查看: 4683|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. / O& @9 u- Z; O0 M% J, g8 V
abc conjecture. ) c X6 C# b- f& @6 G
abundant number.
/ f/ T& i; R" H7 X. [2 \$ s, rAKS algorithm for primality testing.
" b; j0 o/ ^ z# yaliquot sequences (sociable chains).
) I9 j% Q8 g( galmost-primes. 8 Q/ N: a1 L* c
amicable numbers. & A4 z- r' B2 |. ]. ^
amicable curiosities.
! e; L1 W- ^/ j/ ^& eAndrica’s conjecture.
) y' q' U! X4 j' y5 V% W. Y, Narithmetic progressions, of primes. 0 t' ~) C8 B9 G4 X+ i
Aurifeuillian factorization.
& N$ f/ V: m, S P6 T; j& m# S) @average prime. - z- d1 T1 J3 T, E; ?9 \9 k0 Z0 m
Bang’s theorem.
2 w8 ~' O& M( L. h1 KBateman’s conjecture.
4 J- S& f' {3 G; o5 O2 v! HBeal’s conjecture, and prize. * X* z( ^! b: M8 q/ X$ r& A/ s
Benford’s law.
" d- J% q: Q% c* \; A PBernoulli numbers.
0 F' a3 c+ e O' `( l! \Bernoulli number curiosities. 8 W5 D) y9 F! S( x$ n/ ~' l
Bertrand’s postulate. 2 ~ S$ Z6 d9 U) L2 [; W2 I) ~3 u
Bonse’s inequality. / n, e" T2 X$ q4 v1 y
Brier numbers.
' O9 o& f& V# m! X d4 MBrocard’s conjecture. 0 `1 S7 z3 \9 `8 m0 }2 y
Brun’s constant. 1 C) J2 ]1 e5 _4 Q9 F; ~
Buss’s function.
5 L/ v. v$ s: `Carmichael numbers.
( e* ?7 l+ {8 B# L' _: R7 jCatalan’s conjecture.
# {" s+ k9 H. ~ ZCatalan’s Mersenne conjecture. 3 H; a: V# T# a# i
Champernowne’s constant.
! P% C L L9 r. A4 _champion numbers. ( A. I( E! E6 H9 g
Chinese remainder theorem.
7 z3 N" ^$ g6 l$ P, Z( Qcicadas and prime periods. ! ` B2 C) f- ?0 V0 z
circle, prime. 2 I8 K! f; \# ?
circular prime. ( I7 }, C _* v% U* j# q2 N1 e
Clay prizes, the.
. o2 b- g; |; p8 t! p9 M; [compositorial. 5 a6 y2 v# C7 M% C
concatenation of primes. . m! t( Q3 V# O( l% E$ ?6 X( l4 G4 H- S
conjectures.
3 B$ G9 J+ T, J8 g, lconsecutive integer sequence.
$ T% E: P& S5 e9 x9 h$ ~9 U6 Bconsecutive numbers. , L, C) h( \" J A! z' c
consecutive primes, sums of.
 x: z0 `2 w3 w+ D% @% v' ]Conway’s prime-producing machine. " F, a1 n" G6 ?* q% [3 ~9 _* P& v5 i
cousin primes.
) Z* v2 K p% I" L. U1 l% b- A6 QCullen primes. 4 b) y6 z$ I5 \
Cunningham project. - D/ m8 A8 ?: @
Cunningham chains. . p9 B& ~, I* q5 w7 ~9 [- q" {. P
decimals, recurring (periodic). 7 F5 d$ E. |$ ?% ]" h: u' r8 h
the period of 1/13.
0 ?/ r, |/ f5 Ocyclic numbers.
. r9 ?4 r( i: A0 D5 N; I R" E$ bArtin’s conjecture.
/ T! W: I, T# L6 Qthe repunit connection.
; X h/ [+ X5 K. ^3 J! K, n0 O5 rmagic squares.
- ~% B% J$ Q& j; x! x& qdeficient number.
* l7 }" P% l, k3 wdeletable and truncatable primes.
) f% E9 b' R# D6 ~Demlo numbers.
" F& R4 S4 m& J1 f- s- z0 q; z5 ^( c& odescriptive primes. * T8 E. u' }- @& z
Dickson’s conjecture. - h) T) U+ n6 N! T6 Q, L
digit properties.
$ _: J* W6 H8 GDiophantus (c. AD 200; d. 284).
7 S/ d& }$ u: H {. {! |2 ]! o5 xDirichlet’s theorem and primes in arithmetic series. 0 M7 M" h0 w: | I7 n9 |
primes in polynomials.
& u/ f) E. Z; D) C* `& v4 L4 Adistributed computing.
7 l% Q9 O! q2 h* r0 ~+ Udivisibility tests. , [# G' j; x: u# H- q" M
divisors (factors). & q3 Y/ p& k; N! [9 F: u
how many divisors? how big is d(n)?
; l" T+ Y+ o$ V2 \. Frecord number of divisors.
; z$ v0 D: O! B7 D1 \# ncuriosities of d(n). 8 t) O8 E# J+ S
divisors and congruences. % U5 Q# y+ f# l* b( m! i# T5 Y- X$ w
the sum of divisors function.
6 c; i7 c( z, t* c. [' vthe size of σ(n).
+ b4 b2 r" x1 {: H$ |2 ja recursive formula. ( R# M J* Y/ h9 v+ p
divisors and partitions.
$ x5 q" m& \/ d9 x; v$ Jcuriosities of σ(n). 5 R! J+ w8 R( C2 h/ b
prime factors.
6 |5 }6 l7 g5 o/ v5 r- ~0 O% qdivisor curiosities. ; L- Q W9 l/ K) J8 M3 e. h
economical numbers.
: y" ^" N, F2 G# A; o" f5 V3 IElectronic Frontier Foundation.
! n/ V" o) F3 }2 Lelliptic curve primality proving. ( X2 J0 r8 F. t3 v/ y7 O% I
emirp. 6 r$ C. T! o$ c. u1 N! q
Eratosthenes of Cyrene, the sieve of. ) K N% y' r9 l
Erd?s, Paul (1913–1996). " k& v6 R. s1 ?1 |
his collaborators and Erd?s numbers. O. z1 `2 Q! @+ q! ~
errors.
. ~4 E0 |% {8 q2 C4 A! X3 w' `Euclid (c. 330–270 BC).
7 q) }# c- l" Z$ Y2 I9 l. vunique factorization.
, B% R' u: u' [: M# G&Radic;2 is irrational. 2 a9 ~, o4 D6 G$ R3 a2 e0 u0 u* J
Euclid and the infinity of primes. ( z* L! {- j s5 Z4 N, i; n3 [
consecutive composite numbers.
/ A/ d6 f2 k4 k( e. Rprimes of the form 4n +3. ! [( I+ ?$ g' }: [
a recursive sequence.
, ?- b' }4 e0 X+ EEuclid and the first perfect number. 6 o4 y6 h% G+ P0 g' { u) R3 L
Euclidean algorithm.
$ e! S. n. w) i( d7 r2 WEuler, Leonhard (1707–1783). f# a: E' L$ V% C' \3 }/ E. ^* \
Euler’s convenient numbers. 7 d* K9 {, o8 P" c9 [8 T
the Basel problem.
6 J# s1 }2 w; YEuler’s constant. . q. c* M% z% i1 k: ~
Euler and the reciprocals of the primes. * t2 X9 n3 I& _+ Z3 |6 ]
Euler’s totient (phi) function. 8 A( T1 N+ ^7 { ~5 s* t1 V2 ]
Carmichael’s totient function conjecture. # }% B* \* ]+ n, V$ N: D
curiosities of φ(n).
( B/ Z2 z7 n5 z; {7 SEuler’s quadratic.
- W- u0 O$ n6 z" wthe Lucky Numbers of Euler. - P, t1 E8 J1 B; ~6 X, x( p% [; p
factorial.
' O% m$ z ]; |/ ~! L% Gfactors of factorials.
7 ^. p: e/ `2 }9 a! N! ]1 E2 _/ Efactorial primes. % ]1 n) A9 d+ c* `! H9 S: o9 O
factorial sums.
* p8 y. y2 n& a& Y. r0 Yfactorials, double, triple . . . . * `' f0 J, a7 l4 y8 m% e: g/ W t
factorization, methods of. ; r2 v" h" ^; d4 A9 X8 @* N) e
factors of particular forms.
 O; o0 R. v: c( V9 @9 gFermat’s algorithm. # |! g) d, n& V( u5 t
Legendre’s method. # \; c* s' l0 N: q, r9 \6 N
congruences and factorization. 6 v: ?* x4 |5 E
how difficult is it to factor large numbers? 8 s r% Q4 {. l
quantum computation.
5 G( v. f7 k0 X: R% BFeit-Thompson conjecture. : [: g( O4 X+ g
Fermat, Pierre de (1607–1665).
: N( j% G2 Z+ A/ h% hFermat’s Little Theorem. v: o/ \: W7 J4 f7 U
Fermat quotient. + D9 _& M. g' x; V K9 n+ A
Fermat and primes of the form x2 + y2. " T7 Z7 x+ u" w# V- |
Fermat’s conjecture, Fermat numbers, and Fermat primes. 1 x: W# I. g; v0 l* I
Fermat factorization, from F5 to F30.
9 [4 ^6 l+ Z; dGeneralized Fermat numbers. ' M1 e) Y2 K( q! i. J, y) K& Y
Fermat’s Last Theorem.
2 I6 H% V- E# \( n8 q4 g, Hthe first case of Fermat’s Last Theorem. 5 e# T7 Q# G6 K; _2 C9 U
Wall-Sun-Sun primes. ! r( P! P% a, \ u9 u4 \5 \8 {
Fermat-Catalan equation and conjecture. 8 k4 W# l8 C2 `( R" ~
Fibonacci numbers.
7 `) {" C% ?. }0 i8 adivisibility properties. & r p! t2 m3 G1 b @, Z6 _
Fibonacci curiosities. / W0 O' f7 y, Q* z7 f( g$ D( Z# {
édouard Lucas and the Fibonacci numbers.
4 c& O2 g: N X) o8 `! \ _Fibonacci composite sequences.
1 r' [2 z% |9 J% w1 A) b9 U+ yformulae for primes.
8 N) l9 ~+ D3 k: [Fortunate numbers and Fortune’s conjecture.
' r$ q4 J+ Z5 i3 ugaps between primes and composite runs. 0 Y" H. y8 F4 O
Gauss, Johann Carl Friedrich (1777–1855).
0 u; M# X+ Z2 h' x) s; [0 wGauss and the distribution of primes.
! g ]2 Q: F8 _8 fGaussian primes.
0 E4 O b" j y/ ^1 s" `8 LGauss’s circle problem. . j, y6 L* }: I- b# T% |# w8 P' b
Gilbreath’s conjecture. ; R) p/ n1 c: E* j9 } r
GIMPS—Great Internet Mersenne Prime Search.
 _6 i; [8 l9 {: J* V, iGiuga’s conjecture.
" ~- |- M$ J I( G% f- VGiuga numbers. H- Z% w( v4 Z& ~' e
Goldbach’s conjecture. 8 f* a8 ~' P8 G; G' N* L2 w
good primes. 8 _8 J& q2 h/ F1 m
Grimm’s problem. * I9 k7 Q( Y* p4 i0 [: D9 t
Hardy, G. H. (1877–1947). ! ]) v& [ f+ w' T" l
Hardy-Littlewood conjectures. , W* _+ K0 `! W# Z$ D3 U+ ~+ L
heuristic reasoning. 7 Z2 l) c3 v2 q! I. W
a heuristic argument by George Pólya.
/ u; N* _2 Q- L: @8 wHilbert’s 23 problems. $ H! w- \4 |' B9 I O
home prime. , n$ g$ v+ N9 ~! W: j$ K; \: X
hypothesis H.
, C5 ^0 \ D. }6 I8 Lillegal prime. * D: N3 F; D8 l) h" W: s
inconsummate number. 6 Q5 [6 c+ g8 z. t+ M
induction. 2 [' V, r0 A8 N! W, L
jumping champion.
. @2 n Z, t3 Y+ Nk-tuples conjecture, prime. 1 o/ b' e9 X1 R2 v" f% y2 H8 a
knots, prime and composite. . G; i8 f( J2 r3 n
Landau, Edmund (1877–1938). ; ?- ]% m2 q1 i6 `6 }
left-truncatable prime. ! G$ @* f" M3 N7 y: a
Legendre, A. M. (1752–1833).
9 j( A( K+ ^4 mLehmer, Derrick Norman (1867–1938). % j: J1 Z( v& N G) @1 H8 y
Lehmer, Derrick Henry (1905–1991). . X% w9 }3 |9 U! g
Linnik’s constant.
+ Z& {2 {% @) WLiouville, Joseph (1809–1882).
6 \. ?/ }' G/ ]1 zLittlewood’s theorem. " G# a- m% A7 G9 v
the prime numbers race. / w8 t) k! S( L) L' h
Lucas, édouard (1842–1891). 5 u$ p- A& r! u
the Lucas sequence.
5 X o' g! R3 X! s& R6 [% jprimality testing.
# d' j7 K; i; hLucas’s game of calculation. ! ?; Q# x! P3 Z7 c! x7 G
the Lucas-Lehmer test.
; `: `$ O8 l9 p- mlucky numbers.
! L! G6 Y4 g6 w1 O# h, i) Othe number of lucky numbers and primes. % P1 k* h' |* ?9 C! Q+ K9 Y8 T
“random” primes.
. T6 e4 M8 O$ j- P+ bmagic squares.
$ v8 j0 e* C2 E: VMatijasevic and Hilbert’s 10th problem.
# ^1 l0 m# j) G! U/ R( {2 VMersenne numbers and Mersenne primes. 6 |( _8 w) B* y$ c7 v$ ^
Mersenne numbers.
5 f1 z! R2 B( k. r: U! y8 Xhunting for Mersenne primes. ' O) M, v/ \& I
the coming of electronic computers.
; k; a4 d$ ^ ?2 ?) p1 |2 UMersenne prime conjectures. + X* j1 B8 ~; r- [$ y) {* V2 r# X$ U/ ]
the New Mersenne conjecture. ; I, E( ]' I& T# e9 y: v
how many Mersenne primes?
7 s, _' J4 u8 {, XEberhart’s conjecture.
5 w* H9 n D* Tfactors of Mersenne numbers. U1 s. ~; f, Q/ L# W
Lucas-Lehmer test for Mersenne primes.
# B2 U4 C! h/ G1 u5 Q' I! H3 _3 g8 qMertens constant.
+ s9 H$ G# p- t8 Q Q4 ?5 @Mertens theorem.
3 Z& c1 n6 k3 |, {Mills’ theorem. % z( y; f- \$ K N/ }: H+ |- W0 Y
Wright’s theorem.
4 W% K2 e- G! ]& Zmixed bag. 2 b+ I, E7 P" P
multiplication, fast.
& K% f% V: Y- D2 p# |. ENiven numbers. 7 I3 D/ s2 @( C
odd numbers as p + 2a2. i o+ |8 s# n& N3 n- N: b- d( X
Opperman’s conjecture.
2 u. r( q0 ]0 I; H$ ?4 T% m0 U8 npalindromic primes. j2 Y5 v4 q8 `2 R3 p5 l" l$ ^( ?2 Q
pandigital primes.
* ]( [4 S+ F% j4 ~Pascal’s ** and the binomial coefficients. 9 T @& L/ Q) t, v2 R5 Q( F" j2 G4 f
Pascal’s ** and Sierpinski’s gasket. 6 l) M0 M3 @) z" a
Pascal ** curiosities.
/ ~. B1 Y6 o' ~' Opatents on prime numbers. $ o: J+ N$ G" a H! m* \; I0 g$ b2 |
Pépin’s test for Fermat numbers.
- }. F+ y4 H% u9 M" Z, f6 Yperfect numbers. " l9 h( o8 d4 q' e3 g5 k# F" m4 G- c
odd perfect numbers.
) m, |: S& u- C4 ^; vperfect, multiply. $ \$ s7 e+ j( i' s: e0 g5 t
permutable primes.
) a& K+ c' L' {% T% }% yπ, primes in the decimal expansion of. 1 _2 T1 Q2 D% Z/ u. U2 I u; x
Pocklington’s theorem. 4 }% j: [5 Z0 | }9 I! k O
Polignac’s conjectures.
; p R' Q$ } G8 O3 yPolignac or obstinate numbers. p, G; |+ V$ d# H7 G
powerful numbers.
7 [( r7 l4 w2 A4 X, oprimality testing.
' v% F. P) a2 r1 @probabilistic methods.
# A" r1 B% b* w* G) j2 s# Lprime number graph. 8 D0 L2 Z9 h5 v; a) A+ t( p
prime number theorem and the prime counting function.
; R m7 W( @0 d. W" dhistory. 0 p! d; z( ~" K F! Q3 E
elementary proof. ' u% {* n9 w2 D8 x0 z9 q) d' j
record calculations. - A# _; c+ X, W" F
estimating p(n). 5 ~' y# ~- a6 E T3 S
calculating p(n).
+ m4 E9 L8 j4 S4 b* S8 j, D& ya curiosity.
; L& y3 N5 {5 Wprime pretender. 1 e$ M: j/ ~ [; a
primitive prime factor. - y1 P8 v6 @6 A
primitive roots. / S: f+ J) _$ p" M) L: g
Artin’s conjecture.
& C- }+ g, q1 r q: {5 D1 va curiosity.
) J( q; J1 c: m6 Xprimordial.
# e& U k+ d* L! Dprimorial primes. 8 l7 v0 c2 f! m1 V4 `7 G0 C# k" A
Proth’s theorem.
% Z0 Q( h5 w+ {* Z& g2 W! k- @pseudoperfect numbers.
4 T2 d& o9 P9 Zpseudoprimes. ) B t) x" {6 R( u7 L$ q* W% {' E
bases and pseudoprimes.
( @7 R. H2 i% o; }& l) p0 U1 tpseudoprimes, strong.
% w5 V5 Q6 x ]8 W" I2 z; J. Npublic key encryption.
2 h3 H5 W- H, ^pyramid, prime.
7 {+ f, Q. N7 b# P' I7 xPythagorean **s, prime.
2 }5 k9 ~# N0 p0 Lquadratic residues. 0 f8 B/ G$ k) |; U9 Q5 x
residual curiosities.
7 n/ w( N0 W, I# t+ [& |. Npolynomial congruences.
( K9 T0 W: U/ e; pquadratic reciprocity, law of. 8 Q2 \9 F, F4 S. u" k% Q
Euler’s criterion.
9 a* U- z. U( O) w& t) ORamanujan, Srinivasa (1887–1920). 9 ]; E$ {, ~, }' u/ m% F% U
highly composite numbers. 9 V- Y, k' z& i( x" ^% C
randomness, of primes. 5 G+ l9 v1 a+ I2 L- p
Von Sternach and a prime random walk.
: g4 X# d$ O# arecord primes. , D; J. ?) q# K' _; E) n
some records. " j0 B/ V' {% [* p& `( c- x
repunits, prime. ' G, S! q) k$ P$ J! I
Rhonda numbers.
* [2 a p% a$ F5 lRiemann hypothesis.
, w" v( j6 M; j8 Sthe Farey sequence and the Riemann hypothesis. ! T- j* Z$ K( \( p4 ]# |0 ?0 \
the Riemann hypothesis and σ(n), the sum of divisors function. ) e0 y8 K/ i$ ~9 P/ O
squarefree and blue and red numbers. 3 c7 z! r! n$ |+ C: w# q$ q
the Mertens conjecture. ) @1 H% K& `6 D+ Y3 S$ @( a% Q0 \
Riemann hypothesis curiosities. S* Q( P3 s2 k. m
Riesel number. * z. I* ^- d, {9 f
right-truncatable prime. % O* [- v8 q) A. e- h& V
RSA algorithm.
( |8 |$ Q3 W1 c( kMartin Gardner’s challenge. ; }- U/ e, c1 X. B0 k+ S
RSA Factoring Challenge, the New.
, z* M2 \6 s/ `& {/ k+ ARuth-Aaron numbers.
! Q% _/ k8 a: c) m. ?+ dScherk’s conjecture.
9 d; _) K+ k: k1 d( {semi-primes. 6 J. n% S* T' j, ^" C- M. d
**y primes. 4 h U- H+ ?8 _/ T! }3 v& E
Shank’s conjecture.
; Y0 }" T) M% _Siamese primes.
' n1 L8 ]/ }/ X6 s1 oSierpinski numbers. # ?6 Y. p7 r! D! O
Sierpinski strings.
; {0 h# X( ~5 u) {5 BSierpinski’s quadratic. * S. U5 \; N% _9 |; H0 w
Sierpinski’s φ(n) conjecture. ; H1 E; H ]! F- t: `( r
Sloane’s On-Line Encyclopedia of Integer Sequences.
* B* U1 R- {# a1 n& ]! @$ WSmith numbers.
; b e6 T4 k0 P+ @1 X% y1 ]3 pSmith brothers. & c( a6 W* T4 v* ~; t
smooth numbers. & g; I+ l2 I" e. D1 m3 l* P
Sophie Germain primes. 8 e! h6 J3 o0 {7 U& ?2 }5 ]
safe primes. : c! t0 r8 F0 Q
squarefree numbers.
/ f J8 A$ O" S7 M2 j! r) ZStern prime. 0 a" T, M' W3 o9 J: }2 @
strong law of small numbers.
) P, w& m. b: s7 J7 ^7 t$ m' r/ R+ Ctriangular numbers.
+ H! K. P1 n5 P. n u/ j Strivia. % m' s; p( [0 c! W1 o
twin primes. : n- a) q- I- y. I( s% o6 {
twin curiosities.
 p. a1 X% U" U( [5 uUlam spiral.
8 b M3 }( ^0 r& Aunitary divisors. ) q1 ^) D6 a( b0 I. s) |
unitary perfect.
0 m% J2 V% p# z; ^( Z. e! J& xuntouchable numbers.
$ L# n+ g; a' Uweird numbers. & R, {9 u0 @0 g; y( W, w
Wieferich primes. ) I+ B' i+ z, V1 r
Wilson’s theorem. , {) F* Q; s/ X5 X5 }
twin primes.
9 ?) j( J& J; t9 G" WWilson primes. 7 I4 I' |" k- c9 g
Wolstenholme’s numbers, and theorems. 3 p p# F4 b+ U. _7 X, g: n0 w6 s
more factors of Wolstenholme numbers.
- u; S* U1 u# a& F+ _2 FWoodall primes. : A7 v# c* S! F& }; y) g
zeta mysteries: the quantum connection.