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数字的奇妙：素数

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Entries A to Z. 1 ^ p: ]: K. h6 K6 {
abc conjecture.
; a# }& R! d. f) Y e! d7 K3 iabundant number. , u# ^# M* j5 B" K
AKS algorithm for primality testing.
3 Z" D/ ]! J6 \+ saliquot sequences (sociable chains).
0 d0 k w2 k/ N% A' }/ yalmost-primes.
; |5 d6 _# }0 @2 eamicable numbers.
3 ~* F* b+ l: e( {; z0 n2 Samicable curiosities.
- ?5 ^8 G: {$ c2 o0 aAndrica’s conjecture. 8 A2 \5 q k! {" L- r7 l/ p
arithmetic progressions, of primes. : l3 p/ @ }& p1 T8 ~
Aurifeuillian factorization. ! F! J4 T; X' g& |3 ?
average prime.
" g6 G2 l4 Q' K5 w8 [9 l( d' w9 z8 dBang’s theorem.
- A9 K2 m+ U) @Bateman’s conjecture. % ~' @1 P$ u8 ?1 w
Beal’s conjecture, and prize.
! G' a% D9 W3 V# c; mBenford’s law. 3 D9 |5 |) t5 T4 H& x% n, [ U
Bernoulli numbers. $ z! B |1 `, D0 D: C0 G1 Y Z, c
Bernoulli number curiosities. + V: @4 g: g6 @2 }
Bertrand’s postulate. 1 w3 F) }3 ]2 j& y8 D0 p/ G) q: _9 a
Bonse’s inequality. 5 O+ |" G3 k/ _8 f) C
Brier numbers. 0 ^1 E9 p' m) \4 a
Brocard’s conjecture. 7 h( r. I1 J$ Y$ {- f1 D
Brun’s constant. ! `. x# s2 f' {* @: ^
Buss’s function. . D2 d3 W0 m$ F4 W g6 ~
Carmichael numbers.
: ^1 U& z" B. f- m5 c, RCatalan’s conjecture. ( r& B$ r! K' V6 l# O M: l
Catalan’s Mersenne conjecture. 8 q! f. W7 d# @' i3 Q
Champernowne’s constant.
9 J3 [, k' J, H: n. {champion numbers.
0 _" K; m9 _9 t/ J UChinese remainder theorem.
3 L1 @8 p5 E: O/ tcicadas and prime periods. * x# }6 Q8 ] v5 h" |' f
circle, prime.
5 r; F+ n0 T' U' [4 X4 I( ]" fcircular prime. ; i1 V) m6 Q) F; a0 D3 S
Clay prizes, the.
% o/ Q+ w8 P& ~! J% ? rcompositorial. ; N' k# @& w( t9 \( @$ V
concatenation of primes. 6 c2 y% x. y' G6 g) d! H
conjectures. 7 W8 w& z r$ B2 v( k1 v5 w% ]
consecutive integer sequence. 3 J8 _ \5 n; f& [' q* q/ o1 J
consecutive numbers. . f* q7 x6 i( H+ Q1 B r
consecutive primes, sums of.
" ], g( k* Q4 d6 sConway’s prime-producing machine. $ x2 j* h! y* V( ]) K
cousin primes.
: ?3 ]8 {$ f r, ]- E5 s/ KCullen primes.
- p' F: A6 A' H+ I3 nCunningham project. : f! R! o4 |6 B8 L( w N6 k! ^
Cunningham chains.
' G0 \8 j6 x- J6 r" S: @0 zdecimals, recurring (periodic).
( ?$ s G3 Q& ~$ o U0 ]6 kthe period of 1/13. 7 n: k Z/ g9 Q% v# ^9 y
cyclic numbers.
0 h3 X! r, ~4 h/ W+ ^+ EArtin’s conjecture.
; Z" {$ y' x9 y! j9 Z" n4 ~' {" Othe repunit connection.
1 Q* y- A6 k* b. L2 Amagic squares. & M( O; |8 X; h( U/ j; h" |
deficient number.
( R. N- _4 T5 ^3 M% jdeletable and truncatable primes. - c( P/ x2 x2 `/ F! J
Demlo numbers. 3 L: r3 K" |: |! i) t! \
descriptive primes.
- S6 F4 z1 [: n& \; E+ B* L1 F/ w" BDickson’s conjecture.
+ I R* N1 N& r" N6 Zdigit properties. - }$ R' ?6 h, `, y) w
Diophantus (c. AD 200; d. 284).
2 M7 M1 b& u o( kDirichlet’s theorem and primes in arithmetic series.
" u$ _" o/ d! ~0 M6 pprimes in polynomials.
7 @- W& w. \+ ^# j* xdistributed computing.
" L; o; M" L+ y& }divisibility tests.
9 g+ f+ D' W+ a7 V8 f1 T2 cdivisors (factors). # E& P5 c8 e4 |5 R5 J5 e. j
how many divisors? how big is d(n)?
) n9 c" T/ P" K; j6 e. Erecord number of divisors. % @, Z* |; C8 W3 T( ?, K, r- {
curiosities of d(n). ) ?: k7 M+ B8 V
divisors and congruences. / R, {4 h4 J4 O" N" F/ G
the sum of divisors function. / h# R4 h: s2 m0 `
the size of σ(n). 3 H' p" H, @- T2 `# T6 g( H7 r
a recursive formula. 0 \# r9 U% I" `- W) Z" {3 |5 s
divisors and partitions.
# W% t5 u# z. [- {curiosities of σ(n).
2 _+ m9 Q* G; t1 R. Vprime factors. / l5 x2 @2 `" O I! N# @
divisor curiosities. % l8 ?$ ]: J' |$ Q! d0 J# h7 q
economical numbers.
( ~1 q/ s$ D! Y& I/ v# MElectronic Frontier Foundation. & Q5 N: L0 w3 g* r$ U ~) D o- z; P7 Q
elliptic curve primality proving. ) U W7 ] D" E( B; Y8 H
emirp. 8 V, A8 K7 H5 E, @! c" W7 {
Eratosthenes of Cyrene, the sieve of. $ f) M9 ~4 N% N. b2 {
Erd?s, Paul (1913–1996).
 F3 f% N* h9 x3 c5 p& shis collaborators and Erd?s numbers.
3 G i, E) f! g4 p) W9 R# W0 V, [% Gerrors. ! u0 s# l' \" C4 R
Euclid (c. 330–270 BC). " G- N2 ~: V5 c2 S4 A" c8 r
unique factorization.
1 g# R) S& N, {3 u2 Q! B& @&Radic;2 is irrational.
. w+ N' k5 b) ^0 Y5 Y. i# C' |Euclid and the infinity of primes. 6 @2 y) g# N3 m. ?/ j# A- M$ D7 k
consecutive composite numbers. : B6 F! C6 a, q0 l: q8 |1 V
primes of the form 4n +3.
* y$ U/ y! f! A! ja recursive sequence.
- u% O& W; m' |( o! EEuclid and the first perfect number. 3 V& C0 w. U! y3 ^ }
Euclidean algorithm. 4 r: J' W9 o6 A5 ^$ L
Euler, Leonhard (1707–1783). * m# M% k( h U. c0 o' A" P
Euler’s convenient numbers. - ]! @( z! e1 O, j
the Basel problem. 7 V9 c E' @+ O) m% P4 i- I: [) r
Euler’s constant. 9 x. Q g" Y% }" }4 Z0 x# y) Y* H
Euler and the reciprocals of the primes. 8 ]6 e9 Q/ R3 ^! e6 A$ F
Euler’s totient (phi) function.
; u( W3 \% f+ s9 X* y V, fCarmichael’s totient function conjecture.
) z e, k( K! z% mcuriosities of φ(n). 9 O. L# y. J- o+ ^
Euler’s quadratic. 6 F9 m' U! W0 G( w. l8 B+ P
the Lucky Numbers of Euler. % n% @- x8 f, [7 e
factorial. ! ^0 \) R% q# ^5 P6 P
factors of factorials.
! }; V% T9 x% `7 k5 s" tfactorial primes. , M2 k0 x3 D9 K2 P$ |2 _. ]$ y
factorial sums.
. o; ]& R6 R/ E i! c7 ^3 P zfactorials, double, triple . . . .
5 @! q5 a+ W( ?9 C/ [4 hfactorization, methods of.
9 a7 ^4 E, L6 Q" J d/ Q4 |8 Vfactors of particular forms.
7 v3 Z/ L% }, S- O, g: r; G. `; DFermat’s algorithm. 5 a0 t T- W' _# F4 }
Legendre’s method.
' d5 g8 p; _, {! \6 k9 wcongruences and factorization.
1 p+ N# H2 u& |1 qhow difficult is it to factor large numbers? z3 J" m5 E/ Q0 ?# ~. }
quantum computation. 7 U9 O" I- M7 s
Feit-Thompson conjecture. . c# d2 y/ s, U7 i% T& U
Fermat, Pierre de (1607–1665).
6 y: h2 {1 f# r$ j3 o) o/ ~Fermat’s Little Theorem.
: K0 m7 z- P* R9 ?- _6 SFermat quotient.
, m3 Z2 s; D3 C! V8 A' dFermat and primes of the form x2 + y2.
5 L+ ^; E/ b/ j2 A W) LFermat’s conjecture, Fermat numbers, and Fermat primes.
3 Y' z _' I7 [. B5 bFermat factorization, from F5 to F30.
' y F( y! b4 |3 E6 KGeneralized Fermat numbers.
' H) w1 w7 h1 s; DFermat’s Last Theorem. ! u' O/ x4 ?) m6 _+ p4 k
the first case of Fermat’s Last Theorem. $ b4 ?5 f5 ]; m/ f( v! \" x
Wall-Sun-Sun primes.
: R) \. I: X* N5 c. ~" \& C2 JFermat-Catalan equation and conjecture.
- b+ b: z$ s( W! n% cFibonacci numbers. ; e9 s2 C3 r0 \" L& `2 P/ i
divisibility properties.
* t. e& X/ n! O+ N* Y# [7 _+ MFibonacci curiosities.
( T9 j' F- t2 K) P# t' }édouard Lucas and the Fibonacci numbers. ' x0 N$ r2 e3 c# U$ }
Fibonacci composite sequences. 5 H D7 T( o; e4 h4 p/ e5 e8 Y
formulae for primes. * S1 _( X* g& M6 h
Fortunate numbers and Fortune’s conjecture. h' [( Z) X1 e/ F5 H0 D
gaps between primes and composite runs. & z$ N2 A& h. `% x' w2 ?
Gauss, Johann Carl Friedrich (1777–1855). 6 O1 Q e; {" @# T; ~
Gauss and the distribution of primes. ! j- v; y5 W' d5 e
Gaussian primes.
) {7 y# ~: I1 B! Z% a- S7 b$ IGauss’s circle problem.
) N; Z2 @ k. e6 | S, k7 QGilbreath’s conjecture. : ^# S) ?/ V2 v2 s, V: U
GIMPS—Great Internet Mersenne Prime Search.
& |1 G# }& m: L! X! G3 g I. LGiuga’s conjecture. 9 _6 I. g3 U) K& Z2 f1 i7 G2 v% N
Giuga numbers. " V, f! y- j k j
Goldbach’s conjecture.
: T+ ]( r/ }3 X" s! Wgood primes.
+ u1 F0 z4 H# E# T- n9 Q0 aGrimm’s problem.
5 z* D! f" U) h' u: `Hardy, G. H. (1877–1947). 4 D- N5 q# L" i7 p
Hardy-Littlewood conjectures. 4 O1 V3 m( k/ M- o7 c# ?
heuristic reasoning. . I# e5 E& }8 G& d% f" K# S& ~
a heuristic argument by George Pólya.
& o, j' t6 f9 z9 {0 _9 C# n6 W" KHilbert’s 23 problems. 8 Z4 M; Y& C8 X% s
home prime.
 w2 f/ e6 c6 f+ n; Q! khypothesis H.
' h. V; G; k6 r+ Xillegal prime. , l. l2 X6 K6 G' U u$ U5 D8 P
inconsummate number.
4 u; E2 n6 w8 B" xinduction.
- r7 I7 J( H, v+ tjumping champion. + ~6 \$ u3 B3 \/ ]6 N
k-tuples conjecture, prime.
0 X5 r$ t l- H/ }8 m5 F# Uknots, prime and composite.
- u. O& X4 w3 M& g8 QLandau, Edmund (1877–1938).
. U! F4 a( f ]5 c; uleft-truncatable prime.
2 a$ ?; n: P2 P, F( j* PLegendre, A. M. (1752–1833). 8 m- r/ q; H4 A7 u
Lehmer, Derrick Norman (1867–1938).
& [/ ]' U7 U: |0 V9 `6 j" t( YLehmer, Derrick Henry (1905–1991).
! F' y7 V5 i, R& s# VLinnik’s constant.
* F% @% A) a+ e3 V3 P7 s; }4 |8 ?Liouville, Joseph (1809–1882). : w+ `; F+ H. H/ O( k7 C6 p
Littlewood’s theorem. & {, H5 N( f: I9 ?3 p
the prime numbers race. \# H! Z, n/ _* Y
Lucas, édouard (1842–1891). 7 a& b4 Q* U: x2 K3 d: e
the Lucas sequence. 9 `6 j9 t2 o1 m- o
primality testing.
, P! n9 d+ N* i4 T, H! o9 B1 TLucas’s game of calculation. 4 Z; I5 ^0 F( \ [; v( G6 m
the Lucas-Lehmer test. ( n5 O; e7 C) s7 a0 R! I
lucky numbers. - c% `6 K4 T% r. m( [$ |
the number of lucky numbers and primes.
, V- K. g, \ Q- l“random” primes.
4 o8 {' E* w5 }, Umagic squares. ) Z2 X( X0 N. \# j* c" u: @ b
Matijasevic and Hilbert’s 10th problem. ( I7 ^* n, E2 q2 _2 R) H
Mersenne numbers and Mersenne primes. , c) V: \. P7 X6 F0 l
Mersenne numbers.
# R( H3 E! z# g9 }$ Z2 ~3 ^hunting for Mersenne primes. 4 k/ E& {, Z/ q0 C
the coming of electronic computers. 1 d% \0 x6 Z, A( }
Mersenne prime conjectures. & F: y9 K. X2 _' q- d% h1 W/ ^: Z& t
the New Mersenne conjecture.
8 W5 w, ^2 f8 h1 @! L y6 v( D1 Phow many Mersenne primes? , Z$ A! x5 [. \# d( Q3 q6 h, g
Eberhart’s conjecture. 1 U6 F% k5 {5 c6 W. ?% H
factors of Mersenne numbers.
9 W# ^/ V2 i: E4 A5 a! NLucas-Lehmer test for Mersenne primes. 6 ^" ^- l) g! k0 Q5 V/ ~
Mertens constant. 1 J& w9 ~" v" p/ B
Mertens theorem. ' G# x( g0 m, c* a8 \+ `8 ~8 d
Mills’ theorem.
, f+ h9 P& q" a- v# AWright’s theorem. 7 ~4 |" Q7 p! D1 O. V$ H4 i
mixed bag.
$ m, G3 K- }1 y1 `& b* s& Dmultiplication, fast.
/ r" C- {& U( GNiven numbers. 3 C- u. Z D4 |! D/ ^7 f
odd numbers as p + 2a2.
% Y. u/ r$ z: ?7 `Opperman’s conjecture.
% }: Z. [ E0 i( B6 B- Tpalindromic primes.
/ h8 n: T7 t* |1 D* o8 qpandigital primes.
/ M; a8 V0 ^5 APascal’s ** and the binomial coefficients.
9 x% u: L( j( ?& Q; b! QPascal’s ** and Sierpinski’s gasket. : ~+ _, [# P0 N% p
Pascal ** curiosities.
/ m) k# A' f: Y; Ypatents on prime numbers. ( z% | @& H- @' }" K( M3 _, q
Pépin’s test for Fermat numbers.
6 Y/ [% @8 s" L8 cperfect numbers. 8 E: o/ k- d! @$ c. v, Z$ O
odd perfect numbers. # }1 U' }. l, A; H
perfect, multiply.
% n3 [# V# ^" a/ g# Opermutable primes.
. |' _, @; a& F# `7 c' N1 S4 {" sπ, primes in the decimal expansion of.
( ^) l- a9 X: G3 w qPocklington’s theorem.
& k5 m) \% _" e! ~- n5 SPolignac’s conjectures. 7 n0 B/ P6 e% q. {! Q C
Polignac or obstinate numbers. / f6 k( q( P$ A7 L- @! U
powerful numbers.
$ i1 E( G! Y( r0 s, L, [8 I! Zprimality testing. " J0 q7 I9 Z+ J) N; Q0 Y
probabilistic methods. : a$ F6 P9 z2 f$ t
prime number graph. + N- Y0 m8 H0 l/ n
prime number theorem and the prime counting function.
* Z9 Z8 s0 x, d" I+ {7 qhistory.
) x1 Q5 _% Y' g# O3 o% e1 R/ Lelementary proof. 2 D! K& K: y' r' k! ?5 Y) K" Q! T
record calculations. / G% P! l' Z1 |2 Z0 B; w( a1 H
estimating p(n). ( Y3 `) T8 Y6 C/ ], h# Y% m: Z
calculating p(n). d4 d+ q. j) \( r
a curiosity. 1 R- }, _2 r, _# h, E- V
prime pretender. ) T; D: X2 |2 V$ a+ {
primitive prime factor.
1 B8 I! T! `8 ~5 S% d9 t* S- Uprimitive roots.
+ ^& h1 Z$ n4 \Artin’s conjecture.
: M# N6 [7 b1 v( K" va curiosity.
3 q. B5 ]$ U* b* M& t$ \* F! Aprimordial. . ?" b! U9 f& C$ p* V* w
primorial primes.
: k( f! u$ \0 v2 i8 cProth’s theorem. ) C/ j# g5 N7 \$ l1 |7 p& T* r
pseudoperfect numbers.
- z2 j' i, C- e1 Q8 Epseudoprimes. ( X6 x# V2 I9 ?' d9 Z6 l
bases and pseudoprimes.
6 a% e8 X5 ]& } c3 Y' upseudoprimes, strong.
. ^6 U# X5 N9 D' j) p& D$ H- c: ypublic key encryption. 3 ^9 ^8 L; E; T8 u9 @; Y; K( h' _$ f
pyramid, prime. 2 \$ ^* E' W6 u' w3 q
Pythagorean **s, prime. 0 R- T; }/ j# h8 x
quadratic residues. ; Q n n/ E; ] U
residual curiosities.
$ y4 H& |- J. vpolynomial congruences. 5 [! @: b+ z, H
quadratic reciprocity, law of. : t1 f& [- {5 G" |0 w+ {
Euler’s criterion.
9 @7 V) M; V* `% [! V6 z- \& F& zRamanujan, Srinivasa (1887–1920).
$ n- ^9 r* b* Phighly composite numbers. ; L# ~; x% z& F# z
randomness, of primes. 7 w* e0 v/ P* I: _9 f. p
Von Sternach and a prime random walk.
. L! z k G9 c5 }* orecord primes.
5 F7 r/ v! ?+ a1 Esome records. % }+ D# J6 b! H& \
repunits, prime.
3 N7 P$ z" t3 W$ L& c1 }Rhonda numbers.
6 H k" P, H5 C6 [5 w2 f& I/ g$ TRiemann hypothesis.
; A( p" L, s h/ _& `! N+ S1 S- zthe Farey sequence and the Riemann hypothesis.
6 ?6 s: Q! X+ Y1 ithe Riemann hypothesis and σ(n), the sum of divisors function.
$ d, c9 n b9 Q' t/ X3 jsquarefree and blue and red numbers. $ T' A+ Z5 r- ^/ l( \
the Mertens conjecture. & B' ~) o) V1 c* V
Riemann hypothesis curiosities. 9 u5 r }! h& j$ r1 J
Riesel number.
" L2 P2 ^. g: @( c& b% Sright-truncatable prime.
2 Y) A0 {3 n0 k& k3 M, o! fRSA algorithm.
- Q) y- D7 f9 n2 g2 I9 R/ o( }Martin Gardner’s challenge.
 N1 f' n5 t# X5 D% [6 b, q. ARSA Factoring Challenge, the New. 6 i# {3 |* P! \0 j
Ruth-Aaron numbers.
" T1 U" B+ Z# E/ z* s* y. G5 QScherk’s conjecture.
" ?# m% d( {( C/ m7 |/ T. u j# ]semi-primes. , }6 e" ~8 i$ [+ V* \# S$ `
**y primes.
$ Y/ d. @. k1 m% s) n) QShank’s conjecture. 9 O2 M2 ?* T/ C2 [* L( q2 b' H! ^
Siamese primes. ! L% d0 O8 P" T+ ]* R a' L
Sierpinski numbers.
9 F6 X& k: g: k: ^3 wSierpinski strings.
/ M) R7 r! I' B/ I. uSierpinski’s quadratic. . P6 K" v. F' p$ y7 n$ K2 `
Sierpinski’s φ(n) conjecture. 1 t* _; C: N% p, H- `+ H
Sloane’s On-Line Encyclopedia of Integer Sequences.
2 z" P# K: b! o, @Smith numbers. k0 r9 p% u6 S4 V3 j5 w+ `
Smith brothers. " u& m9 f) Q. M4 Y6 v& m
smooth numbers.
. [$ q2 W; Q4 I3 XSophie Germain primes. # o- |3 ]" l5 G$ v. M3 v U3 t
safe primes. 5 i; f8 p6 }% g! ]
squarefree numbers.
( ]/ g, e$ G: l/ v/ u2 Q6 FStern prime. 9 r1 k; @$ [. d6 t! F9 X
strong law of small numbers. + A& C( [# H4 u( L
triangular numbers.
: [3 u8 ?2 |9 h8 S0 r! A4 vtrivia.
% V- _* E) j3 _! R; utwin primes.
0 v1 x: x3 W! M# f0 H: itwin curiosities.
( ]7 }0 s& Z; f. L4 c7 bUlam spiral. ( F) g" @' c1 s$ y. R% c
unitary divisors.
# H2 U2 a8 V: t0 aunitary perfect.
) H3 |1 T- o/ Z7 v. Duntouchable numbers. 7 N5 i- K% O" w( L( o
weird numbers.
" R" W" e; [5 P2 }/ NWieferich primes.
: ~1 V8 e$ h4 h' |Wilson’s theorem. # s6 F# P# t1 H3 }/ r R$ U
twin primes.
9 c! m2 Y5 _) z5 q q- d0 b1 bWilson primes. " |1 o* [0 F5 C$ K! R
Wolstenholme’s numbers, and theorems.
3 U. [/ k: t v- rmore factors of Wolstenholme numbers. # k" W* E6 g% P/ D. m) p
Woodall primes.
, i1 y) {* y% E+ f: Yzeta mysteries: the quantum connection.