查看: 4688|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. / 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 x2 + y2. + 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 F5 to F30. ! 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 + 2a2. , 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.