查看: 4800|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	7 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. ) Q, t7 I1 }% A- F- ~
abc conjecture. 0 d1 V* l- ~0 r( ^
abundant number. 3 G) [! J5 Z+ M& i3 N+ V$ Y1 V
AKS algorithm for primality testing.
5 h% D: [/ D/ Raliquot sequences (sociable chains). ) a$ D+ \1 c$ A Z9 G3 V' X
almost-primes.
+ j- S& u& P7 {4 r" `amicable numbers. " S& K n- N) }
amicable curiosities.
/ K3 `+ D; ^6 Z& g7 ?Andrica’s conjecture.
4 S- ?/ {7 f: \! @! iarithmetic progressions, of primes.
% a/ X! h- i, b2 T: l eAurifeuillian factorization.
) A: e3 r! q ^& [* x. r0 }6 r1 Vaverage prime.
( m4 u% G, q. A( E+ ]8 xBang’s theorem.
. T+ I2 N9 F" `Bateman’s conjecture. 7 o w) X+ O: q, b R6 d! g$ w+ H
Beal’s conjecture, and prize.
8 z2 n; I8 {" R6 C% p# I4 J- SBenford’s law.
% \* S0 G2 l0 a; D9 _" s1 s$ Q( I* `Bernoulli numbers.
 L E3 K+ ~& j7 \/ }" v P$ jBernoulli number curiosities.
8 `6 n! ? @* r- SBertrand’s postulate. / u" N; q. z' @' e' c4 y
Bonse’s inequality. 2 U7 u! Q1 |1 x* }" ]4 ]
Brier numbers.
* U5 d H$ \* {Brocard’s conjecture.
( s# m3 D& h6 \Brun’s constant. ' L1 D- {3 P6 z% v( x$ I# }% {
Buss’s function.
. D9 ~# z, j$ \; y1 } VCarmichael numbers. 3 g3 ]7 O% ~# e. b( l$ `
Catalan’s conjecture.
0 T2 O. E' F$ @) s2 Q6 pCatalan’s Mersenne conjecture. 6 O3 i6 a. ~; w1 R" Y
Champernowne’s constant. 7 T- |) M; X5 f0 Y7 r
champion numbers. ) \& z, N7 I$ r! J' {. j Y5 q
Chinese remainder theorem.
# h! w. W# Z7 e" t, p$ ecicadas and prime periods.
7 G/ I" t+ M8 acircle, prime. + p1 D ~0 G1 m/ b& x6 {
circular prime. ; P5 O% d' a1 n Z. X9 J' E
Clay prizes, the. . E8 g, D6 I7 a; E j" f
compositorial. ' Q r8 H7 ^0 }# C3 A5 q
concatenation of primes.
' ~1 C3 t3 h E, S( S# O mconjectures. , e: e$ j# d0 I: z0 d# |, ?
consecutive integer sequence. , O9 @5 y0 |+ z" O( t
consecutive numbers.
. B# f& }9 G% O3 v3 y! B* ~consecutive primes, sums of.
$ |4 W+ E3 p1 s. mConway’s prime-producing machine.
/ R# m S' ~* L7 rcousin primes.
$ b+ c# T5 B9 B) c! i0 hCullen primes. ' @! D9 D- [0 g
Cunningham project. " A5 S: U5 M+ w5 V! |! u
Cunningham chains. ' c5 N$ I5 Z, h `4 w- c8 f
decimals, recurring (periodic).
- \! d7 j' H* z" U1 ^- ethe period of 1/13. ) t6 U9 `; B6 C7 y* ?7 v
cyclic numbers.
% M' x! Z4 {$ h8 w7 I2 Y9 Q. G: UArtin’s conjecture.
# e2 o6 J9 A) y" y/ i" ]the repunit connection.
" |/ [5 i! s! o( Umagic squares. # D* `; S' F$ R! E: O
deficient number. . |6 ?* ]2 o: \
deletable and truncatable primes.
4 d/ F$ g/ e+ e5 c. h( h5 yDemlo numbers. $ E! {6 B; f& K) }- \+ ^
descriptive primes.
! j t/ p) J6 i# Q: }Dickson’s conjecture.
/ @: y- B: @ |3 vdigit properties.
! w* l5 E: s- X1 H2 XDiophantus (c. AD 200; d. 284). $ {5 `5 R7 k3 B' i# E& _# q
Dirichlet’s theorem and primes in arithmetic series. O2 W! Y2 [; V5 Y/ s S
primes in polynomials. ; E9 _! X6 L1 \' O# Z4 S
distributed computing.
3 O6 F9 _5 ]; N! L y2 R) r( E2 T6 vdivisibility tests.
2 f8 | J- M# B& ^! Udivisors (factors). 8 |9 Z7 Z. z* D! c( C
how many divisors? how big is d(n)? ' K1 }0 e1 l/ F" z
record number of divisors. 8 W' W- w8 c3 m' _: |6 P
curiosities of d(n).
: K2 _7 E# X0 ~/ b" |1 w! N! [divisors and congruences.
# Z; _+ Q# y8 Ethe sum of divisors function.
4 e- e A w8 s; C+ f& {the size of σ(n).
' d8 ~+ N8 t O& J9 s Sa recursive formula.
( \( Y5 B; g& d# a. z, N8 Jdivisors and partitions. 4 `' S8 O8 B& X' ]" P
curiosities of σ(n).
4 M2 @3 u3 S5 _) l: ^3 }prime factors. , N: t9 [% F- v* `
divisor curiosities. " O! X# ]; L6 T% z
economical numbers. , @ B) X9 ?2 h: j: g* H
Electronic Frontier Foundation. 3 y, ~5 v% g2 a9 j& ^
elliptic curve primality proving.
5 m! Z8 {/ b( b! [6 ~% ?/ Pemirp.
) V5 [& o0 c. j) _& Y4 lEratosthenes of Cyrene, the sieve of.
3 G1 L; S8 @4 `/ \! WErd?s, Paul (1913–1996). 3 d- N) |4 o6 h% F- o6 S
his collaborators and Erd?s numbers.
# u4 s3 y$ J) z4 q2 S, Serrors.
0 f) O& ^$ x; v8 S$ XEuclid (c. 330–270 BC).
) P6 T7 Z# D: L* ]7 Z9 ]: Uunique factorization.
: i p- T: V. f; j! A&Radic;2 is irrational. : ~! x6 J1 g* e( }
Euclid and the infinity of primes.
 |# g' \8 ]* g+ B0 [$ o) [4 j. econsecutive composite numbers.
4 L7 h3 ~* u# Q4 j+ y: b/ Y) l( |primes of the form 4n +3. ! H0 E3 S' Z7 K6 }; T) @( ]
a recursive sequence.
, H/ d& ] e( A) ]. }$ a2 q o: iEuclid and the first perfect number. ! T7 l3 c7 S) E- I: X- H# N9 Y9 \
Euclidean algorithm.
5 d6 v, m, [8 b! f! W9 }$ yEuler, Leonhard (1707–1783).
: X* }9 q, e" n" P) y, eEuler’s convenient numbers.
) G0 W+ Y: b/ ?2 R) T0 tthe Basel problem.
' U4 m- l7 b* g- }! }% i6 H! OEuler’s constant. 3 c4 j1 o8 z2 {7 h
Euler and the reciprocals of the primes. 8 @% ]2 m: M+ n. T( P! I5 D9 O
Euler’s totient (phi) function.
! C7 O. t% J c; t& ? |! N/ GCarmichael’s totient function conjecture.
8 }+ [' z' i5 S+ q) D1 }# acuriosities of φ(n).
4 K8 X9 j" v, n5 ^3 ?- ~8 eEuler’s quadratic.
6 a# M+ j+ _1 O% E* L0 ethe Lucky Numbers of Euler.
7 x3 j* S: Y3 p$ A" X% Dfactorial. ' D" j; ]2 j' `' h
factors of factorials.
, }. l: c4 q* M( Y1 Jfactorial primes.
0 }2 A; k" K y; Pfactorial sums. ) O S1 @8 M# D" y; Z4 R# h
factorials, double, triple . . . .
7 A4 s0 ~% h' y" Dfactorization, methods of.
+ w! P: b/ Z5 l/ Z7 P! w% rfactors of particular forms. 4 x) h. T# N, I+ z U9 Q2 R
Fermat’s algorithm.
3 g* i% g3 F2 V! t1 g: xLegendre’s method. f! R$ p2 u+ v( b
congruences and factorization. & \% d4 i. a% o' }+ V8 \
how difficult is it to factor large numbers?
; Y5 b' ?( D, \* zquantum computation.
! @$ j* k, I1 |( y6 \/ `) T- CFeit-Thompson conjecture. ( j$ L. m! P% V' e
Fermat, Pierre de (1607–1665). " l0 K. `5 _/ S& [) I' [6 k& i- R
Fermat’s Little Theorem. 1 ~' |! T% v7 x, a K2 H: h
Fermat quotient. # p; r0 b1 Q4 E+ @, @7 A6 U
Fermat and primes of the form x2 + y2.
. s+ B. e/ q+ G( a- @, aFermat’s conjecture, Fermat numbers, and Fermat primes.
5 }) ]4 B) F- _+ o& P; NFermat factorization, from F5 to F30. $ S, T8 {/ d7 ]6 q. P1 p; M
Generalized Fermat numbers.
5 n) E* c f5 Q9 F1 h4 x3 o! zFermat’s Last Theorem.
5 `6 b6 P# F* Athe first case of Fermat’s Last Theorem.
3 j/ Y, G7 Z1 _$ BWall-Sun-Sun primes. ; X( a% t0 J- a8 I
Fermat-Catalan equation and conjecture.
9 @, H5 N( {# m1 F' `1 y% d nFibonacci numbers.
- X$ c6 I6 U! @! L2 Pdivisibility properties. , l$ }( A# ?7 |2 i& l5 [
Fibonacci curiosities. * z( } [' l* f4 R0 @) N' x
édouard Lucas and the Fibonacci numbers. , M. X9 |# B3 R% `8 [
Fibonacci composite sequences. * Z1 G7 j$ ]* }; `
formulae for primes.
* e/ b2 y5 h" ?. B: S; y WFortunate numbers and Fortune’s conjecture.
# C( y) C( `6 F% c( Mgaps between primes and composite runs.
( \; A$ m" \2 D+ m9 j* G( y5 kGauss, Johann Carl Friedrich (1777–1855).
& F4 b0 i# j5 Q R$ FGauss and the distribution of primes.
; t9 x1 J. Q, n! v% R/ GGaussian primes.
" Y% U' I# {9 W( i, z/ [2 t% lGauss’s circle problem.
5 w+ c- d9 C- C; UGilbreath’s conjecture.
, h8 A. x; G! d' L+ aGIMPS—Great Internet Mersenne Prime Search. u1 o8 _2 F/ e) i) z
Giuga’s conjecture.
4 {2 D. V6 H- i; b/ S7 X$ kGiuga numbers. ! e. A- z5 M7 A$ D ^ b6 [
Goldbach’s conjecture.
. T: L$ i1 f- B$ Kgood primes. 1 y# g8 x+ f! S; {; g7 @: v: ~
Grimm’s problem. 4 D4 W2 F$ T: e
Hardy, G. H. (1877–1947). - ~2 c9 E1 Q! s+ t8 D- m
Hardy-Littlewood conjectures.
( D- W% Y# Z1 d+ P$ x2 }+ A1 U) qheuristic reasoning.
. w+ v& N* V7 W1 ~a heuristic argument by George Pólya.
7 u8 W `5 }3 ?7 A I9 a) vHilbert’s 23 problems. ! \' q" y! ? d8 \
home prime. * W7 P2 p# V7 B4 n8 v5 n7 o0 v2 L
hypothesis H. : r- G- J, c1 \4 D( t: z" [
illegal prime.
# [0 |1 {/ i1 A' _$ \( A& finconsummate number.
. w& F1 t; U. c, E" uinduction. - G' |; `1 S( i3 ?) q6 n
jumping champion.
, p4 I) W; l6 Y( Bk-tuples conjecture, prime.
! I/ C2 O. f O9 R, lknots, prime and composite.
" |; s/ S$ R* S7 ]/ p, ELandau, Edmund (1877–1938). ) Z6 l; M/ i: }" R0 G* y: x& _
left-truncatable prime. . U9 ]5 G$ O5 d& w/ F: u+ ~
Legendre, A. M. (1752–1833).
, x3 l# n/ _. ULehmer, Derrick Norman (1867–1938). * K0 R! ], j3 s M
Lehmer, Derrick Henry (1905–1991). 4 C0 X9 d* w4 z( r& h: l
Linnik’s constant.
 d8 U' o- x# x; h7 }8 V8 j+ B! ?Liouville, Joseph (1809–1882).
! G2 p# S% q- c7 t8 Z) GLittlewood’s theorem. 7 O* m, \+ W( ~5 Y, _$ T
the prime numbers race.
9 @* ?! [9 k* ?! WLucas, édouard (1842–1891). % p$ R1 s" Q9 T5 B$ Q7 I7 Q. `& J( m* k
the Lucas sequence. 3 J- A$ z; F1 u- y' c
primality testing. 8 ^4 a3 l+ v: j/ ]9 {
Lucas’s game of calculation. 4 G' ^! z+ V/ Y
the Lucas-Lehmer test. & K% N t) C. D# l
lucky numbers. ) {0 L8 T! }1 K2 D. a$ K6 l+ T
the number of lucky numbers and primes. ! Y8 U2 P8 P- }4 d2 d4 G. _8 F
“random” primes.
( m1 ~4 v l2 Y9 c4 H: d7 Cmagic squares.
6 `/ L& h7 u7 q5 @7 v) ^Matijasevic and Hilbert’s 10th problem.
8 O( ^% S' w! tMersenne numbers and Mersenne primes. / ]- ~4 K1 s2 a( j2 o8 a+ z! E9 D
Mersenne numbers. 8 q$ O2 n) f8 r7 b& }$ v E
hunting for Mersenne primes.
5 a6 H. k' l \+ E) ?the coming of electronic computers.
; o. ~! k4 S4 h) ?0 |Mersenne prime conjectures. 8 B* k/ _ v1 Z$ E5 ^
the New Mersenne conjecture.
# g9 U, C2 X* J: d& F, [$ jhow many Mersenne primes?
9 G! O$ Y/ e FEberhart’s conjecture. # {) X" r5 c" d% A- k/ L
factors of Mersenne numbers.
7 @8 D' \8 K7 Y! _+ _Lucas-Lehmer test for Mersenne primes. : N2 ?3 f% x' R% K3 p1 {5 K8 x
Mertens constant.
0 f# |' h% s/ d* l. J9 P9 hMertens theorem.
3 o- O3 j; W2 s2 b: rMills’ theorem.
% a$ [7 V5 t$ F: rWright’s theorem. ' [- V" C! J3 w8 @8 D8 {
mixed bag.
. U, G! c$ j8 Bmultiplication, fast.
/ I. t! q/ l! R3 _- SNiven numbers. 5 U) L! L6 p9 e: a6 K D
odd numbers as p + 2a2. ' c- _- c7 G. G+ P; h
Opperman’s conjecture.
/ E" b/ b6 a# Zpalindromic primes.
+ p' T' c4 K" K' wpandigital primes.
3 K9 Q: m" g$ Q6 V, [Pascal’s ** and the binomial coefficients.
8 {* _6 E. V) w( Y1 |6 p8 HPascal’s ** and Sierpinski’s gasket. ) y" {8 W2 v) G
Pascal ** curiosities. $ L1 C" B# l7 f2 C0 A }; v) w% g
patents on prime numbers.
) [+ e' Z1 |5 g2 M8 H# T3 [Pépin’s test for Fermat numbers. 6 |* Y0 ^$ v& r" m3 {
perfect numbers.
* Y9 m; P: l0 }3 codd perfect numbers.
8 ~) k- a% n4 wperfect, multiply. u* V6 Y# y8 P6 y
permutable primes. ' t' l; ]# O$ W- R7 o
π, primes in the decimal expansion of. # g6 Y; j$ O3 M! H: ?
Pocklington’s theorem.
8 o% y9 J- t7 j9 U( s U, z, MPolignac’s conjectures.
5 h+ L( |) e8 {6 g2 g) t) k! @Polignac or obstinate numbers.
 j! I2 I& w6 jpowerful numbers.
! E% q( P9 `, @2 r7 j2 Rprimality testing. $ l% Y- s: c# x4 @
probabilistic methods.
, x- H9 T9 D, b- h Q9 vprime number graph. 6 ` ~8 b- u" V; F, L3 X
prime number theorem and the prime counting function. 1 k9 ?9 z) ^( Z7 W% ?7 @, }
history. 4 P: O, t6 u5 Q7 c
elementary proof.
4 h) u, z; |# l2 b$ urecord calculations.
' X" C$ \* _' c5 o9 P. |1 s4 |estimating p(n). 7 G7 Y7 P! t, D. b
calculating p(n).
( d$ l5 H: J" s6 r3 Q/ M5 x$ ra curiosity. 6 p, `: e2 h- f( i2 v4 }
prime pretender.
/ N; j5 G5 @# W1 j( C- |primitive prime factor. 2 y5 J; u- r( e* c; A
primitive roots. * `! i+ b4 n; |7 u4 t
Artin’s conjecture. / j* V, x& I( j! |" o
a curiosity. ; d$ i+ t! T. X( T6 ]4 o* F, b
primordial. . Y: e/ P/ ?: R+ e- F6 A
primorial primes.
' I) \ |- o" E2 }: G+ h5 v; EProth’s theorem.
( ?) y5 {, J, H5 c6 L9 R- T( Kpseudoperfect numbers. 4 q' r9 a- I% D
pseudoprimes. 8 F2 @- \' L$ W4 `: R- x
bases and pseudoprimes.
9 X9 F" } O5 ]4 o. E# K5 Opseudoprimes, strong. 0 @6 U) G. Q# Z$ N# ~6 a' Z# v! w
public key encryption. ! g; M9 T5 y3 ?9 [$ c3 l; R$ W/ R
pyramid, prime.
- M7 B$ P. Y. VPythagorean **s, prime. 9 V8 |' T: T# D+ E
quadratic residues.
+ ^1 W" ?6 Y3 S6 Fresidual curiosities.
( t& F$ r7 X+ U/ b0 C$ u. ?8 R! Dpolynomial congruences.
. L1 C. o8 L8 ^6 i8 h9 F) pquadratic reciprocity, law of.
# S" W0 K, d, l# FEuler’s criterion. 7 s! M8 \/ h/ E& F
Ramanujan, Srinivasa (1887–1920).
" M$ b+ w: |2 b9 J# h" ~highly composite numbers. # |5 j! |& n. @+ h+ ]' I; D$ R0 Z
randomness, of primes. 0 U) r1 U1 d3 a3 e& o" F
Von Sternach and a prime random walk. % d$ T7 @! N% c: t" E7 m+ n0 N' \2 B
record primes. . `& @! a' C: @ a
some records.
3 Z2 b9 [% B7 R' \' v. @( ^repunits, prime.
1 r5 U1 v8 x% H4 @) D4 N$ S3 mRhonda numbers. 7 {/ E0 {& v7 \6 i* U! x
Riemann hypothesis. 3 R3 s$ ^( M4 A5 b
the Farey sequence and the Riemann hypothesis. 8 Y1 F) P( w: G& ]. z' d0 H9 b
the Riemann hypothesis and σ(n), the sum of divisors function.
+ k8 g% e# f1 |squarefree and blue and red numbers.
2 x* L1 m6 o, a+ p/ ~the Mertens conjecture.
4 k& C8 {* v6 N) Q" jRiemann hypothesis curiosities. ! L" M1 k$ T; g% i* P" u/ E6 }
Riesel number. - H% a2 _+ }3 x
right-truncatable prime. ; M5 l4 R+ i% p7 _. B# V
RSA algorithm. 7 [3 ]. \: Q( ^6 l7 o( k% h" Q1 L; |
Martin Gardner’s challenge. 1 n' n! [# e- e1 x
RSA Factoring Challenge, the New. 3 s+ o2 x" \9 @8 H) C% S, @
Ruth-Aaron numbers. ! s" m5 ]3 f8 J7 V$ |' p! {
Scherk’s conjecture.
, M4 \0 |* K+ U3 ^: I8 lsemi-primes. / s: L$ ^) P# u8 r! M
**y primes. 2 S5 N1 h2 i$ o) ]- d$ z3 k! x
Shank’s conjecture. ) c5 \3 Y5 j- i+ S# s4 Y5 f
Siamese primes. , y+ n4 z9 F. m, b
Sierpinski numbers. , V2 @ R* _% ^, m8 ]/ Q
Sierpinski strings. 6 a; z/ X9 \& u/ h0 r
Sierpinski’s quadratic.
# J* b/ b; d4 ]8 I& f" e8 zSierpinski’s φ(n) conjecture.
4 E* L! V: k, q# v- {& jSloane’s On-Line Encyclopedia of Integer Sequences. , L2 k7 D% }( k0 c; t/ ~
Smith numbers. , H; N2 L; ^' H- W
Smith brothers.
' `' Q9 B$ f# m' P2 J0 t3 s; vsmooth numbers. " b" x0 T) Y0 C+ h, J* X
Sophie Germain primes.
' k; y7 H4 b/ q" H ]9 esafe primes. , s6 t* _- E2 f( ~6 H( m, r/ d
squarefree numbers.
' L. D. \# y/ T7 q0 O5 b" q. HStern prime. - ]& G0 ]+ R6 K; }3 c
strong law of small numbers.
7 Z/ T" p6 L- ^& [+ u" r! e) n# Vtriangular numbers.
3 O' m6 a' T; K; H* Ltrivia.
# ]" ]5 E( q2 k6 Ktwin primes. , c: U; v' s6 U2 u. W5 O h6 P
twin curiosities.
6 S0 U8 T* e5 ?% L1 {- M" TUlam spiral. ' A( L3 ^9 ~+ D4 B9 _% }: e/ Y
unitary divisors.
7 V) W/ j/ @% U/ e4 x, k# s3 O; w) runitary perfect.
, n& o) q; t- h8 Yuntouchable numbers.
& e+ U5 ~6 z8 P. s4 T6 h/ jweird numbers. * b- T9 m- _; b/ v, U
Wieferich primes.
2 j$ G* S, [- U5 v4 r# NWilson’s theorem.
8 A0 ]- W0 t% v2 Htwin primes. 5 G1 y. A% `+ N; ]
Wilson primes.
3 l6 ^! R3 }3 @: lWolstenholme’s numbers, and theorems. w8 z& i. f# h' i1 ]7 x
more factors of Wolstenholme numbers.
& I' I* ~! f4 q' s/ \# ZWoodall primes.
7 Q' V( b+ Z9 _zeta mysteries: the quantum connection.