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数字的奇妙：素数

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Entries A to Z.
 O' g, B8 B* nabc conjecture.
 b: ?0 @& n7 ~% a3 ~& Vabundant number. 6 {: w( ~; K$ j T8 Z& Q, _! u7 m
AKS algorithm for primality testing.
. l5 I" S$ D( i Q9 A, `7 Xaliquot sequences (sociable chains).
( s8 l- e u8 K3 ~# r$ o3 salmost-primes.
9 r" }7 M0 p4 v9 S& t! Z- \& J( W+ {amicable numbers.
% Y" q1 x( Z3 O# m+ n7 L& N& N* eamicable curiosities.
' t. H; I( k+ K7 V! h$ AAndrica’s conjecture. 0 E' V" x/ n3 [9 _/ J
arithmetic progressions, of primes.
! H( p! {4 K. _% Q4 H6 ^1 OAurifeuillian factorization.
# ~; L: d3 M+ c/ d! g4 D' maverage prime. * k7 o# A+ K& v/ A, |
Bang’s theorem.
* w& T0 L5 X& u5 x# W* h, M9 yBateman’s conjecture. 0 S5 k7 ?$ j2 A8 A: W# x
Beal’s conjecture, and prize. . F* `3 l& W1 U W5 H
Benford’s law.
6 c$ ?! l: K( j! | _Bernoulli numbers.
 n& C( u. j# _Bernoulli number curiosities. 5 \7 d- l& s! q' k6 p. b; v
Bertrand’s postulate. 4 _& Q* o4 z( ^0 u
Bonse’s inequality.
+ H) n/ L# `: M, A3 FBrier numbers. , m4 _/ E/ N0 C# N
Brocard’s conjecture.
$ O) s7 y" k' pBrun’s constant. ) I) H8 R. h) f1 Y1 |% k' B# t$ |7 @
Buss’s function. : U- d5 K4 N. Z3 ~1 B X8 b
Carmichael numbers.
5 l9 }" A/ P/ wCatalan’s conjecture.
1 P+ P! y2 l5 e/ W b$ ~ pCatalan’s Mersenne conjecture. 7 @7 ^1 y$ ^* p3 Y+ l! z/ ?
Champernowne’s constant.
2 u- j5 G+ d% b- F2 P$ tchampion numbers. - @/ w, t2 U+ s( P. q+ g, S
Chinese remainder theorem. 9 G1 ~; G f* K1 s
cicadas and prime periods.
, J; `8 f% l9 ucircle, prime.
" Q8 F4 q" Q R+ _1 Ccircular prime.
0 g+ M" |6 G9 _) Z# H8 X% b& aClay prizes, the.
* j; W& ~9 X- @- N2 Y$ bcompositorial.
. ]7 _" e% d8 G- Q: _' T& Mconcatenation of primes.
' ~8 I' M0 Y; r: W7 Uconjectures. - b0 K& y' F/ t: b% y" P
consecutive integer sequence. ! t$ z9 Y9 T" {1 V0 O
consecutive numbers. * m9 S! N7 W; I- C J! c9 F. ?
consecutive primes, sums of. " O: @0 |9 [1 s- M) ]8 w; A. O3 l
Conway’s prime-producing machine. 1 j3 f, n3 g. m1 P/ Q7 l" G
cousin primes.
% H1 U- U* X/ mCullen primes.
+ [' e) L9 z3 N, T3 a) C, ECunningham project.
2 c% E. B( {4 h/ B' Y* i7 UCunningham chains.
" m* l2 S) z1 d8 d' T f' j! j1 `decimals, recurring (periodic).
; j+ ^$ S+ R& Nthe period of 1/13.
. N1 L: |1 J& U( m1 G: R1 \4 B6 |cyclic numbers.
0 B3 r& d( _9 X3 Z, M) WArtin’s conjecture.
/ A+ ^0 k$ w: J1 z8 S* [the repunit connection. * M; p' t& e+ I+ |: z
magic squares.
* f& \- }+ y6 m1 p9 G4 u udeficient number. : P! q4 O" W) a5 K$ N' _. w R) _: T
deletable and truncatable primes.
) c$ G' c: N7 c: K& ^Demlo numbers. d* I6 Q1 K6 f0 B
descriptive primes.
1 U: D2 @+ l: `/ L, O/ X- r: QDickson’s conjecture. + c* F5 s9 h+ }9 }# O1 W
digit properties. $ ?8 j5 s" h* L/ A) H
Diophantus (c. AD 200; d. 284). 1 f+ p- n+ T/ $ ?" Q& A* g
Dirichlet’s theorem and primes in arithmetic series. / `& ?5 m4 {) p$ M
primes in polynomials. 1 c) P! U* a3 p6 c2 \" D/ c
distributed computing.
! r+ v; m/ H2 U2 j9 P0 L+ sdivisibility tests.
* _" c9 K. F$ i5 P) ~) @divisors (factors).
6 U) T+ Q3 A0 ~* N% Whow many divisors? how big is d(n)? 8 T/ r0 M7 e4 `6 P! n5 X' G- ^3 F
record number of divisors.
' L1 `& m! @5 Vcuriosities of d(n). ; e+ e7 N$ `3 o* e5 C
divisors and congruences.
' I# `7 s% n- z7 P0 o" o! U( ~- Rthe sum of divisors function.
, r( { C# G' V. Q" v* w9 Pthe size of σ(n).
& r. v, M& ?8 f( j" W6 v8 J( qa recursive formula. % Z5 {: }& T3 A6 d
divisors and partitions.
& m: y @: r* `% j) ecuriosities of σ(n).
* c- \2 L$ J! Q& G5 jprime factors.
7 i" T' l! |: o2 v. ~divisor curiosities. & K' B% A) d- M2 h$ $ m
economical numbers. + W" X; [) }' f6 j
Electronic Frontier Foundation.
: R$ u- r5 R8 ~2 Jelliptic curve primality proving. 2 F( ^5 F0 e! F
emirp. . V% Z5 T/ D; O2 K) U4 e3 r
Eratosthenes of Cyrene, the sieve of. 7 o7 t6 `6 J! U" Z) f+ y
Erd?s, Paul (1913–1996). 6 n: l" q2 @. i& g, J: N. ?) C
his collaborators and Erd?s numbers.
7 }: W* E+ l1 ?1 F' werrors. 7 e9 V' r! B5 G; |
Euclid (c. 330–270 BC). 8 f7 j6 p3 D: B v1 h. \" Y9 P, Z
unique factorization. 2 n% e: q. G% ^6 z. [
&Radic;2 is irrational.
" z1 P% L2 ^6 [5 \Euclid and the infinity of primes.
5 i: f* ]/ M: |$ F2 w5 I+ Q% Jconsecutive composite numbers. 4 M7 V$ t! p: w$ E7 h) z4 {
primes of the form 4n +3. 6 n( B, j. U6 H: k( p
a recursive sequence.
; V8 q: W. S* P5 o- H4 U4 oEuclid and the first perfect number.
4 D$ _' C1 S2 G& a. d4 ]* P* hEuclidean algorithm. % I9 N1 p3 L/ W! d" C" |0 [
Euler, Leonhard (1707–1783). , s! h5 w5 k6 N; i+ A6 _9 j- D
Euler’s convenient numbers. ; \- _4 Q6 f2 U
the Basel problem. # K. J' F# V5 ~# f1 T
Euler’s constant. 0 h( J2 T8 t. `6 e- d
Euler and the reciprocals of the primes. 3 v; B+ Y2 ?1 _* f8 Y9 e( B, K
Euler’s totient (phi) function.
7 V! b) ~$ L! dCarmichael’s totient function conjecture. , }$ N, }1 j. T& V1 C% [
curiosities of φ(n).
/ `' [" I; W) o3 F9 KEuler’s quadratic. 7 R. K. s K9 \- C2 Z+ [
the Lucky Numbers of Euler.
4 d# z) t3 e8 F9 _9 d( ufactorial.
" d* U7 \5 J9 q/ W4 q" Tfactors of factorials.
) G: E" b$ L# W! [( Z/ dfactorial primes.
/ C% e3 u" H/ s: Lfactorial sums. & T8 E) ]9 v" [) b
factorials, double, triple . . . .
6 n* @$ {- I6 t5 K5 [: H: [factorization, methods of.
: J/ i' p7 c( M: M( Dfactors of particular forms. @- `9 H4 n1 i0 z! w* F
Fermat’s algorithm. % U" {' i9 } ]1 k
Legendre’s method. / O- C2 Z0 b; y) L0 _
congruences and factorization. 2 |; I# K" d. g
how difficult is it to factor large numbers? % M9 V: ?1 j/ [ M; e
quantum computation. 4 o7 U, [1 }/ P" c# a
Feit-Thompson conjecture. . ^3 i( i/ H: e M7 F7 Z* V* i
Fermat, Pierre de (1607–1665).
% `( z" l# D% I0 r, Z$ gFermat’s Little Theorem. ! N: B. y% o# c' `9 p- J# y8 |$ @8 V
Fermat quotient.
1 S4 I! d [+ w, y+ P; l; V! cFermat and primes of the form x2 + y2.
6 ^* B0 y+ U- X3 Q, M9 MFermat’s conjecture, Fermat numbers, and Fermat primes. + O& [, W2 b4 X" y' p c* Q) ~* v5 ]
Fermat factorization, from F5 to F30. / O7 }0 O8 }/ b" d
Generalized Fermat numbers. 5 c" ?7 h* T% e+ u0 N1 {+ s" X( d
Fermat’s Last Theorem.
" h- ~$ X& v' k* K1 t' lthe first case of Fermat’s Last Theorem.
1 C* s7 j D1 [, xWall-Sun-Sun primes. ' R& v& V x6 {+ x
Fermat-Catalan equation and conjecture. * a* d+ w& w& Q+ P+ N; d3 [, Z
Fibonacci numbers.
1 w1 f. I4 s) `4 ]" H: M6 Vdivisibility properties.
9 H6 E8 E2 Z S' |+ R4 hFibonacci curiosities.
7 U" E6 e9 x4 ^; Q6 qédouard Lucas and the Fibonacci numbers. / O# Z, l: q P* {4 j
Fibonacci composite sequences. : `$ C- H$ w/ a
formulae for primes. , E: M0 s' S ^+ y3 o. @
Fortunate numbers and Fortune’s conjecture. 5 H; z: T0 C( X) h" Z- r ~
gaps between primes and composite runs. $ m }) }* i# ^$ e O
Gauss, Johann Carl Friedrich (1777–1855). 7 U; B/ d4 h8 ?; ]
Gauss and the distribution of primes.
8 A; v6 v& M& W" y) W2 J- M3 z3 }( o+ _Gaussian primes.
7 r# m* D" g' O- ?2 CGauss’s circle problem. , |9 l. ~: y9 f
Gilbreath’s conjecture.
1 o3 Q# F7 V. v! F6 E: t8 O* \* VGIMPS—Great Internet Mersenne Prime Search. ' c7 G! U* i; a+ f0 H- n
Giuga’s conjecture. 1 z- f7 Q! G- A7 l% I
Giuga numbers. 0 T8 l; T {) v& }% d, n8 x+ }
Goldbach’s conjecture.
5 v% R7 {& D8 dgood primes. * g' `6 c2 P6 P; W
Grimm’s problem. ( N' r3 e; |; s' S0 p' ~
Hardy, G. H. (1877–1947).
0 g# s+ t* b+ z5 E" H2 jHardy-Littlewood conjectures.
" C" Z1 P. H: {8 C! Z' hheuristic reasoning. 4 X) I; u) U; |* Q
a heuristic argument by George Pólya.
, v1 R g3 ]# uHilbert’s 23 problems.
' U) ?- l, [! j; ^! I& {6 T/ Zhome prime.
1 k- N, M" E; q# l" Y- m3 yhypothesis H. 2 K) Y7 w& J: @ p. s7 y
illegal prime.
# P N' p- E, @) y2 c: b+ ?inconsummate number.
9 z7 r6 A# w1 `, g \induction.
: \* p, G( O7 B' Kjumping champion.
% W# _, B2 j1 M2 bk-tuples conjecture, prime. , _4 n9 w |8 h8 b/ P
knots, prime and composite. 9 E9 J, F# |& f& O& j0 c
Landau, Edmund (1877–1938).
* e% O/ C M0 X- gleft-truncatable prime.
: L% a/ \ r8 E9 DLegendre, A. M. (1752–1833). ' P2 L$ @, I7 v9 s% o
Lehmer, Derrick Norman (1867–1938).
; E5 R1 Z: c- ALehmer, Derrick Henry (1905–1991).
& z2 }7 K8 b) o5 g$ d. g) XLinnik’s constant. * U5 U8 h* i, v: J* k$ I. e" X Y8 [0 O
Liouville, Joseph (1809–1882).
9 x; ]8 v# W3 VLittlewood’s theorem. Y4 A& r% ^1 k7 e0 ~3 Z! i, V; G
the prime numbers race.
, A# G4 |5 l; q1 [$ |# K+ q0 Z uLucas, édouard (1842–1891).
3 z/ e5 ?: _3 F E2 J3 Sthe Lucas sequence. 5 x, K! c S, W5 l4 ]
primality testing.
 c# d% R' D) O8 R$ d) _ r4 ]: ]Lucas’s game of calculation. # }$ Y* l. ?3 G: ~9 z3 p
the Lucas-Lehmer test. ) f$ D) A e5 n- P
lucky numbers.
& A6 g( i/ s0 Z _6 Zthe number of lucky numbers and primes.
6 Q/ `; {6 t& f$ |“random” primes. : c! L/ B1 d/ q! ~
magic squares. 3 W: Y0 U8 _) O0 E0 x2 z8 T: t
Matijasevic and Hilbert’s 10th problem. " G( L/ D8 o$ Y
Mersenne numbers and Mersenne primes.
. p# r4 Y: H* B+ u% t& nMersenne numbers.
/ C/ k4 C* N3 ohunting for Mersenne primes. : F* T+ s) w+ {5 s6 A1 [
the coming of electronic computers. * ~0 J, }/ H7 |1 |, R
Mersenne prime conjectures. - p: }9 C; v& ?8 F
the New Mersenne conjecture.
+ {) D0 @. w$ @. H2 a( d( K: \how many Mersenne primes? # Z6 J) d( r# B3 ^+ g" }
Eberhart’s conjecture. 0 s4 y4 c; M/ f
factors of Mersenne numbers. . u! `* \# _- E8 N
Lucas-Lehmer test for Mersenne primes. 5 v$ Z7 O# f3 F
Mertens constant.
& H% S4 ]/ c6 W6 wMertens theorem. . [& e' e$ ~( V9 n% |1 o
Mills’ theorem. " z I% z/ Z. `# V
Wright’s theorem.
9 }; I; j1 Q2 X7 |9 f) ^" ]mixed bag.
6 D4 {: r d9 bmultiplication, fast. ( b1 F3 f E; @ m. p: V2 ?. J
Niven numbers. + J5 u5 c d/ L! t
odd numbers as p + 2a2. , [( ] v: o% P- D T0 `% B- d
Opperman’s conjecture.
3 [# F8 i- f0 k5 H/ e5 n5 Epalindromic primes. 2 S l( |, L/ P; q/ A9 ^
pandigital primes.
! f8 i2 n( C7 b) t3 vPascal’s ** and the binomial coefficients.
* c t& I) g( f L/ [Pascal’s ** and Sierpinski’s gasket. 8 Z! z. }$ \8 T( `+ F& A
Pascal ** curiosities. 8 x& c7 H8 J3 Z7 P
patents on prime numbers.
5 G4 \# w4 d! N% ^Pépin’s test for Fermat numbers. 9 E% ^# a1 |9 |9 x- U* Y
perfect numbers.
* x7 \. D) G2 l) Modd perfect numbers.
! B! N) L2 X3 L7 U1 U" A6 Q5 J, Hperfect, multiply. " T, B2 W) k$ K6 m
permutable primes. , z2 Q7 K7 K" Q3 w/ |- i E
π, primes in the decimal expansion of.
, V R2 m2 ^3 u8 t5 k1 }Pocklington’s theorem. - x) p) J1 n* [+ t& d+ L A
Polignac’s conjectures.
! g: ~7 L" d- s& b. v* f' MPolignac or obstinate numbers.
$ D: N- \ b) R. @powerful numbers. / I9 m q; M& a1 A9 h# g: C" V: v
primality testing. 0 z/ n3 ^/ [6 O
probabilistic methods.
# m/ x9 e# F. {! ~" K; Wprime number graph. ; P2 `& ~1 S7 c9 i
prime number theorem and the prime counting function. 9 _% o) d- P4 P s
history. 9 d& W# T* ?! d3 c+ h( L2 W7 c' c! P
elementary proof. ) U9 c, l- J8 c) F7 A" B( o! j3 A3 A
record calculations.
" [" ~5 m. c; e. ?% J/ ] {estimating p(n). 4 |5 L( o6 x# A& V
calculating p(n).
, @2 z' Z3 f* V2 `2 O6 Na curiosity. ' r5 I9 `7 L5 K0 B F5 O. j
prime pretender.
" K$ L5 ?8 e: Tprimitive prime factor. : M* u! B5 m( q- y+ x7 W
primitive roots. * } v. M5 U4 A/ F9 D6 D
Artin’s conjecture. 3 S8 r9 m' W! l3 F7 c
a curiosity.
4 @$ D) I& h5 l# t% c1 ^- Sprimordial. h# m% N: u$ q# H4 s
primorial primes.
+ d9 I1 H. A& ]Proth’s theorem.
5 Y5 I: d6 p4 m8 Zpseudoperfect numbers. ' Z$ }) Y$ N: P
pseudoprimes.
% V7 I, s, ]; @# |' ~bases and pseudoprimes. * K% H- d1 x5 y+ S5 _
pseudoprimes, strong.
& G( V/ F6 q# z: C/ t9 h1 ^public key encryption. 2 G6 f( p3 E1 v4 y# S
pyramid, prime.
% D" t! C! d( p) a) V% WPythagorean **s, prime.
: l6 [3 p( F0 _quadratic residues.
# b, b1 K/ ~( j0 O$ ~* S3 nresidual curiosities. 8 t( A" X8 X6 k, o. R3 e# T5 D
polynomial congruences.
, S" @; I7 a/ j. k0 fquadratic reciprocity, law of.
. i9 z: I0 }: d5 fEuler’s criterion.
+ e) ~5 Y; w8 [6 \( ]. jRamanujan, Srinivasa (1887–1920). ' I! y G" w% V) C
highly composite numbers.
( [- _7 s# Q0 [randomness, of primes.
* g* @4 Z# L0 gVon Sternach and a prime random walk. 9 n: ]# X2 A M$ q
record primes.
( ]8 ?. O: Q- W; fsome records.
, Q+ k0 C) G/ x5 r3 b, C! c( z# \% Frepunits, prime. % P$ ?6 s" b7 e" F: \, e* k3 l% r
Rhonda numbers.
 L8 Y, H4 T* S8 W% Q. dRiemann hypothesis. * x3 b/ F6 r" I( K5 w
the Farey sequence and the Riemann hypothesis. ! ?2 m% K: c- L& w# G6 I
the Riemann hypothesis and σ(n), the sum of divisors function.
" C& n) v+ E" Usquarefree and blue and red numbers. ; @* F5 Z* p8 W9 _! ^
the Mertens conjecture. " D' T; h% m' G7 J
Riemann hypothesis curiosities. ' h( _* e8 v( Y- t( U) t
Riesel number. 6 ?: h' b# J9 G' N
right-truncatable prime.
 y5 R2 v0 A, i' q/ ~RSA algorithm. : G, }: `& N$ Q$ h
Martin Gardner’s challenge.
: x, e& }3 {% w i& hRSA Factoring Challenge, the New.
' y: b0 X, f, ^2 o7 uRuth-Aaron numbers. " h4 W- N, @7 s3 w3 \# g6 w) A; f
Scherk’s conjecture. 1 \" d* h8 r, a! ]! U$ P! O6 Y
semi-primes.
: T/ l1 F2 Z# r. G% @**y primes. $ N: E3 c# J6 s' K/ `% _
Shank’s conjecture. . O& b/ @1 y" S; k
Siamese primes. ) Q/ E0 C' B5 K: g* w
Sierpinski numbers. 3 I, T8 z* f4 G3 i, v
Sierpinski strings. # d. U/ h4 e% X4 V6 t, J3 w3 n
Sierpinski’s quadratic. 8 ]: V8 A: C( m. s4 P) ^
Sierpinski’s φ(n) conjecture.
5 ~/ \# N6 a0 b5 Y$ GSloane’s On-Line Encyclopedia of Integer Sequences.
% g# w& m( W$ q. { c W& GSmith numbers.
' p! k2 a% v+ j8 e% x2 C1 J* mSmith brothers.
+ B. K9 d2 e1 P g1 ]; Ismooth numbers.
, g5 J$ l6 ~$ D) t0 {Sophie Germain primes.
# S6 h$ p7 v) t: a) O1 |safe primes.
! A6 h: I. l! ?( W& x& Y9 Usquarefree numbers.
# [" N0 D: K* |: S5 g/ F) y) oStern prime.
 `# R5 N: Y- d6 W; H4 C6 ostrong law of small numbers.
5 B6 |5 r( R8 h. J3 h9 d! h2 rtriangular numbers.
8 M) O# a) B8 N% Y; @trivia. 3 {$ B6 `1 \/ `* \5 k
twin primes. * N( |6 i9 \% J& ?
twin curiosities. 8 }8 W. {0 D3 k' S3 X4 K
Ulam spiral.
. h: B2 m/ K1 W& z! bunitary divisors. 1 N6 l0 B) [7 p
unitary perfect.
- R. O( M% x' Luntouchable numbers. 0 q- ]2 [3 M) S# g. B* c
weird numbers. ! ^+ C/ v0 b+ y; { H
Wieferich primes.
2 g' v/ J# M% A" Y6 ?) iWilson’s theorem. * ]/ _! _, p( e1 R
twin primes. ( i& ^. v& `* u& @
Wilson primes.
) X' E8 e* v }: v( jWolstenholme’s numbers, and theorems.
5 N. x1 @, {3 y* w C$ ~. amore factors of Wolstenholme numbers. ! t6 z8 i! @ [; n
Woodall primes. 3 X7 P$ ? h: p- S
zeta mysteries: the quantum connection.