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数字的奇妙：素数

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Entries A to Z.
) |5 v9 q) v8 S1 i# {# q4 e {abc conjecture. % ?& V: q, F; H& U# D3 Z4 d
abundant number. / B7 Q& T: a; ]5 q8 K/ |
AKS algorithm for primality testing.
- Z/ U7 \/ p) Taliquot sequences (sociable chains).
& c8 y1 m* c' E3 S3 m7 V1 ?3 ^& ialmost-primes.
- Z4 h2 B5 v2 G8 H. a. J% v T# A, namicable numbers.
8 @8 b l$ P2 O# v8 x8 gamicable curiosities. # E1 ?( W6 m7 k% N
Andrica’s conjecture.
; x, B: d( `5 G ~9 T& ?arithmetic progressions, of primes. # J; {' I- W' m+ F2 u9 S
Aurifeuillian factorization.
3 l; c& ~) c- @/ n3 E% I5 Iaverage prime.
7 O& F+ E. R# D- f7 c e- ~Bang’s theorem.
$ P+ C. X/ q) y" x- [# mBateman’s conjecture. 5 I/ D- B L* H% h- e
Beal’s conjecture, and prize. g2 @: l& [- L# i: r
Benford’s law. ) V9 ^( r* V, `- U5 `! Q: q
Bernoulli numbers. 2 q, X& K$ w; Q/ D3 ?
Bernoulli number curiosities.
# x" G! ?6 l1 \( m" L7 y& FBertrand’s postulate.
3 e# }' s- Z e8 Q" b0 h/ ^ pBonse’s inequality. # |# q0 t" r, j. d& k
Brier numbers.
% v3 u8 Y2 I" o( g" v% l! HBrocard’s conjecture.
; e3 @2 Q* f# p8 r4 U7 _Brun’s constant.
* N" T' g- q! V( H& A j8 h- GBuss’s function.
* W* }$ r: A6 ]8 q4 i" aCarmichael numbers. 7 W& ]5 l% O/ x
Catalan’s conjecture.
( W g- H7 B+ l1 n" O3 K2 kCatalan’s Mersenne conjecture. * T' u7 g* ^+ W) |2 ^
Champernowne’s constant.
8 g$ U7 }5 p: |1 l ichampion numbers. ) S8 O& L; B# J
Chinese remainder theorem.
: f/ R/ z9 ^* a7 Zcicadas and prime periods. ' D5 Y' z% F# J6 k7 M" \* _2 Q9 G. F
circle, prime.
8 b! {/ y7 U( G6 ^9 Ucircular prime.
0 m+ w, v% X9 F4 ~, m& pClay prizes, the.
/ X) `5 X5 E$ `5 c& k# i0 icompositorial.
3 T0 i2 E; ], v# sconcatenation of primes.
* l8 \/ Y- `1 A+ [4 `2 h! \2 rconjectures. 7 x" @( V+ o. ~# w
consecutive integer sequence. & b7 {3 V$ G3 Q* Q- c, M
consecutive numbers.
! z5 f9 Q- @/ C6 fconsecutive primes, sums of. & [' r# ?" |9 [( {1 @2 ]. ^! ~
Conway’s prime-producing machine.
3 z' f* |/ V: z# Ucousin primes. 5 B! d4 h, [% }
Cullen primes. ( r A# D0 E, C: z8 G
Cunningham project. ) ^0 ]7 C4 F1 ^- ^% Q: G: F6 n4 S
Cunningham chains.
" P! X0 j7 k1 l$ ^1 g4 jdecimals, recurring (periodic). 6 q3 u5 K7 s# w9 d- e+ X# R5 g) b
the period of 1/13.
* o( F8 I% R% {$ Pcyclic numbers.
- |! I( G9 h) @Artin’s conjecture. # K1 Z/ A4 [) W9 E% o. u+ S
the repunit connection.
( k* @, l3 o0 H0 g0 ]magic squares.
* W5 r4 J. E$ }# L/ l2 Y# ydeficient number. ! @8 a D) p& A
deletable and truncatable primes.
; B% o1 I' {3 aDemlo numbers. % s& ^1 @: l" C0 }7 s( A
descriptive primes. r& u6 H4 f* H9 y% X9 ~4 P( G {
Dickson’s conjecture.
5 c3 R; K( ^" y2 e; ]/ ^digit properties. + p6 J: d* Z1 r" N" R9 O/ u! N" ~, Q
Diophantus (c. AD 200; d. 284). + r$ O( p' S' f4 r3 F* B
Dirichlet’s theorem and primes in arithmetic series. % |/ W4 D0 p1 r
primes in polynomials.
5 \6 c( n3 S6 V: c$ W3 x- n6 Sdistributed computing.
" S/ a5 e0 P5 R- h9 _5 N8 {divisibility tests.
* A# q/ Z, A- r: {, p# ]0 _divisors (factors).
7 q% F c$ a' m6 h& @how many divisors? how big is d(n)?
# I' n+ r/ |4 Z) j- n; G; y. Arecord number of divisors.
7 o# t8 A' B/ v1 t8 S1 Ccuriosities of d(n).
+ b1 G6 M8 R2 p& d9 r5 jdivisors and congruences. / w: V' p- Q: I8 t
the sum of divisors function.
9 R) f3 q) X4 ^9 Y; X* Kthe size of σ(n).
2 m6 s0 e- J" N a! [7 @+ _a recursive formula.
) V4 c/ f8 y- }! Q) b1 x' [5 T- L$ sdivisors and partitions.
3 L: H3 a" G- p5 A1 W+ }: _; Wcuriosities of σ(n).
' J+ ^# \3 d5 |4 Uprime factors.
, [3 Y" v) r' x* ^0 s/ a( qdivisor curiosities. ) q9 E6 L- o3 G: A8 J3 U! }4 |
economical numbers.
% b$ `9 T$ s. _4 H$ xElectronic Frontier Foundation. + W q' J; g8 A( ?
elliptic curve primality proving. ! M F9 D& Y q& T" A, z9 I
emirp. . j7 Z2 N* Y7 g9 }. i' g
Eratosthenes of Cyrene, the sieve of.
+ Q' T$ p8 [0 p- y3 n* lErd?s, Paul (1913–1996).
! I2 {3 } A# y& D! u# hhis collaborators and Erd?s numbers. ) p6 n2 e. A$ I. z7 q F; C2 h
errors. : R: k7 @' Y) ?7 [
Euclid (c. 330–270 BC).
: j6 k5 K4 g4 Sunique factorization.
8 Z& K) [; ]7 r2 K S. M, Q- p&Radic;2 is irrational. 3 U9 [7 K& `4 v. E& K/ t8 |
Euclid and the infinity of primes.
9 E6 q% V; ~/ `6 g- G# [consecutive composite numbers. - Y( O. ]( P) d K' {
primes of the form 4n +3.
2 T3 a: V6 {7 Ha recursive sequence. , C; L% ?- b9 M+ g3 u
Euclid and the first perfect number.
: z+ F. }+ |* Q6 sEuclidean algorithm. # D8 R# A/ T* W1 k. X0 ^
Euler, Leonhard (1707–1783). 8 ` W9 W8 ]$ G7 k
Euler’s convenient numbers.
& Q0 ]8 z) m+ E' t% w" X Wthe Basel problem.
" y0 G+ P& f- K: j }Euler’s constant.
2 g Y& o/ ]* @. Z/ M" e; tEuler and the reciprocals of the primes.
4 S2 i9 I, G5 c8 O- {7 i( s. l' aEuler’s totient (phi) function. 0 c% U# D# [# q [
Carmichael’s totient function conjecture.
8 ~$ e- f9 |7 ^3 ~. e5 X$ Wcuriosities of φ(n). 5 N' F' j5 e9 E7 m$ g) Q
Euler’s quadratic. 1 T: B7 E" P, C6 |% e
the Lucky Numbers of Euler. : t+ \( H% m0 T
factorial.
4 B5 f8 c% j. V/ Dfactors of factorials.
: E6 g) I4 l5 s9 Hfactorial primes.
* V4 c* V T9 Mfactorial sums. * K5 b$ Q, [# o+ }
factorials, double, triple . . . .
# `7 A3 e3 T% H* x) Z5 ufactorization, methods of. 3 F" V5 \" Z, y
factors of particular forms.
9 k8 |) t" I* f: p) p6 tFermat’s algorithm.
( q' g7 ?" M) V y5 TLegendre’s method.
8 C" @- a6 V( \3 i! I+ V0 vcongruences and factorization. & @9 V1 j2 k& H1 k# |
how difficult is it to factor large numbers?
: s) u8 \: i* E# Q4 z2 l0 i+ nquantum computation.
' {1 V8 H! z' V# ?Feit-Thompson conjecture. : ?( e7 d# Y* }
Fermat, Pierre de (1607–1665).
4 ]" c* N3 w$ hFermat’s Little Theorem. % \5 ?) W! z' f# T4 G* _: Y
Fermat quotient. % b: M6 X9 x: Y" v2 Y3 [, d) r. u) |! K
Fermat and primes of the form x2 + y2.
1 F* p! P' r, v. M, f8 L4 DFermat’s conjecture, Fermat numbers, and Fermat primes.
7 |! M- C8 q: t6 RFermat factorization, from F5 to F30.
9 S$ f7 L _& A0 b3 kGeneralized Fermat numbers.
1 k9 \. {5 d5 h# l' z% P- H8 DFermat’s Last Theorem. $ u3 u# @: a7 y8 M0 a" [! \$ @
the first case of Fermat’s Last Theorem. & e4 a2 \0 }7 p7 s1 h5 l
Wall-Sun-Sun primes. 5 z y* i4 Y8 _! e$ W
Fermat-Catalan equation and conjecture. % r& [* J% ?: L* f# o! ]
Fibonacci numbers. # B$ R, d: X, Y0 c8 r7 _0 f" Z, X
divisibility properties. ' j! C# J% Z3 A- d1 C8 |
Fibonacci curiosities.
) k+ z! a9 U% X9 V, c- X# uédouard Lucas and the Fibonacci numbers.
# T3 M6 K! d7 R( k: j$ k) fFibonacci composite sequences. 8 b) a9 h6 Z- A: n; e
formulae for primes. ! T9 H) M8 O. b4 z4 T, E
Fortunate numbers and Fortune’s conjecture. ; h r7 ~3 f0 a6 l: E' L/ r, z
gaps between primes and composite runs. 1 M# F/ G, i6 O# X0 U/ E1 S& r% _. ^
Gauss, Johann Carl Friedrich (1777–1855). , [8 d4 }- m, G+ H
Gauss and the distribution of primes. ) m% f4 l* q# p/ i' X
Gaussian primes. $ b3 L" Z( p' z2 F0 L8 r h
Gauss’s circle problem. . @# b% i) v+ L, u$ i$ t
Gilbreath’s conjecture. R5 O% Q+ [2 m* p5 ]
GIMPS—Great Internet Mersenne Prime Search. 8 z4 P; |) j& Y2 O. U: F& U
Giuga’s conjecture. - s: ~8 s9 f- x$ h' ?
Giuga numbers.
; X$ t( B5 i6 x2 [: ^Goldbach’s conjecture. ( t6 Q& J- ~4 p4 i. c
good primes. . L7 x% ]* N9 W2 T+ Z: m. G
Grimm’s problem. - k8 J, q5 P! b/ }& @ ~
Hardy, G. H. (1877–1947). ! i/ x" H7 S7 B: a2 U3 [
Hardy-Littlewood conjectures.
 v# l0 Q0 n3 @/ X8 nheuristic reasoning.
2 \8 J/ `, d4 r0 R0 f$ v2 Ka heuristic argument by George Pólya.
! W2 P8 B, A; N B$ [* SHilbert’s 23 problems. ' |7 D$ k) v/ p7 |! Q& d
home prime.
% u) P# z0 a1 X fhypothesis H.
% d7 x/ L% t+ p1 Rillegal prime. + x5 u% K" Z$ p; y+ f( n
inconsummate number. 6 @* z2 g" l8 O# K2 ]
induction. , f) L9 {# n" n. r# d v2 u! A0 ~
jumping champion.
: O/ y( j* J0 t* h2 U9 F- gk-tuples conjecture, prime.
, ~3 a* \, D& @1 h9 zknots, prime and composite.
; u; U- b: e& a2 T lLandau, Edmund (1877–1938). $ ^) n: Y+ }8 w
left-truncatable prime. ! K7 O5 ?3 p9 [
Legendre, A. M. (1752–1833). * q# w6 A0 h" A& J/ K' E1 Q
Lehmer, Derrick Norman (1867–1938).
( \+ k/ T9 F7 ^, {: F2 L0 uLehmer, Derrick Henry (1905–1991).
) n h3 Z5 `8 j. j9 z, ]Linnik’s constant.
; j& Y. z. s" ]+ p( NLiouville, Joseph (1809–1882).
* Z9 |/ s& g% `+ gLittlewood’s theorem.
' t# ^7 }' q/ I. E3 C! s" |. xthe prime numbers race. : f" ^+ a% f# P2 i6 c/ h J
Lucas, édouard (1842–1891).
* L% m; e6 q8 |4 Uthe Lucas sequence.
primality testing.
& d" X8 ^$ N5 g U1 K: P* I) kLucas’s game of calculation.
7 C0 t* h# K! _2 r( a3 ]the Lucas-Lehmer test. 0 |- O- r- W4 s+ D9 z1 P
lucky numbers. 0 ^; v- B" v5 y/ K
the number of lucky numbers and primes. 9 s: r7 y4 T! ?# X# q+ [2 `
“random” primes.
' K) X8 V6 M6 k* s a# B) p) s2 Ymagic squares.
$ o! ~! a. P+ T/ ?; @; [- RMatijasevic and Hilbert’s 10th problem.
! l- }2 Q& g* h' u( j- [! w* uMersenne numbers and Mersenne primes.
; F+ H4 u$ i3 J% }0 Q& RMersenne numbers.
 r+ O) g/ L1 Q( u7 [: k* hhunting for Mersenne primes.
* O$ w) `' W+ @( i gthe coming of electronic computers. : {0 p7 _$ d$ u( H: l
Mersenne prime conjectures.
' X8 n7 g8 q& M0 k4 O5 x4 `the New Mersenne conjecture.
1 W& a+ u3 I' l: ehow many Mersenne primes? 0 O& s% a0 d- B
Eberhart’s conjecture. / W* a) u$ \% t) ~* C" u: r
factors of Mersenne numbers.
2 s2 r; i4 U H/ Y5 LLucas-Lehmer test for Mersenne primes.
3 L5 R) ^4 v8 v3 s: V4 x7 u# r! `Mertens constant. ' ?. k1 Z ]0 {! a$ O4 m
Mertens theorem. % O3 |, Y& Z/ E
Mills’ theorem.
3 n! D2 J3 q4 YWright’s theorem.
: G( c/ w5 L8 @/ tmixed bag. ( s% S7 E1 s) N* e9 B R( q
multiplication, fast. 2 h$ u0 I) o! M! j
Niven numbers.
" J9 r4 ^4 Q! }5 q: w' {, {odd numbers as p + 2a2. 6 Q3 M8 ]0 X/ V4 F0 R
Opperman’s conjecture.
& w' x" {& L, q, rpalindromic primes.
. N N0 n* f! k& e! ~, X4 Lpandigital primes.
. ~, K/ |. Q0 c1 D6 L cPascal’s ** and the binomial coefficients. 6 X* U( g; \- h$ G X
Pascal’s ** and Sierpinski’s gasket.
$ ?! a* D: y( IPascal ** curiosities. # N+ f4 W& z/ f% r4 h1 J( E2 F
patents on prime numbers. , J$ j$ K% |5 `- v& c
Pépin’s test for Fermat numbers.
4 ? ?0 p* `+ `: [perfect numbers.
9 `) k& t! ]) G) `odd perfect numbers. U9 w1 N2 k( d" H
perfect, multiply. ( b6 q3 A& T4 c
permutable primes.
( A2 C& t! [5 b. w- B. d! |" D! Qπ, primes in the decimal expansion of.
" r9 W, C7 B0 K, Q& FPocklington’s theorem.
6 B/ i. \( q* iPolignac’s conjectures. : A; @0 L" l$ X! [4 G4 E
Polignac or obstinate numbers.
, I7 P' H' h) t7 J5 Q7 \! |powerful numbers. 2 M8 D% ?7 O. [; y& R( \+ |- f
primality testing. 8 v, b) C3 a" u2 O" k2 c1 b# J7 @
probabilistic methods. 2 k8 t9 ^5 u8 C, X' k
prime number graph. 0 X0 J- I# U/ G/ O# ~$ J# S9 N
prime number theorem and the prime counting function. * J9 e7 r# D' {: r
history.
' ~1 A1 {1 P) b9 o, C: }elementary proof.
8 i% `0 j. N( k E" R( [7 Orecord calculations.
: {4 I+ H6 u5 Z" ~3 G; z# H8 U% jestimating p(n). % Y3 E& K; |6 \4 D, x6 v6 b: n1 T/ ?7 \
calculating p(n). " `3 W: @; W# |% F
a curiosity.
 n* J( ~/ M4 z: M+ l6 Y0 Dprime pretender. - r$ D b- h0 R9 _
primitive prime factor. 0 z% s$ s, T" |7 c$ T$ c
primitive roots.
5 t J6 v! G8 @3 v/ S/ WArtin’s conjecture.
# X* _* q+ `' `5 z, f1 x3 Ua curiosity. " X d. F! p8 u( V# j7 f% v
primordial.
& I3 s9 [$ L. D; |# U$ R3 F, Nprimorial primes.
0 W, X& ~1 l1 H! G9 ZProth’s theorem.
$ B+ _% r4 Q6 r; }8 W2 v( cpseudoperfect numbers.
8 [2 o# N; V2 M& r2 Npseudoprimes. 4 ]" O6 z `5 K2 B9 S
bases and pseudoprimes. 5 x4 ? g: R% y% Y- |
pseudoprimes, strong. 3 a+ Z0 q; v- E8 }) F
public key encryption.
 `6 Z/ H9 O \! j* Mpyramid, prime. ! J& _0 M: } {0 r, u- p! {
Pythagorean **s, prime.
: ^( P% u. n$ ~0 _- k. Zquadratic residues.
9 l/ ], {$ L6 _' D4 t( ]residual curiosities.
 G! t/ ?0 l3 W7 B) u) Y$ [polynomial congruences. }: W% n, j, |' g; |* n3 Q
quadratic reciprocity, law of. 3 I [0 i$ {; A3 C
Euler’s criterion. 5 C2 s8 O2 W# F$ J5 L5 { H
Ramanujan, Srinivasa (1887–1920). ! Z) L6 M8 K$ K- A& y9 x- y3 O0 _
highly composite numbers. " m) Q; c3 @" o7 A- m3 g
randomness, of primes.
* M0 f* f s9 z; _/ H1 MVon Sternach and a prime random walk. ) G+ m% N U( T" c
record primes. + n: k+ {' l/ e
some records.
7 Z) U6 A# f; R+ O5 q E) krepunits, prime. & Q) @+ k" V$ U& _& F& @( z
Rhonda numbers. : A/ m" r' M% k- n/ Z; U, {
Riemann hypothesis. 0 d( ^* @7 k7 m8 Q# s: L8 T
the Farey sequence and the Riemann hypothesis. * r1 s1 f6 @, h$ s: t" t# g
the Riemann hypothesis and σ(n), the sum of divisors function.
, j+ b$ d* x& N7 x# m! `squarefree and blue and red numbers. 2 r) R, u- n( O! ~
the Mertens conjecture. + j! r) i' L. I$ e4 M
Riemann hypothesis curiosities.
/ p6 {! T* [7 ~+ Y* PRiesel number. 7 m) _, t0 D9 W1 Y' |9 J7 {9 n
right-truncatable prime.
5 h7 A; Y4 D4 i0 S9 ]RSA algorithm. 4 V0 n8 J. H3 Z( @9 X* H! J0 q1 ^
Martin Gardner’s challenge. 3 x* p# @, `$ k
RSA Factoring Challenge, the New.
( P4 V" }# A) b; H5 g8 iRuth-Aaron numbers.
( `5 y. d: R' L2 o7 [3 m- EScherk’s conjecture. 9 F, t: ]8 [6 v" E
semi-primes.
1 y9 b) u% l) C1 I! q8 l**y primes.
. {: W, q! }4 i* {* N( WShank’s conjecture.
5 D/ d+ Y) Q' ]! n' t) BSiamese primes.
$ q" z& e% C: FSierpinski numbers.
6 U) H: Q9 j1 j5 t5 @( H# W' }Sierpinski strings. 9 T7 h) S9 O* P% L
Sierpinski’s quadratic. 1 x. Q5 a' O2 x& ^1 o
Sierpinski’s φ(n) conjecture.
% ]$ w( V) m5 a0 u# e6 C6 n& j$ ZSloane’s On-Line Encyclopedia of Integer Sequences.
' z! D+ ^ B9 c" O+ i, `; R( y0 CSmith numbers.
: K" Y1 P: Z, Z3 u) h6 b- n. `7 lSmith brothers. & `1 K, g9 @' V z' c4 V
smooth numbers.
8 [* y# h; O! ISophie Germain primes.
$ m4 v i j5 V' p1 [- x+ xsafe primes. 7 ~9 F ]" \2 q2 E4 k& l5 K8 M
squarefree numbers.
3 `$ i d6 @1 h& Q6 M/ ?Stern prime. 2 y+ c" @8 R ^% a* i; u
strong law of small numbers.
 ~" ]3 ~, i# T. n" \* ]9 a* gtriangular numbers. 0 i- `! U: r3 q. @
trivia. 4 f% x O& ]+ N, T
twin primes.
4 }, f9 u7 Q, m/ E( }( [twin curiosities.
; E' ?, L6 K- eUlam spiral.
1 x3 R9 I" \" x/ ounitary divisors.
2 z. L3 a* Z* ~- d5 g- lunitary perfect. $ `& A% f9 _6 j4 U: w" h
untouchable numbers. ! `7 u. l2 k) F: d2 ?
weird numbers. - y+ a( E4 q9 ^" _* y" X5 u
Wieferich primes. , Y5 T1 r, m& `
Wilson’s theorem.
9 F1 p% p! O3 m3 ftwin primes. & n' H n* Z7 {1 z n3 Z, @
Wilson primes. # [" H% g7 b# S0 Y/ ?. B( T
Wolstenholme’s numbers, and theorems.
0 O3 |1 h4 `) _$ C9 L0 kmore factors of Wolstenholme numbers.
+ z( \' v% R7 R8 l$ c* n& QWoodall primes. * c! V; J! a, l$ i' f5 w
zeta mysteries: the quantum connection.