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标题: 数字的奇妙：素数 [打印本页]

作者: clanswer 时间: 2010-4-13 11:41
标题: 数字的奇妙：素数
本帖最后由 clanswer 于 2010-4-13 11:43 编辑

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Entries A to Z.
9 [- r8 v- D* l& q4 B% j1 j' I- ~abc conjecture.
" Q& P& O! H- L" ^abundant number.
* ?. o l5 d# i* @, W/ {8 oAKS algorithm for primality testing. & F5 Q0 Z$ D! A
aliquot sequences (sociable chains).
" }* S2 \% P% l6 V' {: Y/ C0 z' ?almost-primes. & @$ b8 P$ M" o4 s+ z O
amicable numbers. " _0 n) e* I" k4 a% c$ r; b
amicable curiosities. ; m/ x& Z" Q4 F: C7 F; V
Andrica’s conjecture. : }7 ~7 r6 r$ C8 g: D x6 H# q+ \
arithmetic progressions, of primes. - T1 ?5 x( I# w
Aurifeuillian factorization.
3 j- W( z" d/ ~average prime.
9 L6 f. y! `7 _Bang’s theorem.
' x. T: A+ b& {+ s: r! sBateman’s conjecture. / }. P& \: G5 B B) C2 d9 A* z; Q
Beal’s conjecture, and prize.
+ D& _. X, R; N: d- U8 O. W; P; hBenford’s law.
3 ~2 K+ L) }# ?) h/ v1 S2 UBernoulli numbers.
0 B+ I0 N$ F$ k8 z/ Z: _Bernoulli number curiosities. / _6 s6 r5 w# }3 P% w' [% T
Bertrand’s postulate. ' \) q+ G) }. z+ k
Bonse’s inequality.
 S& T$ A2 x9 i4 B5 KBrier numbers. % y. \$ R: Q$ y" R7 D
Brocard’s conjecture. 9 g- A4 }$ F5 A4 L
Brun’s constant. + |; }# J7 ~. P" M- L4 L+ j
Buss’s function.
8 U, I. f$ z# i& F: XCarmichael numbers. - e y) }" x% e- s6 X6 C
Catalan’s conjecture.
" N% V6 w+ j+ j" uCatalan’s Mersenne conjecture.
- \+ M2 l2 N( w" o/ N- J, |9 m) SChampernowne’s constant. 1 u7 T. ~9 S7 N6 z8 {2 w1 ?1 R9 w @8 c
champion numbers. 4 _5 w# l$ K7 X# P x7 ~
Chinese remainder theorem. ( p) x1 t' g( m8 S8 H
cicadas and prime periods. ; a* E/ P, E# _
circle, prime. 7 K% b) K8 g" k6 I; q, X4 }: h
circular prime. 2 H- f {* V$ p3 U
Clay prizes, the. ' Y' S# |1 e4 ]2 U7 Z7 U, \) L
compositorial. ' Y; [7 I% F, m( K' C4 G% W0 n
concatenation of primes.
" O1 }, v' ?2 D$ V0 @conjectures. " Z( f( j9 K% C; L, T
consecutive integer sequence.
6 {# A/ k1 M: ^# _3 r& Cconsecutive numbers. & h" s. A' @ |# q
consecutive primes, sums of. & a! t. H9 Q: H' u+ p) [- W) d2 k
Conway’s prime-producing machine. 4 ^( ?( B4 I( \" q7 D+ N5 U6 T G" V
cousin primes. 6 C. p: y2 b# l$ t% \4 u& t! q" e
Cullen primes. q; u" J% Z3 W3 V9 O8 ]3 F0 H
Cunningham project. . D. A: d5 B7 Y! {$ {, Y4 p a
Cunningham chains.
decimals, recurring (periodic).
2 d: E; P2 c" Xthe period of 1/13. 6 q1 c) [7 R* k' {4 m0 Q4 `2 i
cyclic numbers.
" N8 ?/ n- j" { C8 FArtin’s conjecture.
9 w6 S2 _* s0 m5 Tthe repunit connection. 5 I; w3 V9 \. T7 f) T
magic squares.
7 \# ?) g, k9 n" L" Kdeficient number. 9 ^5 w3 T1 R! C! }6 Z e
deletable and truncatable primes. - t+ a% k; I0 R
Demlo numbers. ! Q( q# t% P& g2 Q6 `4 L
descriptive primes.
4 \; W4 \( ?1 g1 w9 T# NDickson’s conjecture.
% w1 {" d s7 O7 Z2 Z/ n5 \# Bdigit properties.
& y* r& w4 T y! L vDiophantus (c. AD 200; d. 284).
: m5 w& s$ Z1 ~. gDirichlet’s theorem and primes in arithmetic series.
! r' t* _, x$ E. W8 }3 ?. @( o4 Fprimes in polynomials.
( m. C1 N& k6 i& ldistributed computing. & o" q" i( G! d& {( z
divisibility tests. ' d( M8 `/ c) |2 R5 Z' Z' b/ ]
divisors (factors).
1 B4 g5 B) v7 khow many divisors? how big is d(n)?
 _1 h8 X& [# a, j! T6 wrecord number of divisors.
) m" o3 g; |( h$ L- g ecuriosities of d(n).
2 N. |9 y3 o0 g: j/ Ddivisors and congruences. 4 @3 u- C' D9 t3 [+ ?8 o' j, Z! M
the sum of divisors function.
! `' [1 y) L& X! V: Q4 r: Xthe size of σ(n). 4 H: L4 ~+ i; o4 R$ T6 {7 W0 P
a recursive formula.
, o& M( `, o6 F+ g1 M5 kdivisors and partitions. 5 R1 `) B1 l3 G& w0 M
curiosities of σ(n).
* j5 S( o- d, ~7 ]; {prime factors.
7 \, u: r$ c4 M) ldivisor curiosities.
 L- {6 o" `5 M+ I [economical numbers.
" j; O3 G- O+ IElectronic Frontier Foundation. & w7 q" L; F" K6 O* U$ F, q
elliptic curve primality proving. 5 M- ]9 y2 Y# c0 H, j6 \
emirp. ' k1 c, g' C- Z* L
Eratosthenes of Cyrene, the sieve of.
: U4 m( g$ P- p! x) uErd?s, Paul (1913–1996).
* F; K3 M) F+ Qhis collaborators and Erd?s numbers.
2 w: f2 S X+ S; E% f$ n; Terrors.
( e; P% |- M) ~+ ]! N# s4 P i7 TEuclid (c. 330–270 BC).
# z% k% C, c1 M& Munique factorization. ?7 X* @5 J9 k+ D2 I, J* f
&Radic;2 is irrational. 2 z a: g8 e' Z: M/ o9 I& J
Euclid and the infinity of primes.
6 D7 J7 V& v7 c4 X P. \consecutive composite numbers.
+ m1 B6 c# s- N5 Mprimes of the form 4n +3. 4 I* ?& m4 Z Z9 V( X8 M
a recursive sequence.
Euclid and the first perfect number. 0 w. x6 w* X! W' W0 v1 b( [! E
Euclidean algorithm.
. C: b$ s$ G, x/ x& y/ yEuler, Leonhard (1707–1783). ! E7 n6 R N6 E7 C; o
Euler’s convenient numbers.
 E- B+ ?" _. _the Basel problem.
4 A7 m' t* L- g9 A, A2 Y' d) K3 gEuler’s constant.
, ^9 B3 G/ N' F$ v* FEuler and the reciprocals of the primes. , q! a% f( m$ k0 G4 x8 u
Euler’s totient (phi) function. % u+ E1 \3 e. l L6 X3 B& `6 \% I) [
Carmichael’s totient function conjecture.
* y! P" [/ l8 r. Acuriosities of φ(n).
, l! [3 K. y+ |- PEuler’s quadratic.
8 B3 n7 b" O2 S3 Sthe Lucky Numbers of Euler.
3 T3 O+ j2 e6 }! `( Z1 f8 O4 v4 [factorial. / `& b0 W/ _+ L; r1 r, o2 \8 [
factors of factorials.
7 H3 K3 ]. p4 d$ b6 [: l$ B1 Kfactorial primes.
4 r' W0 ^# ]( i% A7 x: J; R: tfactorial sums.
/ v- n4 x3 [# _& ]: ] x4 hfactorials, double, triple . . . .
/ b9 n. Q% ^1 S) U/ j! Nfactorization, methods of. ' m! T* w4 s! R/ Q$ f1 M, R7 F/ V
factors of particular forms. ' a+ \1 L9 J$ l8 U2 d i3 p4 b
Fermat’s algorithm. 8 F4 {! {7 n1 \7 h5 P/ u
Legendre’s method. : T; w# `, R. M E3 S; B; C
congruences and factorization. 3 p. ~8 v% {" S2 `' S
how difficult is it to factor large numbers? 3 {. g7 ` m1 l/ l2 C. X
quantum computation. J" h$ Q% s0 }- ]
Feit-Thompson conjecture. 0 o7 `2 A( \& a9 V
Fermat, Pierre de (1607–1665).
8 f$ K$ h' U: K2 ~Fermat’s Little Theorem. - C) p0 l* A* M0 t& u3 @2 u4 w; R
Fermat quotient.
, c7 c+ o2 U) G' u9 c" RFermat and primes of the form x2 + y2. ( Z. t2 K$ V* B" d$ Y. _" z( Q
Fermat’s conjecture, Fermat numbers, and Fermat primes. . G# J, L/ m& N- G) _! q
Fermat factorization, from F5 to F30. ' x% b. T6 t; @& V% j! C
Generalized Fermat numbers. 9 T2 W: {; R0 Y+ `
Fermat’s Last Theorem. . u- G2 x$ m0 j
the first case of Fermat’s Last Theorem. ) ?& R- H/ }( e/ O# U, h
Wall-Sun-Sun primes.
/ P. ~& o% l2 X% F4 I3 XFermat-Catalan equation and conjecture. Q6 n) j2 i4 \9 f: c3 F s' P9 h
Fibonacci numbers.
; S6 F* s: `+ |5 x: {divisibility properties.
 N$ y5 ~& ^0 [' ~) `% J1 f/ x) h* tFibonacci curiosities. 9 O# a4 U% D# Z7 @3 `- k* h9 X* b
édouard Lucas and the Fibonacci numbers. 9 K- `1 Y) l5 N: x
Fibonacci composite sequences.
; J3 E3 `1 A2 t; q8 f! D+ V, bformulae for primes. 2 j/ U5 k2 O+ ]( w$ e, T$ A { _9 g
Fortunate numbers and Fortune’s conjecture.
( E) \- \% y# [% Dgaps between primes and composite runs.
! J, u' Y0 }! n5 M' {. ]Gauss, Johann Carl Friedrich (1777–1855). 9 ?* u2 q& Y6 \
Gauss and the distribution of primes.
5 u" h1 k; g& \+ b* u( }Gaussian primes. 8 g+ i& ^. \, t+ f2 c. o+ P; c0 q9 N$ ]
Gauss’s circle problem. - C2 h# x1 x) ^# v
Gilbreath’s conjecture.
7 L% W! p* w- xGIMPS—Great Internet Mersenne Prime Search.
" j4 K! l9 o8 p/ [/ x1 K/ kGiuga’s conjecture. ' D+ H$ L2 n' l; F" o# ?
Giuga numbers.
' L) X' I9 L4 F* V' d% |Goldbach’s conjecture.
! z- I0 i0 v" U: pgood primes. 8 l' u8 n) d+ Y9 O- _3 P
Grimm’s problem. ( t1 F+ K I3 i! |/ p w u
Hardy, G. H. (1877–1947). " l0 l5 m& |/ ^9 \6 v- ^
Hardy-Littlewood conjectures. ! F" u, q8 m+ Q" ?
heuristic reasoning. " P, } Q0 J" J
a heuristic argument by George Pólya.
, h. X% a3 o: y1 |Hilbert’s 23 problems.
2 K3 k) l9 v1 B: @* Mhome prime.
# x# h( Q' C7 h; hhypothesis H.
. M" `- q3 \1 O( }" k/ p0 F8 w1 Tillegal prime. : e$ Q* W3 C e: ^
inconsummate number.
/ T/ [3 y3 P7 D7 O6 `! ^8 linduction. " n; j6 x' _( c: ^) g3 l( F
jumping champion.
8 f x" \% o$ `# s% }3 M0 ?k-tuples conjecture, prime.
5 |4 E9 I# x+ o% ~; H; p" C3 P Tknots, prime and composite. ) E) ?; o& ?5 u+ o0 G, Z
Landau, Edmund (1877–1938). 6 o9 p: V7 P" o
left-truncatable prime. ! o0 F& g0 O' e. p' y4 O
Legendre, A. M. (1752–1833).
7 ~( s. S5 I. L. qLehmer, Derrick Norman (1867–1938). 9 Q& H& u/ f! v
Lehmer, Derrick Henry (1905–1991). ) l$ f. [" Z- d" X
Linnik’s constant. ) I6 f0 u) R; Z! Q% F0 K
Liouville, Joseph (1809–1882). 1 Z" k) a7 Y# t0 |8 n
Littlewood’s theorem.
& L/ X+ R: t! Qthe prime numbers race. 0 Q$ W4 X% r: b
Lucas, édouard (1842–1891).
- o d/ V$ K# m. X+ Y0 T9 c/ |1 sthe Lucas sequence. ' z& H, y* k! `: i! l; s6 `3 o
primality testing.
7 u* f3 M8 a; h9 V' nLucas’s game of calculation. 2 l/ V# Y6 f8 B: p) @" X* u
the Lucas-Lehmer test.
5 |1 j8 _ C b- X3 k7 r j/ Glucky numbers.
# z# k0 S; q, N/ O# Mthe number of lucky numbers and primes. ' E% N0 g& i* e# j; i" z% w
“random” primes.
6 m. U. b0 C( r; u5 r. A8 \magic squares. % Q2 x/ {# o( E" g
Matijasevic and Hilbert’s 10th problem.
1 V* Q8 G. w4 KMersenne numbers and Mersenne primes.
$ `( i3 f `# ?/ r6 W+ O% FMersenne numbers.
* ]4 |& Z# O# M& E* G9 x8 nhunting for Mersenne primes. ' s9 A. s7 s& K# H) Q
the coming of electronic computers.
! k; L) i+ J; H- y) J3 o9 YMersenne prime conjectures.
$ V3 O9 r) J" Tthe New Mersenne conjecture. ' ?, D9 Y: h, K7 i1 b8 m
how many Mersenne primes?
% ~) J% v3 t# J! K+ z9 C6 K9 o% }Eberhart’s conjecture.
# d; q, s) ?: b: w, _! g: ?; Z3 Tfactors of Mersenne numbers. * {! G+ i9 M1 p% T4 G$ B
Lucas-Lehmer test for Mersenne primes.
 W" o# z1 w! S4 ]+ q3 s3 h" aMertens constant.
+ \5 X' J! x4 J. q0 \Mertens theorem.
2 P& S% C2 j2 d. l7 X; v( ?Mills’ theorem.
7 b6 Z8 [( B9 R$ Z- ^# u* a: ZWright’s theorem. $ y" ?4 ?% ?% i1 \
mixed bag. 1 O% W$ A; D3 @4 X, g3 {
multiplication, fast. 9 _/ x* F2 f) _. a) Q0 ?; b
Niven numbers. ' F f0 y& u* I% B
odd numbers as p + 2a2. + Q8 s5 }% l6 h! |: V$ q. f
Opperman’s conjecture.
# c1 g" c6 P3 m$ E3 @ c+ Jpalindromic primes. 0 i# r% ?. f& i0 [8 _7 q1 @
pandigital primes. ' C9 a" T5 P7 ~) f. W0 K0 ]5 L3 W
Pascal’s ** and the binomial coefficients.
. ~8 ~4 Z) c7 ]4 s9 PPascal’s ** and Sierpinski’s gasket. 9 j8 F7 B2 T1 Z5 X
Pascal ** curiosities. ! p0 s: U3 H5 \- ~ x
patents on prime numbers.
- p6 I! V* w+ m" N: {; z( VPépin’s test for Fermat numbers. 8 f4 M: I$ d$ a! M+ a3 O
perfect numbers. * N* X* T: u6 q+ M
odd perfect numbers.
 ]2 n0 Z) ]: ^0 Nperfect, multiply.
2 z" k$ a. z8 k) ^) ]5 H6 S* Vpermutable primes.
8 o5 X$ e5 P3 {) B9 M$ x0 Tπ, primes in the decimal expansion of. ' e! C6 Z$ A$ `9 B$ z! {0 B
Pocklington’s theorem. 7 c! W* F/ ]: l, T7 E
Polignac’s conjectures.
3 S( d1 d r1 Q8 M% @ L9 ]Polignac or obstinate numbers. 3 P4 e* f9 m9 H! e
powerful numbers.
' A; J2 l$ ]; J0 ]$ s3 P/ d/ ?primality testing. 1 s( X3 i! j3 l) S: Y; L
probabilistic methods.
! A4 ?4 T7 b4 ?- z4 fprime number graph. # f- f& M$ R0 U7 G
prime number theorem and the prime counting function.
$ A. ]9 p. K0 I; O+ phistory.
8 n! q4 W2 M, i4 q+ z, G' @1 `elementary proof.
7 W+ G4 K( G4 i1 w ~/ y urecord calculations.
! t; L' V3 X# z7 Q; R0 i9 Jestimating p(n). - @( C; l m" q L% ^, X
calculating p(n). ' I2 `$ g5 u2 n6 S* S; Q5 `; d/ q
a curiosity. ; I' w' o" Q: t+ R, H
prime pretender. , t$ [: U; c: c; ]8 g# U0 c5 h/ T
primitive prime factor.
. n9 \2 a( V/ k, G5 c" sprimitive roots. 0 ]! q- S" A3 Z2 W5 h$ B& a5 e
Artin’s conjecture. e. S( m# {# t
a curiosity. / G7 V, e5 n5 J, Q
primordial. 3 X. T y+ S2 d; t" Z, |- O
primorial primes. 6 U5 m; D& V E
Proth’s theorem. 3 o+ y, {' q) X1 N
pseudoperfect numbers.
/ P) y" C2 s8 c# Ipseudoprimes.
' b* A3 c( U, S! C' C1 K& pbases and pseudoprimes. 5 L/ q: @7 n( @% J0 J( U
pseudoprimes, strong. 4 ?! f: H7 A# S" C6 k
public key encryption.
" V* Z* c) C& F; B; f( b$ Q+ npyramid, prime. ; N9 O( c8 {& T
Pythagorean **s, prime.
+ \! H1 D$ o# H/ M7 Aquadratic residues.
- x; p4 r e- k- a+ Eresidual curiosities. 2 v0 ^. X# t7 X$ b4 |
polynomial congruences.
0 n* s4 C$ n- gquadratic reciprocity, law of.
1 l! k! \! o9 u2 r: dEuler’s criterion.
+ s* X& {. c! C3 t( WRamanujan, Srinivasa (1887–1920).
( I* j7 g* V4 L$ a# b9 qhighly composite numbers.
* I6 _ K" L- d4 yrandomness, of primes.
$ t, Z3 t, n5 d9 j1 j! [" g- R; s/ u. pVon Sternach and a prime random walk. * G5 G# @; d9 a& O
record primes.
" H1 T7 p. B$ vsome records. 4 {! h: {( x: x d6 G; ?
repunits, prime.
 i2 m5 p8 T- c: K4 h) O; vRhonda numbers.
# e! }$ ?' }4 \' b, d: T3 ]. qRiemann hypothesis. 4 A* n- C) A# H4 N( q2 u2 |9 Q' A
the Farey sequence and the Riemann hypothesis.
0 g, w7 N# [+ B3 ~# ^/ ]; a- _$ Ethe Riemann hypothesis and σ(n), the sum of divisors function. + n# S$ ?& G# j. r- ^. W% j" t
squarefree and blue and red numbers. 6 y/ Q1 A; | @* ^5 P+ v4 w" j
the Mertens conjecture. ! k$ S9 J* v+ r
Riemann hypothesis curiosities.
, n* ]( c( R2 yRiesel number.
) P0 Y' B6 f6 k Y# H0 tright-truncatable prime. # n$ K; x1 D4 r# |; u4 M) p
RSA algorithm.
& u% H0 K X0 V* n ] G% qMartin Gardner’s challenge.
/ l a/ p( }: ERSA Factoring Challenge, the New.
! O/ q5 D# ^% B( w1 ~Ruth-Aaron numbers. 4 W* ]7 G" Q* A! p
Scherk’s conjecture. : q5 `. Y. w+ n1 O
semi-primes. U7 W4 ^, Q2 c7 T
**y primes. % W* L! d6 R& C2 Q
Shank’s conjecture.
. K5 X; N8 r3 |) I# @. sSiamese primes. 9 O9 v$ c" V% b# H7 a
Sierpinski numbers.
( r/ M1 J1 }' L. n. ~" W* @9 M; \Sierpinski strings. P ~5 }2 L% h
Sierpinski’s quadratic. 3 ~# l9 c1 Q0 C! S8 i5 e
Sierpinski’s φ(n) conjecture.
! K x# K; b2 r8 O+ ?2 H' JSloane’s On-Line Encyclopedia of Integer Sequences.
" v" w1 u/ C; F; nSmith numbers. + j" [( s3 |7 x( A9 H" Y' t
Smith brothers.
- i6 Q- t9 `( r' f8 V& c2 ksmooth numbers. 8 t" I/ _, f; d( j9 b( t2 m
Sophie Germain primes. ' N5 j" C3 u% {2 ]! U; f
safe primes.
3 Q% r; }' |2 u& \9 u& e" m2 {8 Csquarefree numbers.
6 Q9 d$ ]6 C- M) c3 f' {Stern prime. 1 u+ P! f- _5 R! g: v
strong law of small numbers. ; p+ Z4 F# \; ]( J0 Z. H" z: G
triangular numbers.
, O! l" p( G& s% ~9 F& w+ ctrivia. * q `; ^9 ~; Z2 r- J2 F3 r$ ]
twin primes. 7 M8 r4 m5 l1 w! H9 ?
twin curiosities. 9 k+ U- \8 C' q
Ulam spiral. 4 v2 @/ A% j) M5 Q+ t
unitary divisors. . u9 q$ k# j! J H3 e4 k
unitary perfect.
1 u1 d2 z P# K4 Q0 ountouchable numbers.
8 H0 y, S5 a; j3 M2 F+ d/ L" B: R3 |weird numbers. ) i/ T2 e' m. l D$ F; J- O6 |
Wieferich primes. - n N* K5 p& B: D4 D! h" U
Wilson’s theorem. 6 G, ^4 o& ?1 Y7 A) N
twin primes. ) C, t9 ] ~9 ], ?4 f
Wilson primes.
* X: T4 J! C" b* d. Z( OWolstenholme’s numbers, and theorems.
) ]5 {. z% m1 C1 c! ^more factors of Wolstenholme numbers.
) B* I# l& F) kWoodall primes.
; C. F$ ]/ ~2 e$ M m3 czeta mysteries: the quantum connection.

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作者: risiketu 时间: 2010-4-27 18:48
解压密码是什么啊？在哪里能找到解压密码呢？

作者: risiketu 时间: 2010-4-27 18:48
不好意思我找到了解压密码了谢谢大家

作者: mightyrock 时间: 2010-5-8 20:12
楼主强大，支持楼主，不过我就不下了吧~~~~~~~~~~~~

作者: clanswer 时间: 2010-5-8 20:18
回复 4# mightyrock

多谢支持

作者: 风痕 时间: 2010-5-14 22:39
似乎看不懂………………………………………………

作者: clanswer 时间: 2010-5-14 22:44
回复 6# 风痕

哦？是吗？呵呵

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