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数字的奇妙：素数

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Entries A to Z.
, W. y' J! [- L2 k0 B# g1 Wabc conjecture. 2 d0 Y# ]; U' Y9 j9 L
abundant number.
. ^) U/ s* M9 G9 r6 f O7 ^AKS algorithm for primality testing.
/ I b, F1 ~# D- A) G" B$ baliquot sequences (sociable chains). 5 n' Q: z, t& ~& l3 _
almost-primes.
+ q4 J3 U; `3 g! e* L! w8 O9 uamicable numbers.
( C8 m! i2 {% @9 d; lamicable curiosities. : o2 Y7 r8 k+ v( Y) A7 ~5 G" F
Andrica’s conjecture.
) }7 M2 r) x' larithmetic progressions, of primes. 6 H/ p" J8 x8 L" G
Aurifeuillian factorization. % W- w6 h5 d! r. b
average prime. " M3 W( o% H; e9 z
Bang’s theorem. ) A! q3 [6 {0 V; G! k
Bateman’s conjecture.
$ H, h$ z' `' w7 G* BBeal’s conjecture, and prize.
# }3 o' T- @* [. @Benford’s law.
* T4 ?5 i/ p; B. p$ wBernoulli numbers. 9 e! `2 ?+ p1 h+ V; Z
Bernoulli number curiosities. 7 e9 y- [, Q; G9 B9 d/ m& S ^
Bertrand’s postulate. ; l5 Q% V* N( u' c5 Z- H
Bonse’s inequality.
0 @$ O/ y2 J9 N9 W/ @- ~1 O( S8 rBrier numbers.
0 q3 r" V- m, {( h3 O- D3 e1 K9 }) qBrocard’s conjecture.
0 E, Q$ ^+ i0 ABrun’s constant.
5 G) X: z% E9 @6 r, i5 b# oBuss’s function.
6 T F" S7 y1 L1 }; @Carmichael numbers.
, S( e* j; F0 D5 ?Catalan’s conjecture. 1 h# ~7 C L' U; N9 n8 [) f
Catalan’s Mersenne conjecture. ) b$ @6 v- k- [, `% Q
Champernowne’s constant.
' K: k; Z# I- V8 V& }champion numbers.
' L9 L% ^4 F) W% KChinese remainder theorem.
5 e8 B8 ~9 P- r+ x: m0 ]+ H( Gcicadas and prime periods.
3 b& ~6 f7 ^- h5 T/ N0 Ncircle, prime. % I3 G- d9 ~5 ?. t! _
circular prime.
! n" l# K0 @2 i& n2 R; m0 l( O' k, `( HClay prizes, the. ) {# a1 m o8 ~$ ]
compositorial. 7 g; q) H. B) Q3 f$ B% h
concatenation of primes. ) D. d$ ^) ^7 m0 F) d: y3 |
conjectures.
5 Z5 C' h) U* H2 f1 lconsecutive integer sequence. " f C* h, y& N( c6 U
consecutive numbers. * B8 r/ r" Y- S
consecutive primes, sums of. i. P( g. q+ {( l) Y
Conway’s prime-producing machine.
& q' y9 I$ o4 K# Q$ h' u& Y: Gcousin primes. / h. F3 k3 L1 P* k. ~
Cullen primes. / v$ j4 }( [/ g
Cunningham project.
9 V, C; R' V* i$ v. w6 u+ ICunningham chains. 0 s/ d2 S6 `4 E) F" S( {/ E
decimals, recurring (periodic). 8 W8 [# F' V7 z* Q8 q
the period of 1/13.
, o7 x) {9 M0 W$ O( J+ Ycyclic numbers.
( O5 J, y0 p* k7 {$ X! \8 zArtin’s conjecture. / k6 K5 a/ v" q& [
the repunit connection. ! m3 D( ~4 p8 `1 L
magic squares.
4 Z7 V+ \0 u5 ~/ ]1 @deficient number.
" x/ a# W! I1 c4 w6 V h( C9 Ideletable and truncatable primes.
, ]: J- x4 q; JDemlo numbers.
2 k% j& m4 n+ i0 U9 V% Xdescriptive primes. . ?& u, k6 m. E( u+ ~
Dickson’s conjecture.
9 S5 |* F- I$ f- r4 qdigit properties.
4 A; ?" ?- g+ K" E% {; T. y2 aDiophantus (c. AD 200; d. 284). $ ~6 G+ k& C: T3 ^; ?
Dirichlet’s theorem and primes in arithmetic series.
9 W# J8 c. ^$ m2 u" z$ _) s; nprimes in polynomials.
! ?7 h* Y: ~ }, w6 C3 q' Ldistributed computing.
- c/ @' Q9 m% P. n* Q' }5 l0 I2 e xdivisibility tests. 0 t8 X3 @! h# v
divisors (factors). # x1 @5 ?& V: H& ]! s- X
how many divisors? how big is d(n)? % d3 P' q# J& R# `, d% y( u
record number of divisors. 9 v7 F! C) P# W! O5 m1 E `
curiosities of d(n). % T' M# J1 F1 R& b
divisors and congruences. 3 P. p7 \; Y( g- j4 A
the sum of divisors function.
+ p( u3 q" O' a/ D6 a) Y4 `) @: ^the size of σ(n). ( B4 q8 E1 [* ]6 y5 c
a recursive formula.
5 f% t- `3 j% J* \divisors and partitions.
( k! C0 ^7 B/ ?- fcuriosities of σ(n). ! X8 Z9 J# }9 c; Q% E7 a" K- ?( L! K4 W
prime factors. ^8 _* C4 ^- J o3 N3 d& z1 b
divisor curiosities. & p1 n$ O1 G5 L! x7 u1 N+ ?
economical numbers.
4 ?* R$ Q) h8 {1 v0 k. DElectronic Frontier Foundation. 2 r. _; M( b# B, F9 r, i& h
elliptic curve primality proving. / O9 b1 [& P! B; |( K9 m
emirp. - E% `6 d. m5 D# w9 c$ K
Eratosthenes of Cyrene, the sieve of. 4 w# v, } C* |/ E7 A# [* \# J
Erd?s, Paul (1913–1996).
7 K8 r7 q5 J! [9 D1 H4 xhis collaborators and Erd?s numbers. ) _7 K {4 I1 f( h
errors. ; k! b6 N/ \: N8 R! \
Euclid (c. 330–270 BC).
% B4 i+ P. v! I% d/ x8 I/ L2 dunique factorization. & @* `, v' `5 J4 ?; E* I( d
&Radic;2 is irrational. 3 M6 Z1 T* I: u" ]
Euclid and the infinity of primes. 3 ]& f$ y! d0 g; g0 w$ N8 A
consecutive composite numbers.
% E. T1 x/ l3 W/ q( t# {- w7 Nprimes of the form 4n +3.
, M# j6 t/ h; K3 v1 \a recursive sequence.
0 ~2 M+ O* e( G/ z% {' PEuclid and the first perfect number. * G3 w% R! ~" ~; ^# G
Euclidean algorithm. ) R0 I. j4 P3 K! t) `$ }
Euler, Leonhard (1707–1783).
* j. U( d8 E* ?1 l) T8 s! FEuler’s convenient numbers.
1 P; ^$ x. j6 v7 mthe Basel problem. 7 f, D$ O) I! |6 l8 i
Euler’s constant.
) t T: D: L- Q6 n# O- B1 WEuler and the reciprocals of the primes. : _) J7 a! N4 c4 X( [5 Q
Euler’s totient (phi) function. - T; d, L; C- B: b6 W! m a6 t4 C
Carmichael’s totient function conjecture. 4 M% V; s" ?% v1 F, k4 f3 p1 |1 C
curiosities of φ(n). . u$ L8 s6 O4 S- k" W
Euler’s quadratic.
; b+ D) O6 ]& C; e( zthe Lucky Numbers of Euler.
+ }, I/ s+ f, T3 nfactorial. d- ?* ?, G5 A; k+ [/ A' ^" e( Z6 s
factors of factorials.
) M# X, P3 ` l2 |/ K ifactorial primes.
. p/ \5 `/ C* l" N8 E2 ?3 o# c" v+ ~$ Sfactorial sums.
6 h0 d. a C' M W1 Wfactorials, double, triple . . . .
/ S L3 j2 V H4 Y X& Rfactorization, methods of. - g2 i& w; w" Y
factors of particular forms.
( @( K9 a* z7 R# A3 }Fermat’s algorithm.
. q) K( `0 \' N3 L; l! }- FLegendre’s method.
" E* Y1 C; V6 K) wcongruences and factorization. 6 s7 B9 J8 _1 S4 Y. P& J6 Y* W
how difficult is it to factor large numbers?
1 m( _/ \/ L" Z% g8 b7 j' ^" jquantum computation.
" V' Q: R ^* z$ r% r. a- U7 zFeit-Thompson conjecture. " u- Z3 ]+ I+ h% `* O
Fermat, Pierre de (1607–1665). 2 Z- _) q1 J8 p/ b% X7 {+ F
Fermat’s Little Theorem.
1 _6 x4 }0 @* Y8 u! j/ MFermat quotient.
4 a: ?: f5 m( Y# b( @Fermat and primes of the form x2 + y2.
/ [/ p4 j) E& R: `* f7 Q+ j7 tFermat’s conjecture, Fermat numbers, and Fermat primes. + Q {! p. J3 {1 T% D
Fermat factorization, from F5 to F30.
$ }$ E; t8 h1 kGeneralized Fermat numbers.
* W J6 x \& C b! x: CFermat’s Last Theorem.
9 z \6 U# S7 D9 `/ W' }1 g! j. ethe first case of Fermat’s Last Theorem. L: b6 w$ {7 n! U4 M9 p5 o; G1 `
Wall-Sun-Sun primes.
& @; U6 B* B3 NFermat-Catalan equation and conjecture.
2 f- ]$ `1 P8 |# {5 Q; w! rFibonacci numbers.
% S6 M5 z6 h: Mdivisibility properties.
 s6 C. [2 q4 J# b- j( VFibonacci curiosities. 2 q+ d6 g& {5 Z3 i: E
édouard Lucas and the Fibonacci numbers.
% r0 O" T7 Q3 b' [Fibonacci composite sequences.
$ I, o {! O- [. Xformulae for primes. 9 U6 J5 g/ e) E9 h! q. b( I( S; m U
Fortunate numbers and Fortune’s conjecture. , l$ Y# p3 L4 v; B
gaps between primes and composite runs. ; |8 X$ Q7 E8 ]
Gauss, Johann Carl Friedrich (1777–1855). : @9 U9 t# `. f1 f/ i8 e: {
Gauss and the distribution of primes.
' G, d; ]/ c: m. JGaussian primes. ( [- B! s- Q. n8 w9 d7 X
Gauss’s circle problem.
/ r; _7 e% J# ?& z0 t, ]& FGilbreath’s conjecture.
' V- B) ^4 c$ k0 A l( GGIMPS—Great Internet Mersenne Prime Search.
( H ?8 ^* G$ l [1 m6 jGiuga’s conjecture. & x+ I% s8 H0 x+ `+ N' y
Giuga numbers. 1 [, v% _" X0 P# B, L- [5 \; x4 L x
Goldbach’s conjecture. 5 ]' d* M9 i1 b: d& l) I. \7 R0 R1 O
good primes.
- F; W8 F% k6 P' w2 HGrimm’s problem.
' S+ g! ^5 h9 H# d7 V% X& oHardy, G. H. (1877–1947). 0 H1 n8 v2 y0 y
Hardy-Littlewood conjectures.
7 W# `% _: n$ Pheuristic reasoning.
0 S3 Y/ Y W h- B1 ma heuristic argument by George Pólya. 8 f% e( c" t* |4 y) F5 [. t' D4 J
Hilbert’s 23 problems. ) Q# B3 e. y7 w, j1 w
home prime. 8 i3 _. u$ f: l( A) n
hypothesis H. + X/ \' B" k$ \' V! d
illegal prime.
5 G% z" Y5 L' Z, ~' x9 b4 A2 |) ~inconsummate number.
0 Q) S5 Z' S, T6 ?induction.
, B* k/ d; R# d) n: N0 o* d% vjumping champion. ' V9 _+ d6 P' n. y! k7 `# n
k-tuples conjecture, prime.
* g' ?1 e: L& s( j: w+ X4 U: D7 aknots, prime and composite.
+ k& T, \* W$ l" XLandau, Edmund (1877–1938).
, n. l# ]9 d9 @# I4 ileft-truncatable prime. 8 `2 y7 ` Z; t0 Z) A3 _) ~
Legendre, A. M. (1752–1833). - k9 _2 G/ y$ v# K
Lehmer, Derrick Norman (1867–1938).
! x# J4 i% u7 Z, B* i. v/ {6 _( p( SLehmer, Derrick Henry (1905–1991).
# o3 [) ]6 N+ H" T+ xLinnik’s constant. & g& I2 J* z+ j( \5 A
Liouville, Joseph (1809–1882).
: k' O$ | q2 ILittlewood’s theorem. U# s- Z; p J" H
the prime numbers race.
+ o4 K2 W5 U( u) A. _: x2 \Lucas, édouard (1842–1891).
. Y. \7 O3 r( ] |the Lucas sequence. " H8 T+ D1 w$ U/ |) P9 K% Z
primality testing.
* T) h! ~6 A6 \$ U; w6 r6 P, O3 HLucas’s game of calculation.
& }+ ?% `7 c1 v0 Cthe Lucas-Lehmer test. * n. B; f4 E& p5 ], I3 g
lucky numbers. 9 A/ V3 e" P- h6 f
the number of lucky numbers and primes.
$ Y( e" l6 t! t7 ]( i7 i“random” primes. 2 \: I5 v: |: C; [7 L* y, {
magic squares. $ w* N1 v5 {, y: n
Matijasevic and Hilbert’s 10th problem. 3 r8 ^; C3 c: J) W U0 A7 ~& t
Mersenne numbers and Mersenne primes.
( G5 }% J$ M" e B. K2 s* ^Mersenne numbers.
" @; r8 p" X- T! d8 {, vhunting for Mersenne primes.
 D, l* {% l' }, athe coming of electronic computers. 2 `$ @2 U7 H9 _: s
Mersenne prime conjectures.
* ?/ S4 [3 i0 e6 v8 A( V( @the New Mersenne conjecture.
9 J9 I* W+ q$ q. chow many Mersenne primes?
- m2 x% P$ b- x5 J6 j8 e" QEberhart’s conjecture.
. C( W8 Y/ C2 f. @; gfactors of Mersenne numbers.
& y$ ?" Y3 |) L' a7 f2 ?$ F o& jLucas-Lehmer test for Mersenne primes. ' d& }! _4 L- J
Mertens constant. L3 P6 v5 _; x: x6 E; E" y% M1 ?
Mertens theorem. 2 j: ^' Y X1 \
Mills’ theorem. 4 @; v8 r2 w9 [- @: B0 d
Wright’s theorem.
7 l! q- P& c$ Amixed bag. ( B% f+ O7 Y1 Z) I: t+ ^
multiplication, fast. 3 f7 Z0 N% O( J5 w1 v/ l
Niven numbers.
' a0 _: V0 ?) [3 x0 z, } u7 `odd numbers as p + 2a2. " z3 p* [5 z8 ]* D9 ~
Opperman’s conjecture.
 V" Q% p k5 Zpalindromic primes. 9 R8 M$ n$ W' C
pandigital primes.
; {9 A% G' X+ \' ?" t9 iPascal’s ** and the binomial coefficients. $ e6 G, N4 a e/ J$ H( q# A* W( `
Pascal’s ** and Sierpinski’s gasket.
7 T3 _' V% B9 D* tPascal ** curiosities.
& X3 T: s, L+ e. F# V6 }( R- Kpatents on prime numbers.
, H& z9 |# ]/ F# q1 M4 ~- ~Pépin’s test for Fermat numbers.
& ^. A8 n; x* i, g! N4 ~* b5 wperfect numbers. * L0 E8 G2 s9 t" K& k7 _
odd perfect numbers. ! ]/ v5 {6 ?: e1 _
perfect, multiply.
) y0 j, i( k0 y& B. ^' cpermutable primes. ) ^2 m2 v: P4 ~, m6 h
π, primes in the decimal expansion of. 6 z% |/ T! q0 x8 ~- k) \ @
Pocklington’s theorem.
$ a- K: R; x1 J1 L& K% IPolignac’s conjectures. ' w9 Y6 d4 u, J& F
Polignac or obstinate numbers.
$ p" S8 `4 q1 k5 h* w2 tpowerful numbers. 2 V& e4 _9 \) _+ r. ^& n3 b
primality testing.
$ L, F% }6 E% b. l. d( a1 cprobabilistic methods. 7 P% b( e2 W+ F l! n; [
prime number graph.
prime number theorem and the prime counting function. , w$ G2 u9 F0 `; r6 O7 d
history. # ~3 L5 I3 `" W6 N4 z! B
elementary proof. % J/ S9 m9 |& J! f! L8 F
record calculations.
' a9 X9 T# R. B+ o5 k5 ?- @: Oestimating p(n). 0 _! W1 Q2 j* V5 [) k" d
calculating p(n).
$ b, q' r& [3 i; N& ~8 x3 V( g% aa curiosity.
* E1 K! y3 U/ T+ Q/ oprime pretender. * Y" u7 H8 J \' y2 I
primitive prime factor.
" F* ]# U( Z& D4 e2 L) X' u4 \primitive roots.
' R1 f, t$ {5 X) g# |7 GArtin’s conjecture. 5 M3 b# F6 j; w9 A4 _& a2 u4 ^
a curiosity.
" [ [: t$ n# G; y; C5 U( [0 }. j( Fprimordial.
 @* O" S3 a& t2 {2 wprimorial primes. - e( B! | t7 t! L3 W
Proth’s theorem. : ~' x& C% C5 |. Z6 L5 r! J
pseudoperfect numbers. . J1 G6 Y z D |) z% p( u: E* W
pseudoprimes.
- L! f! m% M5 Ebases and pseudoprimes.
- L! [6 I' w5 a$ J3 Fpseudoprimes, strong. + s# C2 ?& f! H$ x
public key encryption. 7 H% L" Y! Z/ p, \
pyramid, prime. ; S* v8 \/ c% r& {9 _: {
Pythagorean **s, prime.
" E, k f. ^7 [* N; A/ bquadratic residues.
1 U7 R$ T+ G" i2 p$ C6 u, ~residual curiosities. 9 y; |# X& ~% ?0 E
polynomial congruences. : T T5 e T; R: l# {1 N
quadratic reciprocity, law of.
/ Y+ F1 W1 L3 P( c! |: [: F# u4 cEuler’s criterion.
& R( K0 |, s G5 \ e# n% ]* TRamanujan, Srinivasa (1887–1920). 6 @9 S1 r0 k6 F0 l) h' ?
highly composite numbers. 6 Z; t: [$ C' V5 m p& Y
randomness, of primes.
) I0 |7 N$ w" p# H0 DVon Sternach and a prime random walk.
& i# b5 D x, X2 J; ]0 d# Z$ precord primes.
9 n+ d" O: ], L4 D7 U+ \some records.
3 K4 Y/ @. ?, ~* l. c- F$ i! Z& q+ ]' irepunits, prime. ! s- y+ T: m i- S
Rhonda numbers.
. C9 ^9 s5 N* s0 V# g. |4 E& U; XRiemann hypothesis.
6 S/ _3 b7 Z4 t0 e/ cthe Farey sequence and the Riemann hypothesis. $ d$ g& x: l) g9 {/ G1 f% d
the Riemann hypothesis and σ(n), the sum of divisors function.
- a- Q+ D) Z* i" e5 g4 ysquarefree and blue and red numbers.
( f# l3 x' A+ T( hthe Mertens conjecture. ! x1 J5 z6 `: x3 q) c5 i
Riemann hypothesis curiosities.
- s: o2 Q1 s: m* `1 g$ T1 iRiesel number. * o+ }( s. n0 H$ l
right-truncatable prime. ; ^4 x/ Q+ D6 ]3 O% g
RSA algorithm.
4 n$ M, W5 R zMartin Gardner’s challenge. 8 S7 o' C( o9 g+ {6 l# J+ a+ I3 d
RSA Factoring Challenge, the New. + \! ~. V; Q7 C3 }( A
Ruth-Aaron numbers. 4 ]' R. c& z) Q- }
Scherk’s conjecture. 2 F* l% b0 v& \3 x" {
semi-primes. : p3 s j9 m* M, K
**y primes. % K% u* T* m& u. O* {
Shank’s conjecture.
# @5 N5 W+ [8 K$ qSiamese primes. , \, S2 d% O2 @! o8 m3 k; U) S/ g( w
Sierpinski numbers. $ {2 z" N! g7 h/ l7 m& _# {/ P
Sierpinski strings. 2 @* g: R7 D+ ]9 Y# ?
Sierpinski’s quadratic. ( {) a2 J% P' v' Y0 }' E0 ~
Sierpinski’s φ(n) conjecture. ) C `$ q* H5 y/ z c$ X6 P
Sloane’s On-Line Encyclopedia of Integer Sequences. O0 l2 e6 k }1 V" o4 L
Smith numbers.
* J) S3 |% |6 ^3 U) R2 ^8 FSmith brothers.
( r6 M# x+ Z, W1 r2 Xsmooth numbers. , `/ ~9 z/ V3 B
Sophie Germain primes. m( o8 V; @% h* J1 Z
safe primes.
( S! b0 c8 r" j7 ?% v1 o4 Usquarefree numbers. ) h/ T' u% z" r6 l1 I
Stern prime. - O% |/ C \4 D6 C: P
strong law of small numbers.
8 ^1 q7 v& ^2 @/ W% c2 G# b* @3 Ztriangular numbers. 6 }9 j2 h" { [6 ^# V. v
trivia.
. Q8 ~ r/ w1 V" u% N+ [twin primes. $ y' X, j; z+ j" `2 ?; o- G- L( \. X
twin curiosities. ' v4 @1 i( x. @0 I/ I) D# r- s0 ^
Ulam spiral.
/ E5 N* c- V0 a. H$ Ounitary divisors. ; `( |3 d" L7 I
unitary perfect. 7 t. O) S1 G0 v2 l9 W3 r) |% ?0 R& i
untouchable numbers. + ^3 B$ l* B; w' \- H( z
weird numbers. % F Y$ V: h6 k2 |. n/ h
Wieferich primes. ' c7 I# D9 ]* S4 X% I+ J* \
Wilson’s theorem. 8 n8 L* w6 T2 M+ }0 G1 R
twin primes.
( n' \: ?( i0 p rWilson primes. " G4 y# `( }5 Z! z! Z' w7 ?7 n
Wolstenholme’s numbers, and theorems.
, u! [8 `8 B" T, ^; Ymore factors of Wolstenholme numbers. * w1 L! |% K' y9 C
Woodall primes. v2 g9 L0 g( o
zeta mysteries: the quantum connection.