0 Q+ c, p( N" G1 uGauss’s circle problem. ; }0 E. u- ~ p* i4 j
Gilbreath’s conjecture. / t. l* V, p# [- n" S$ k
GIMPS—Great Internet Mersenne Prime Search. ) d7 |" }6 ?1 m! K/ {
Giuga’s conjecture.
; ?# g2 _) S/ X2 j$ RGiuga numbers. 5 |3 h* x; b. B1 Q0 f# j( \
Goldbach’s conjecture. & C/ ~) G# }1 l# Y1 F8 A
good primes.
! w& A; Z2 n3 L. |# Z8 iGrimm’s problem.
3 x; |' `* ?# k3 {1 `Hardy, G. H. (1877–1947).
& u' a4 m: s; NHardy-Littlewood conjectures. 9 g$ w6 [3 B/ ~+ e5 w2 B6 |, s1 A
heuristic reasoning.
 V$ U1 Q' R0 Z. p+ I( z6 W* Q# e1 Ya heuristic argument by George Pólya. 6 R/ m/ C( {/ z* J4 W
Hilbert’s 23 problems. $ n# h( w6 o( @& \. s6 e- e
home prime. ' j$ M/ Z" b* l& s
hypothesis H.
( Q9 r3 i- ]+ m, a6 Sillegal prime.
, |" C+ }$ m; J/ p- k5 g# ?inconsummate number.
! m9 Q, Z+ j: Einduction. 8 |4 j+ @5 `, Q2 s& w* _& l1 m
jumping champion.
! F$ E" D0 @1 d: Z( f3 n1 Ok-tuples conjecture, prime.
; `5 m4 W7 Z( M; pknots, prime and composite. . f1 Q& n4 V# n$ K% w1 @ S# W6 o9 {
Landau, Edmund (1877–1938). 4 j& ` h8 J2 |' R1 d1 P
left-truncatable prime.
5 {7 a% X Y2 @2 R) ]( g5 C8 CLegendre, A. M. (1752–1833). & {% v/ ~8 |* U0 Q0 @
Lehmer, Derrick Norman (1867–1938).
& z0 e T9 Y- F. F0 y( f) J; Q" fLehmer, Derrick Henry (1905–1991).
+ G! W! s# p6 b+ nLinnik’s constant.
1 _ ]2 M+ r7 A7 v( DLiouville, Joseph (1809–1882). 1 h) B7 J2 W' q% V5 O# Y& @
Littlewood’s theorem.
6 g. |/ E: y5 t }7 {, bthe prime numbers race.
% c2 Q% n% \. C2 QLucas, édouard (1842–1891).
3 D5 V2 Q2 |1 v( g/ C+ R- }/ @the Lucas sequence. 9 \: l4 i& X# z( Z5 `
primality testing.
! m0 T8 }3 w& fLucas’s game of calculation. - y/ J, q% U6 h7 ~2 l* G. q7 F
the Lucas-Lehmer test.
: n$ Y% s7 j6 a- `lucky numbers.
# n, Q I6 ]- {! F+ K; r5 Ythe number of lucky numbers and primes.
- r" ], h. w& }# v“random” primes. " e: K# O$ r& W8 _# N* N
magic squares.
6 A, S1 d) y$ N, Q5 f! HMatijasevic and Hilbert’s 10th problem.
% v+ G$ l+ K2 M( |+ H* I( yMersenne numbers and Mersenne primes.
% I3 O; d0 T! Y! u2 sMersenne numbers.
" f" E3 S. c! R. Y; E9 uhunting for Mersenne primes.
, g/ ^6 P$ \, k6 Z: o$ Ethe coming of electronic computers.
( e2 Q5 R% P) P3 eMersenne prime conjectures.
6 g* P/ w9 } T6 R$ a5 E6 r Kthe New Mersenne conjecture.
$ l8 r$ i3 |0 v, ghow many Mersenne primes? 3 _, [4 L' N, ]% Z6 f1 H- ]5 H* r
Eberhart’s conjecture.
; P# a8 [2 S8 t+ c; X; R; q0 Rfactors of Mersenne numbers.
3 {$ C5 Z' P+ qLucas-Lehmer test for Mersenne primes. 9 m L, K" Q: N
Mertens constant.
3 Q4 K }5 P/ @9 z& n- eMertens theorem.
0 ?+ d8 Y& r9 R8 j' TMills’ theorem.
3 C0 Y" e6 S, \8 s2 |- u m- iWright’s theorem.
: b5 D$ { E! X, l# Hmixed bag. 4 L5 H+ z0 L* V3 O
multiplication, fast.
: ]0 x: s6 H- o/ M' P9 uNiven numbers.
0 G3 Q% n/ D' ]' U/ N; p: uodd numbers as p + 2a2. 0 ]; D& R# \* e0 e f. @
Opperman’s conjecture. . \% S+ ~% g }: O5 _4 }+ i# k
palindromic primes.
7 |+ p- g, J Upandigital primes. 6 t+ X; z0 e" \4 J# E
Pascal’s ** and the binomial coefficients.
$ u! W7 s7 C1 |4 Z, [Pascal’s ** and Sierpinski’s gasket. 2 U6 p9 C. d0 B/ T1 }$ j2 X9 O% r
Pascal ** curiosities. 2 f) N k* E9 U K [* S0 Y! L2 G5 {
patents on prime numbers. 0 s. R8 W. n( c$ W$ v3 B$ @
Pépin’s test for Fermat numbers.
: {, S) J& Y% z; o" x& dperfect numbers.
: N) `$ r* Y: L- [9 l8 ~odd perfect numbers. & V7 U, K& D. E; f8 Z
perfect, multiply. ; h' }; ?# N: a8 j+ `7 u2 T
permutable primes.
5 e! v8 f, E! R, r2 Z' {" wπ, primes in the decimal expansion of. ; j: g0 X! U; j, G" E
Pocklington’s theorem.
+ ? `& y$ h2 R4 c/ ?2 PPolignac’s conjectures. % o3 T0 c f" M$ i8 e9 v* f
Polignac or obstinate numbers.
6 t* V. |! n& ]' D# B2 {powerful numbers.
( S5 X0 V5 {- u8 gprimality testing. ) e6 A+ B+ U2 z& @1 P% ?3 [- y
probabilistic methods.
1 u3 F) }. i# _( Y$ ^6 `3 hprime number graph.
& f+ f. F/ Z/ U$ l9 Tprime number theorem and the prime counting function. " D/ T5 }* h) Z" h( H& Q/ B+ k' W# X% g
history. % f$ n3 P; y; Z4 H* M' x* n
elementary proof. 1 Q/ m6 c' B& a7 M& k' G
record calculations. 2 D9 F4 a2 n. W* b( ~5 U
estimating p(n). 1 f6 L7 T# D7 F+ ^) f7 A- R
calculating p(n). ) o" [+ |4 x0 j; M+ X- H* _
a curiosity. # @. c1 }( G! W0 w
prime pretender.
4 M; R, g4 T8 l3 U- ?/ V9 ^9 Lprimitive prime factor.
1 G F% }" D; Wprimitive roots.
, U% Y0 F2 ~* q9 |! U3 F* JArtin’s conjecture.
, b$ c" X5 K& K$ _4 v% Oa curiosity. ! V$ b$ \& t7 L4 V `5 ~; ^
primordial. 4 y, L6 L: c/ M# V2 h' y
primorial primes.
6 z6 W6 h' Y% G! t% V; f6 IProth’s theorem.
/ O5 Z' e$ ~) V6 Upseudoperfect numbers. ' ^1 z7 k) l- i+ n: Q' q [2 {+ D
pseudoprimes. . `0 z' C# n {2 [+ @' G
bases and pseudoprimes.
6 \* p$ d" F ~) k5 ypseudoprimes, strong. ! s* U* l0 S+ Y; ~! y1 k9 M
public key encryption. $ Z n, n. Y- E# [+ g+ d7 U8 [& d! C
pyramid, prime. ! p: d+ a" h Q$ H
Pythagorean **s, prime.
) b# M0 b; O2 ~ Xquadratic residues. + \( J0 m$ m# t# n. ?
residual curiosities. 2 s+ o; _) J4 P
polynomial congruences.
$ Q5 z/ z' R7 ~6 r5 bquadratic reciprocity, law of. & F) Q" Z$ E: s# F/ ~5 ]
Euler’s criterion. " {. T, K$ u' l) K7 T
Ramanujan, Srinivasa (1887–1920). + d4 m4 x) C m. }
highly composite numbers. 0 _% g: j4 C9 E
randomness, of primes.
8 O% b2 K7 \' k6 e6 LVon Sternach and a prime random walk.
& p( ~3 ~7 {7 `4 G4 h+ Q2 Erecord primes. ! T, |% W1 W( p. x8 F
some records.
- t8 N c% {8 F3 D) yrepunits, prime. 8 Y' H! k! A0 p k9 k" p
Rhonda numbers. & p) t- q; G7 c; s/ M1 E5 K
Riemann hypothesis. % W) f3 o3 l1 b1 c( i1 G
the Farey sequence and the Riemann hypothesis.
5 B/ V, _7 ?$ P& j: Nthe Riemann hypothesis and σ(n), the sum of divisors function.
. r$ n0 W8 Z$ E) Tsquarefree and blue and red numbers.
" }9 m- E# D/ j$ X5 [; e. Bthe Mertens conjecture.
, [8 Y- f+ @8 L% l. wRiemann hypothesis curiosities. # v7 Y" a6 V6 h$ d0 A1 ~
Riesel number. 2 U$ A8 x# f7 _1 _( B+ G1 q9 ^* @
right-truncatable prime.
( ~6 }; Q5 t4 K; d% b# K! D' hRSA algorithm.
; E9 H2 f$ n: h* r5 |Martin Gardner’s challenge. R- [4 b2 P& K1 @* y/ G. K
RSA Factoring Challenge, the New.
2 q3 B4 k# x3 z5 a, QRuth-Aaron numbers.
0 k: Y! F8 E3 C3 r( HScherk’s conjecture. ! J) E8 k; q; N s& L
semi-primes.
( f7 p. V1 u4 F+ K' @7 @**y primes. 1 ~- [8 B( ~$ x; y, H9 @( Z
Shank’s conjecture.
3 @9 E2 D& v" N4 s4 jSiamese primes. & m, @% c0 w0 I0 ~
Sierpinski numbers. ) a' t0 R5 S/ }1 u+ Z% ^4 z
Sierpinski strings.
: V6 Y# L+ t2 w' W9 B, L0 ASierpinski’s quadratic. % ~- d' |7 u0 r
Sierpinski’s φ(n) conjecture. ! n) V" Y2 ~# ^! I" `7 c
Sloane’s On-Line Encyclopedia of Integer Sequences. , J, V5 |. N) p
Smith numbers. " l; L3 f8 T4 h+ c
Smith brothers.
 F2 q$ r. v& _* X& s2 hsmooth numbers.
. q7 C1 u* e: _8 jSophie Germain primes.
5 Q8 K9 c# C5 X# v/ C; G( Q2 x; Y @safe primes. ^) }: r. w; S7 S9 p w
squarefree numbers. $ U* b# z* [; Z3 n
Stern prime. 0 m/ {! W( a! |* V, v! ?
strong law of small numbers.
& J! |) M6 @1 B8 htriangular numbers. ! z, I. L) f' `5 z/ g" M' m
trivia. + E( ^# t7 k- p$ J% F
twin primes. ! \3 N) u" }$ r# [; B
twin curiosities. 6 W5 ~; |) P h; d& y+ e; j- x
Ulam spiral. ; ^) B& w9 p, R6 I8 _" g" t* r
unitary divisors. " H* O( Z/ R* c
unitary perfect. 7 h1 K( r+ g8 a5 W6 }, U3 c
untouchable numbers.
9 u3 [, u; g( @6 eweird numbers.
# f% b+ Q# D$ X6 [- \0 Z9 mWieferich primes.
# N! }: j, @/ `9 G9 BWilson’s theorem. 9 c h8 ?$ C, t- C( p
twin primes. ; p+ l6 U6 \6 N# G
Wilson primes. 3 X% C( o! V) ~4 o, p; w
Wolstenholme’s numbers, and theorems. - V9 R O, }- H: D
more factors of Wolstenholme numbers.
: d: ]! U2 r$ ^$ O- pWoodall primes. 2 E/ K. i# S6 L5 K
zeta mysteries: the quantum connection.