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数字的奇妙：素数

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Entries A to Z.
/ l* }0 `. k# [" V' p6 b% Vabc conjecture. ' T2 B# S# P; ^: G7 [# O
abundant number.
5 z+ X, s6 E: q" d x4 oAKS algorithm for primality testing. ; L: I- ^# \* z$ K' A! i6 Z T
aliquot sequences (sociable chains).
$ Y b) [8 }, e1 j1 Malmost-primes.
" X+ g8 a& t9 Q7 |2 xamicable numbers.
" L' I$ M6 J$ `6 {amicable curiosities. ) n" {. I$ q* c; k. P
Andrica’s conjecture.
' q* ]. j+ ]2 W+ |+ harithmetic progressions, of primes. 8 g. |5 F6 x8 J4 h
Aurifeuillian factorization. f/ ]) j! y) Y7 N6 {9 g
average prime.
: z3 @3 t, w6 f9 b0 ABang’s theorem.
$ W9 y3 o: N0 ]. U2 S4 Y/ t, Z* ?Bateman’s conjecture.
5 y/ |- R/ H" g! F3 N: B7 QBeal’s conjecture, and prize. ( m ~, X, h8 o- K8 h- a! y
Benford’s law. 2 p& B, f6 N8 j5 J0 C* \& w
Bernoulli numbers.
7 @5 x# F% H: h7 XBernoulli number curiosities.
* g' o+ ^8 c2 z9 S! S1 n9 CBertrand’s postulate.
! V" j: [# ]* c1 i- D; sBonse’s inequality.
9 Q/ |$ w) ?4 bBrier numbers. 5 W( y0 v6 Y- e( x
Brocard’s conjecture. 7 |1 m3 h, J* x) r% i
Brun’s constant. 8 f% |1 ~1 R( L6 O7 j1 k6 X
Buss’s function. ; `3 p5 W( I& T* j2 x) d2 X# Z. [! y
Carmichael numbers.
- {1 |% ]# s. }3 j0 c+ wCatalan’s conjecture. - N! n& A) T& ?3 U$ l+ v6 H. `
Catalan’s Mersenne conjecture.
4 [$ R6 S" f0 ?- D- W- v aChampernowne’s constant. x( z0 u Q, F' e$ Y
champion numbers.
' \. E- D c# J8 W& W8 L$ `3 p1 L: wChinese remainder theorem. 4 A, o9 o1 F" H. ] ^8 ?
cicadas and prime periods.
# W+ w5 p5 X' l7 b. S& `circle, prime.
# h. C& Q* k. ~, z) Gcircular prime.
: |/ m2 J+ t7 ^, j& S5 IClay prizes, the.
% ^3 I/ h. R E9 o# Q3 }! {7 h! Gcompositorial.
% V6 u/ a& |& |7 U0 _: Lconcatenation of primes. ( O# a( w! }5 G' |9 q
conjectures. $ d% j) Z% Q k: S! i0 u
consecutive integer sequence.
/ \6 x. [; f5 b# l2 _consecutive numbers. 0 ~; O5 F; R u+ v% a. q, q/ M( P
consecutive primes, sums of. 2 B/ |$ i3 S5 x+ \. R
Conway’s prime-producing machine.
1 L: V: ]7 [7 W& Ycousin primes.
1 S( t+ e9 m6 R0 t0 tCullen primes. 6 d/ Z8 K; O/ t* B
Cunningham project.
: c; N$ V# S8 v+ c+ ?; WCunningham chains.
. |2 g |+ m5 J% ~+ l0 O+ fdecimals, recurring (periodic).
0 Q4 `* C4 o/ b# K! Q$ Bthe period of 1/13.
( C& ~) N' X8 ~4 ]cyclic numbers. : V5 ~; S d: b0 M {* ]1 R
Artin’s conjecture. 0 i% j- o& Y' F$ d Y
the repunit connection. 3 g+ W$ U2 Z% t# a- u% `
magic squares. ! K) t7 {* L" j
deficient number.
7 [. r. T2 P5 p5 V- e, W) Gdeletable and truncatable primes.
. s3 ?8 o6 M0 M6 L3 L$ T9 BDemlo numbers.
4 c0 d: S( Z% U# L8 W7 S8 kdescriptive primes. " I/ g$ [, l* d( d& Q) L
Dickson’s conjecture.
1 B, k6 o+ Y+ {1 c# a3 ndigit properties.
. n& V* \. ?6 G1 g* x; q% MDiophantus (c. AD 200; d. 284).
( V5 ^! o& e5 _7 z4 |Dirichlet’s theorem and primes in arithmetic series.
: Y1 u" A+ a1 j' Z$ d' Z3 a! sprimes in polynomials.
8 c) w% P+ T8 t5 mdistributed computing.
, [" K2 o% q. m/ h' T. ~0 N6 ~divisibility tests.
. w$ P6 w- X& S* |& U6 M# v, Q3 idivisors (factors).
! c4 n% b) A8 X, I: s8 ]0 u) _how many divisors? how big is d(n)?
* k5 b; Y% x- y( {7 Nrecord number of divisors.
, k" s) J Y# g: a0 D! Z" xcuriosities of d(n).
: m, @/ E9 q3 y8 Z7 Gdivisors and congruences. 0 e. k K* Z2 O8 J5 u0 V( u7 g3 ?
the sum of divisors function.
9 x- m" N( A! J" qthe size of σ(n). - b' K4 L6 Q/ ]9 @% X
a recursive formula. 6 q- |# j" [1 i% v
divisors and partitions. & B" A. m' }2 Z) e) [, i+ G' z% C
curiosities of σ(n).
6 x! K1 K D( Jprime factors. ; K3 [) P+ D0 v4 B
divisor curiosities.
9 S8 H" ~% ^% H3 a9 N4 `economical numbers. : e0 K/ F5 x0 Q5 [3 x" C
Electronic Frontier Foundation. ! D* b! R- N% e! N: x9 z% `
elliptic curve primality proving.
! g1 w; X, K4 |; s2 U Zemirp.
& l0 w, x2 @) ?6 `- B/ a5 c3 m8 ~Eratosthenes of Cyrene, the sieve of.
8 F4 [; v5 z2 R. FErd?s, Paul (1913–1996). 7 v2 b2 E% ]* O7 ~) k L
his collaborators and Erd?s numbers. 5 L' P h( A0 k2 }. w
errors.
- q0 v$ O) \% u6 C# KEuclid (c. 330–270 BC). ( }& [+ q5 c- p1 C, K* f1 _6 U/ x% t9 x
unique factorization. + S' C3 @* A/ Y7 P5 e8 I" B
&Radic;2 is irrational.
. i3 h$ X4 A+ t$ B7 h U1 xEuclid and the infinity of primes. - w/ x" K6 F* `9 M$ a( S" R
consecutive composite numbers.
+ V7 j0 u! |7 a& Z' xprimes of the form 4n +3. $ e9 ^, t2 v2 J
a recursive sequence. * X% Q, n6 Y; n% B
Euclid and the first perfect number.
4 c# M n* H4 m+ \( }Euclidean algorithm.
3 K2 H4 @- a* K6 dEuler, Leonhard (1707–1783). 8 z! N0 q3 z, B1 Z
Euler’s convenient numbers. : e/ V( r; [9 p) U) _: _9 c
the Basel problem.
# _4 [+ {- [% Z6 lEuler’s constant.
6 k* Q! ~. Z. dEuler and the reciprocals of the primes. ' L O" L+ J3 U3 i. A) F, |
Euler’s totient (phi) function. 3 E. t$ k# y4 G' g# T
Carmichael’s totient function conjecture. 8 [( f- t2 ]( ~( u2 ?, g
curiosities of φ(n).
! f% Q0 {7 S9 l- [( OEuler’s quadratic.
/ T+ E) j }0 V1 f7 C" J8 {the Lucky Numbers of Euler. 8 _0 T' g0 K, s3 `- J/ P
factorial.
7 [0 f1 F& l+ F) R& ifactors of factorials.
/ k- Y! K/ k) rfactorial primes. 9 ~0 J3 ~ ]4 Q4 c
factorial sums.
; p! z% d7 z$ m: ?factorials, double, triple . . . . 5 } _3 u9 l3 m# Z8 h; Y
factorization, methods of. 1 Y; z3 P0 c1 q/ n0 |# ]
factors of particular forms.
' t, [, v! b9 L7 F+ I2 Y* {Fermat’s algorithm.
0 ?' B% F' M, r$ Z7 o9 i0 zLegendre’s method. 9 z6 V4 A/ M8 p
congruences and factorization.
; ?% j4 ?; F, khow difficult is it to factor large numbers?
6 }& S. D m: E: h" T6 b- yquantum computation.
2 v/ P5 s/ R6 T5 P; u# uFeit-Thompson conjecture. $ N9 o: o" [$ ]& R$ n
Fermat, Pierre de (1607–1665).
/ z! J6 d0 E" uFermat’s Little Theorem.
3 ?/ G, O0 C8 qFermat quotient.
8 q( v5 F* E* R/ {7 LFermat and primes of the form x2 + y2. & f( t. R% u, k
Fermat’s conjecture, Fermat numbers, and Fermat primes. : Q5 T& H A8 q' E" P
Fermat factorization, from F5 to F30.
 d/ c! x) D/ N5 Y( G8 oGeneralized Fermat numbers. + E/ U1 {# L' n
Fermat’s Last Theorem.
" q. w) _* C n0 D' M; F! A6 a+ lthe first case of Fermat’s Last Theorem.
, a/ u. f' u j+ QWall-Sun-Sun primes. ' j# ~% | i; S
Fermat-Catalan equation and conjecture. 8 t' T1 x/ Y K! B+ f
Fibonacci numbers.
! ~4 c5 p3 H+ N: Bdivisibility properties. * n. p1 W+ _, Q" p& j! a
Fibonacci curiosities. $ _8 w& @7 _+ w
édouard Lucas and the Fibonacci numbers. 6 b6 }3 J: E: W
Fibonacci composite sequences.
$ s+ X7 H$ {# W \formulae for primes.
; ^5 g1 n% o. G3 h6 k8 n$ J1 R5 rFortunate numbers and Fortune’s conjecture. 9 `9 N, K2 q! Q6 b, w
gaps between primes and composite runs. ' g: e8 v( R4 x* K! z
Gauss, Johann Carl Friedrich (1777–1855).
) h; d6 L/ B1 n2 Q k7 zGauss and the distribution of primes. 9 W& i6 |8 `; @
Gaussian primes. 5 n: v6 q. q y) F
Gauss’s circle problem.
9 \2 I4 f" W. {, \- M/ j7 \6 rGilbreath’s conjecture. # u# i1 K$ [ _# z/ D: e% d
GIMPS—Great Internet Mersenne Prime Search. % O$ ~0 B2 V, h- t1 I
Giuga’s conjecture. 0 F5 a' _% b; D" u5 F, v3 T6 J8 x
Giuga numbers.
, J- Y/ k3 E; o7 I. ~/ \Goldbach’s conjecture. 2 s/ k$ `( @/ D1 M0 I
good primes.
7 Q6 L& {' ~4 [3 o" aGrimm’s problem.
 ]; n. S, y/ B) q% f2 IHardy, G. H. (1877–1947). ! |! t2 s) a x( V+ c( v
Hardy-Littlewood conjectures.
4 {. v9 G6 W. Q# z. k2 Uheuristic reasoning.
" l" I; G* D# b* x" [a heuristic argument by George Pólya.
. a$ @8 b& E; I* k; c& v* a+ tHilbert’s 23 problems.
+ D9 _# k0 h; k9 Q2 L& Ahome prime.
" T/ `5 A+ H# O1 }4 _; |% Nhypothesis H.
# E+ J0 S1 L! P( T8 ~ O5 G- tillegal prime. ' N% g& ?0 u; A1 {2 \. K3 A: j
inconsummate number. 0 c6 w; Q5 K$ ~% `. g# h
induction. ( v! K& w% h& e& U1 }5 D
jumping champion.
3 U [+ Y: z+ ~# h+ N( Xk-tuples conjecture, prime.
0 f1 e) h6 Q9 v, y& c1 |3 [8 pknots, prime and composite. 4 L. b, q" E0 W/ s/ U9 c" W
Landau, Edmund (1877–1938).
3 k7 ]( W- o, k1 R3 {# _left-truncatable prime. U8 Z6 f( `& r& W. t
Legendre, A. M. (1752–1833).
3 g( Q, K2 W0 Q; J# B# wLehmer, Derrick Norman (1867–1938).
. {8 z7 l" y; X3 j- DLehmer, Derrick Henry (1905–1991).
1 t$ c5 p4 Q: g* m* g% Z% R& Z2 YLinnik’s constant. $ [* K+ a; {7 A! v# Y! e
Liouville, Joseph (1809–1882). ( o5 A& s: ~! r5 s4 r' s
Littlewood’s theorem.
! r, K W1 }: N- n& | fthe prime numbers race. " E# w, M4 Z& k2 E2 }
Lucas, édouard (1842–1891).
" i1 F* _% Y# `- Z0 p% K9 Jthe Lucas sequence.
2 U! h/ z8 Q3 I# U* L& n% zprimality testing. " x. E5 {2 h! b6 [
Lucas’s game of calculation.
( s2 Y; J, w# a, N' g4 Ythe Lucas-Lehmer test. 0 f! c6 S3 W- c( R0 P8 y: U. K
lucky numbers. $ \7 d5 Q6 S3 d# x; }4 v7 e* k; @
the number of lucky numbers and primes.
* F: \8 s1 z5 U9 N; `9 V“random” primes.
3 ]/ _1 ^( a5 b3 Vmagic squares. 4 n- j3 \" D! }4 q, X$ `) A* B% z
Matijasevic and Hilbert’s 10th problem.
& L4 Q( W+ Y q7 C. T$ E- ~$ GMersenne numbers and Mersenne primes.
4 a! B) `0 {( g' IMersenne numbers. : e5 @/ f: W9 e2 R* t# E7 L# Z1 o
hunting for Mersenne primes.
3 t* J' q; T, i5 T }/ e4 Y1 o0 ~the coming of electronic computers.
; z3 N# Y9 V( BMersenne prime conjectures. / x2 q$ o' z8 d9 e `
the New Mersenne conjecture. : [" L) ]: K( h3 H5 D8 b
how many Mersenne primes? 6 t9 J! ^" v2 ]3 _" b2 ~
Eberhart’s conjecture.
% Z8 n1 K7 G+ y3 u" e: Bfactors of Mersenne numbers. ! ~5 {8 ]+ [) E' A- R7 F) [
Lucas-Lehmer test for Mersenne primes.
3 `; j) H: T+ d) d7 ^! lMertens constant.
+ _ L) F% K' ^7 y9 X( K% UMertens theorem.
2 l0 e3 z) U4 {6 wMills’ theorem. ( p5 Y, A Y8 Z. G+ j T% c/ c8 \
Wright’s theorem.
) G5 F; P( \! t9 d" `mixed bag. # A5 v, S/ k s
multiplication, fast.
$ w2 a. z1 t. T4 C* j* u7 W' L# ~Niven numbers. ' J6 u! R" d1 ?( ]% W4 t
odd numbers as p + 2a2.
2 B& W, L) t2 v6 wOpperman’s conjecture. " A( s' w& G$ Q9 C7 U
palindromic primes.
1 t' ~' z5 l3 ]pandigital primes.
8 @, e$ M3 Z% aPascal’s ** and the binomial coefficients.
6 ^* d1 s Y" }" B% tPascal’s ** and Sierpinski’s gasket. 9 v. A/ Z2 Y& C+ v/ u
Pascal ** curiosities.
, C1 }+ s) I* x, e% ]patents on prime numbers. ) t h% X, }8 s2 o% G. [
Pépin’s test for Fermat numbers.
* e3 G; n. X' n6 K: q5 _1 tperfect numbers.
) O7 Y, E6 a7 N: t7 Vodd perfect numbers.
) V3 o6 P1 q: W+ C, qperfect, multiply. ) B) U/ I5 q$ O/ q
permutable primes. . O3 N, n$ s# F- b ~/ w5 M
π, primes in the decimal expansion of.
' C+ a6 }/ p( Y# aPocklington’s theorem.
5 H0 W, @4 C$ h/ T! QPolignac’s conjectures. 2 y: p% \7 d4 s
Polignac or obstinate numbers.
0 a+ b7 L" M6 h+ n$ jpowerful numbers.
* m! v$ E ]) M* z9 `. c2 U8 |primality testing.
, y# Q! ?) N! W0 e |' Q) X: x4 y1 jprobabilistic methods.
' x. b4 T% ~1 ], ]. l% ]prime number graph.
4 C) U: _% S9 j5 H2 ]prime number theorem and the prime counting function.
4 q, z+ h% k1 P2 t) c* ~history. - p; U# }1 n2 L4 u F6 C2 w( i
elementary proof.
) k9 b k) S$ k1 Brecord calculations. & D5 a' H) P4 |8 t, D4 E& l
estimating p(n). 3 b% {1 p Q3 L
calculating p(n).
, x0 }. a' i0 Y$ {3 w [a curiosity.
( E6 F& i/ s/ m. a' _5 l* Z1 sprime pretender. . \* s2 ~! k j0 ]' R4 K7 v
primitive prime factor. . d2 c1 z5 e0 f7 R5 w: D. ^2 A$ U5 j
primitive roots. g- C1 t; B* |8 s/ V- q
Artin’s conjecture.
1 D* Z( a% g/ p9 T) ~a curiosity.
$ n- U6 X! r I- p' c+ @primordial.
: w# D1 l4 ?' k" _primorial primes. ; L: a: @% u, L2 s% B, q% v
Proth’s theorem. / ?$ A, ~0 |- [- Y: N! j
pseudoperfect numbers.
. I0 o' n! V+ e( p& v$ a Opseudoprimes. 7 ?3 `! i# M/ V4 V: Q) t5 X2 D% |( U: j+ Z
bases and pseudoprimes. + l' o0 V9 E2 x
pseudoprimes, strong.
# F" n+ x: e, K$ [public key encryption. R$ `6 Q; V4 ~5 d7 y) q% ~
pyramid, prime. 9 M# ?4 U- z5 Z- F# [
Pythagorean **s, prime. ! l& k3 I6 D- |( A3 M+ r) }& J
quadratic residues. 8 }. i/ d! i, K M
residual curiosities. 2 L# n+ Q9 f, f9 T
polynomial congruences.
# G) O/ U/ N: C+ q+ wquadratic reciprocity, law of. ( l% t( ^) [# K
Euler’s criterion.
9 W1 w! [- |4 v X8 k$ J/ hRamanujan, Srinivasa (1887–1920). 6 C& u- e0 q; v9 A' W/ z% V7 s
highly composite numbers.
! S: S' z. S' M" o9 c0 P- }randomness, of primes. 3 _- A* c& k% r9 o- C6 L3 M [( z
Von Sternach and a prime random walk.
2 y% e% {1 ?- w1 G. x+ ?* Nrecord primes.
% N: ]: K' Q& `& v& Csome records. 0 I {% [* Z! N7 A4 g& g% T
repunits, prime.
. _" ?+ S2 Q# {5 f, F c/ NRhonda numbers.
) m- r7 |' b. E/ IRiemann hypothesis.
* E1 h4 s) w& Z M" ithe Farey sequence and the Riemann hypothesis. 1 V+ ~: ^1 c0 B3 C* P/ O
the Riemann hypothesis and σ(n), the sum of divisors function.
7 Z1 H! L; { Ksquarefree and blue and red numbers.
. N+ C. I' e' m2 c9 cthe Mertens conjecture. M. q( T) Y' r1 m" v
Riemann hypothesis curiosities.
 L6 Z7 U3 S j" {5 v) o3 mRiesel number. 2 m$ j O8 s& H w. y
right-truncatable prime.
1 {! X0 p5 Q, L1 L1 HRSA algorithm. 1 K! L7 s' w8 V
Martin Gardner’s challenge. * }% v# S7 g+ _7 a5 ~
RSA Factoring Challenge, the New.
5 P3 x% S$ j8 i. W* E3 U) f. ^2 `Ruth-Aaron numbers.
! X% F& H4 J) NScherk’s conjecture.
3 x; N4 N0 u% T+ K& L9 gsemi-primes.
, t7 J9 k4 ]9 Z: [**y primes. ( q. P# d M6 Z; g$ `, d1 G
Shank’s conjecture. 1 x: W6 S% R- n0 a
Siamese primes. $ p4 n1 w1 Z% J4 J3 [1 `! q
Sierpinski numbers.
, c; c$ I- c4 rSierpinski strings.
+ D$ Q, w! c+ x9 |9 ZSierpinski’s quadratic.
0 s p8 U4 I+ J" X$ USierpinski’s φ(n) conjecture.
: }- Q9 k9 `- J- d9 C8 Q( JSloane’s On-Line Encyclopedia of Integer Sequences. 0 |( g# n' a2 b' z" Q+ ?1 [5 c7 r* `$ P
Smith numbers. $ G8 H" v6 j8 J' b
Smith brothers. 7 h9 A/ H- G/ ]: J6 p' O
smooth numbers. $ `8 D$ R9 y: `5 S. I
Sophie Germain primes.
( ]3 l/ k5 ]1 p1 Q$ Rsafe primes.
: [* q* k4 \" S9 d# |/ P( w, Asquarefree numbers. * ~4 K1 o, \5 a5 q0 R
Stern prime. & |: k+ T; G. n1 [# K/ W) P& c
strong law of small numbers.
) y* w0 ]( w6 [" p- A* @# Ltriangular numbers.
" U" q+ {+ r7 w q# F# o1 mtrivia. ' C, u+ R/ `2 N+ s, X/ c
twin primes. . _6 E' t4 p. O9 A }
twin curiosities.
: g/ X4 R1 }9 rUlam spiral.
. h8 G# i5 q% N: J7 i0 _unitary divisors.
1 M/ U' E7 A" a* ]+ ~$ f9 b# Q2 Uunitary perfect. % q! @5 J/ q0 M- _2 n
untouchable numbers.
1 r+ N( R* r. o4 rweird numbers. 4 t6 v' [0 b$ O/ k( E
Wieferich primes.
! }7 Q, B* B( y7 {/ bWilson’s theorem.
# Q1 t1 P# U' M& D" o! stwin primes. ; g) w' n, o6 q9 ^- @1 ^& G
Wilson primes. " G% f3 E8 i S# g2 u5 }+ g
Wolstenholme’s numbers, and theorems.
0 p; I: \& [. x' Omore factors of Wolstenholme numbers.
) q/ o2 Q$ }! m7 iWoodall primes.
9 ?& x* W5 h3 w/ U- A. v2 ]* B) @zeta mysteries: the quantum connection.