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数字的奇妙：素数

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Entries A to Z.
4 L8 P7 O: a7 z) j% Gabc conjecture. ' C5 z G1 Q' D# `' s" ~: s; F
abundant number.
+ r5 K7 U0 V0 R3 |0 h2 H6 qAKS algorithm for primality testing.
7 W0 {/ ]( D; R9 @, A, saliquot sequences (sociable chains).
, ]! `( j6 {4 k5 r; u8 {" nalmost-primes. 1 A" n, k/ b+ C% d4 }1 X' M
amicable numbers. ! T' R+ ^2 v+ G- ?& h( u5 _
amicable curiosities.
0 \* h% a0 D* p9 x, {/ j" |Andrica’s conjecture. ( t" j6 i% ?4 X* p6 }/ w! I5 ?
arithmetic progressions, of primes.
! ]3 M$ E, G" d+ p7 OAurifeuillian factorization. / t( S* V+ r2 S! N
average prime.
) g M; [) H8 @( }: S6 D2 r6 [Bang’s theorem.
+ F* V$ E& Q% r1 z! LBateman’s conjecture. + ^7 d, o$ p& X
Beal’s conjecture, and prize.
" c$ l' z* b4 W5 l7 _+ x( o2 `Benford’s law.
! W5 U6 S& i0 ?; _7 J$ sBernoulli numbers.
5 b9 i" @4 c' `Bernoulli number curiosities.
1 [* i N0 |' {- i4 x* L- o8 _1 HBertrand’s postulate.
& I$ M* }6 ?5 C6 @Bonse’s inequality. , m3 [/ f8 G0 o! E. y
Brier numbers. , B. E9 n" X% k
Brocard’s conjecture. / s9 ], q9 N+ F% W: C
Brun’s constant. + y% R: L% h! S! W/ q8 G) p/ F
Buss’s function.
) C: ~5 r3 x. x. s: j8 d) D$ k1 OCarmichael numbers.
* e* \& l# }7 y8 XCatalan’s conjecture.
, B1 g1 B4 h0 c" @" ]5 |. eCatalan’s Mersenne conjecture. @3 ^$ t# `, F' }9 u4 G
Champernowne’s constant.
) I/ i4 _, r, K2 [/ G4 @) K4 ?champion numbers. + K e0 p0 e5 u8 I. ?6 {2 Y
Chinese remainder theorem. + z( k* d8 `2 J9 C
cicadas and prime periods. % v5 ^0 J- d+ z% C8 g
circle, prime.
7 ]2 e3 t: a3 r" p7 f% ycircular prime. ( u2 A6 y; Z) p- {1 Z3 f
Clay prizes, the. 4 x% a0 d6 O3 y/ X9 k/ C: f7 ~
compositorial.
9 D, z1 V9 P1 m! g, C0 Nconcatenation of primes. - q; n9 F( _/ f
conjectures. " j. {, f) l {: y1 j P0 {
consecutive integer sequence.
+ O5 V/ c$ t: ?# H hconsecutive numbers.
: g+ k: [8 x3 T) l' Q6 }consecutive primes, sums of.
) I) q$ y! Y5 Q, d0 mConway’s prime-producing machine.
( d- W# @, g" h9 f: Z( b# ycousin primes.
2 \9 k( G: M7 _- u$ _Cullen primes.
; U) s5 ^. |- l& J" XCunningham project.
! n: r. R% z1 u- nCunningham chains. , Y+ k, P8 R' o9 c4 q# q
decimals, recurring (periodic).
# l" v4 N: R5 R) Hthe period of 1/13. : S" V y" d& O( S
cyclic numbers.
6 z( P$ _' }, o9 S( FArtin’s conjecture. 8 R; e) G& |+ b4 B- `! a( v0 Q
the repunit connection. + [* X- |, ]2 c/ |8 l2 q
magic squares. # v6 c9 D; s* }& C5 Z& A. e' V
deficient number. ; [# i. q0 C8 _, C0 I+ r
deletable and truncatable primes.
, l) Q9 y$ o! v6 U) I8 U. g! RDemlo numbers.
" b& e1 e/ F% xdescriptive primes. ( T' D0 i% [/ I; X; b$ W0 S
Dickson’s conjecture. ) q. ]) `) d2 k3 v' l8 d$ O
digit properties. a4 L% l. ?- G) o) \9 C
Diophantus (c. AD 200; d. 284).
; D1 ?( c0 N+ K. fDirichlet’s theorem and primes in arithmetic series.
+ G! w9 W) d) k1 M, ]2 Fprimes in polynomials. & j8 Y3 l. H* A) ~" I# V! g
distributed computing.
; D6 v% l) V6 v$ Adivisibility tests. ) D" z0 p) r* V4 u' r
divisors (factors).
( k! K8 {4 V4 a/ M; `how many divisors? how big is d(n)? ' c1 K% G+ f2 B2 `' y4 E, r
record number of divisors.
5 {! j, k/ d9 k9 A* l9 P+ ^& L' K1 ecuriosities of d(n). ) I4 U8 P9 f9 L. ^
divisors and congruences. ) Y9 ?4 X- S% H* h
the sum of divisors function. 4 S- `3 }+ _$ ~
the size of σ(n).
! o; d+ y" [9 U6 \a recursive formula. ! n+ Z0 y: o T+ J
divisors and partitions.
- E2 d N0 n4 icuriosities of σ(n).
) l% H7 b5 @- B; Sprime factors.
) T5 ^! \+ d, H$ ]divisor curiosities.
# l& Q, Z% l3 Q) [+ d4 }1 peconomical numbers. 2 ]. |1 Y5 L5 H- [
Electronic Frontier Foundation.
' O+ j$ k& z' J3 ^9 O3 }elliptic curve primality proving.
( [- j9 j: V2 N/ lemirp. % e$ k) U, a7 }/ q
Eratosthenes of Cyrene, the sieve of.
! a. C: D! Y S; n4 B" eErd?s, Paul (1913–1996). 1 p7 [; r3 x* n6 x9 P! v; J% v- y0 C# e
his collaborators and Erd?s numbers. / P$ K2 \) v' b3 q0 Z
errors.
& o% p5 S( F* ?' l. F5 n8 D9 ?Euclid (c. 330–270 BC).
) I D. g4 S: k- j1 i8 d3 k: H5 `' @unique factorization.
( s8 C- ~7 N# I; S* l/ G6 Y, `&Radic;2 is irrational.
 ~& R7 F- P# ]+ Z2 [: ~4 \Euclid and the infinity of primes.
3 o l5 o& G- k6 Sconsecutive composite numbers.
+ z) J$ b f, I, _ ~$ m& sprimes of the form 4n +3.
) s/ N/ k( J, N, J; K% ha recursive sequence.
1 X9 @9 \6 c" g: i" _/ oEuclid and the first perfect number. ( l" X% }: l- S+ ~4 u% \' a4 B- M
Euclidean algorithm.
& [# q! C# A# _' a; YEuler, Leonhard (1707–1783). 4 A+ U: A7 J+ G$ W3 i, I# m
Euler’s convenient numbers.
* D3 N+ g+ n Bthe Basel problem. $ O; Q& i: t7 y* K
Euler’s constant.
: ^% L* h t$ x9 I: VEuler and the reciprocals of the primes.
 `# j, y, A% }9 U x2 h+ O9 HEuler’s totient (phi) function.
9 o2 L2 w1 l7 o9 B! uCarmichael’s totient function conjecture.
* r# ~3 K$ ?% a% Bcuriosities of φ(n). / m. C8 |7 V" o8 k7 }' g8 [5 z& C9 w
Euler’s quadratic. 1 O. M# `4 y2 {4 U5 L( T: v
the Lucky Numbers of Euler.
factorial.
2 _8 Y+ ^/ L$ S/ I$ yfactors of factorials.
; z% }' U* m7 i o! Q' j- d4 }factorial primes. 6 o8 k" r$ L$ _
factorial sums. # n2 A1 j; l6 v2 |
factorials, double, triple . . . .
( W# y( e% N$ w/ [: A9 k; jfactorization, methods of.
+ K% O4 p3 d" K4 t6 ^2 _, e- a9 ]6 |factors of particular forms. 0 r4 h' L, p, G
Fermat’s algorithm.
5 O6 G7 \) h+ b. R& E) zLegendre’s method.
- J& s" v! y& p* h3 G3 y5 Q% g( vcongruences and factorization. ; _. g6 l0 |" y0 ]: o
how difficult is it to factor large numbers?
) B8 N% {- s! C# y5 pquantum computation.
, r8 d- P/ I$ A# r& v4 a* lFeit-Thompson conjecture.
& h$ C' @. Z7 F# o4 T* D/ D% MFermat, Pierre de (1607–1665).
1 V$ e9 _# D1 e6 }5 ^Fermat’s Little Theorem. 8 _7 L" W0 o0 @7 v* d
Fermat quotient. 2 W! @. z/ A, t. b6 N3 r5 t
Fermat and primes of the form x2 + y2. 5 U9 i6 G6 V( B- C, b
Fermat’s conjecture, Fermat numbers, and Fermat primes. ( K$ M% ^" v I# }1 }
Fermat factorization, from F5 to F30. 2 R: D6 t' _1 _: w" N3 U
Generalized Fermat numbers. / C0 X9 n( T9 h. G+ m4 Q: C7 |3 o
Fermat’s Last Theorem.
+ J3 P+ I* o" D9 Z- p4 Y5 kthe first case of Fermat’s Last Theorem.
- X& e. `" L. S; W( B7 }Wall-Sun-Sun primes. " S, r) f3 f* `2 I
Fermat-Catalan equation and conjecture. % u" S# {8 F( g1 ?
Fibonacci numbers.
9 \* g6 N- w( {% h1 n% ^3 Adivisibility properties. + F5 S4 P! v: G$ I& i+ ^
Fibonacci curiosities.
; D @- o9 r# R& X9 V3 [8 Oédouard Lucas and the Fibonacci numbers. 9 R- Z( h0 P% Y5 M D5 j# \/ n* S
Fibonacci composite sequences. - X1 g4 z$ a8 y) j. V
formulae for primes.
/ r+ n$ O3 Q, X1 {8 ~) E, OFortunate numbers and Fortune’s conjecture.
; J9 ~; J6 B, o6 [$ |gaps between primes and composite runs. ! G8 f6 h# m% B4 v3 o
Gauss, Johann Carl Friedrich (1777–1855). ' B# Y# m/ |; I: D: j, n9 R
Gauss and the distribution of primes.
; }5 ^2 p2 u K7 n+ JGaussian primes. . T) D6 W B C6 j: ^
Gauss’s circle problem.
# b% G7 m. v8 b- V( ~3 }2 lGilbreath’s conjecture. $ l7 l7 w' Y h/ U$ [) |9 I
GIMPS—Great Internet Mersenne Prime Search. , T. J) y$ p; v9 e
Giuga’s conjecture.
' y$ S) o+ X, iGiuga numbers. 7 o) M$ A0 F( y. p5 Q9 q3 X( O. ?
Goldbach’s conjecture.
; H0 O. j7 Y: H) b0 e( Igood primes.
8 B$ b$ S3 T/ o9 e+ |7 @! QGrimm’s problem.
9 W- R- E% f( S8 y8 j7 bHardy, G. H. (1877–1947).
( o. E2 [' N( l5 WHardy-Littlewood conjectures. 8 b6 ]9 U/ l+ O/ X9 }
heuristic reasoning. ! R3 @: ^' ^, Q3 w! K! m( P
a heuristic argument by George Pólya.
) i' D) w) d4 \) M4 x+ d% ZHilbert’s 23 problems. 4 q6 R/ C4 A: I f/ _' X$ L/ {% `3 t
home prime. 2 W- K* ^: K( q
hypothesis H.
# x h, g" z% gillegal prime. / p, T# f, \; ~* a" \7 d) \
inconsummate number. ( G) d: M; J0 i) e7 T0 g
induction. + P, h) I6 z8 H6 K( y
jumping champion.
2 m. {% h+ K ?% v2 \k-tuples conjecture, prime. ! {0 g4 L% o8 x7 J. F
knots, prime and composite.
: c. J) v2 x7 N0 {: I/ GLandau, Edmund (1877–1938).
/ ~( X- v3 m$ Kleft-truncatable prime.
- k3 N6 p' D- c: |! ~, F7 [" ]$ ALegendre, A. M. (1752–1833). : r4 M7 i8 W5 b5 ^; v; T
Lehmer, Derrick Norman (1867–1938). ; I; C: [" H- J+ e3 X" q* R4 y9 x
Lehmer, Derrick Henry (1905–1991). 3 j2 w' D" Q. q: F, m6 E
Linnik’s constant. 2 B' u3 b2 s3 I6 D3 N8 n4 [
Liouville, Joseph (1809–1882). $ `7 }# c& a- L! O
Littlewood’s theorem. 3 [: B$ e j" r+ \7 y# T" T+ ~4 g3 X7 \
the prime numbers race. & r& r0 B/ Q6 h
Lucas, édouard (1842–1891).
; k7 E( B7 N, ethe Lucas sequence. . c! e. m1 S$ J+ N& H0 R+ j* T
primality testing. / V8 r* J! j* H3 ^; ^+ D
Lucas’s game of calculation.
2 g1 f" T" m2 ~& x4 ithe Lucas-Lehmer test. / |+ i4 L& q: t
lucky numbers.
# Z: V V( ^( E- j9 W7 Athe number of lucky numbers and primes.
- k, V8 M) Z5 |3 \: s2 s“random” primes. 0 [: X* ] H/ |2 |+ Y3 K
magic squares. . A& c+ R$ X9 m9 h, C) _
Matijasevic and Hilbert’s 10th problem. ; d0 M |0 y8 `& }, E2 @
Mersenne numbers and Mersenne primes.
* T8 H' I' _1 @9 v( ^- ^ eMersenne numbers.
9 W0 s7 t7 q0 G2 |hunting for Mersenne primes.
$ Z( Q- k9 Z& }. N& Z. Q e5 ]' Ethe coming of electronic computers. : I, t( I- U2 p5 n u
Mersenne prime conjectures. $ i3 E( e6 T4 Z! ^8 O* N
the New Mersenne conjecture.
' v0 Q$ H& s. q% }9 phow many Mersenne primes? + e- r. P# ~& _4 p' P9 g8 s
Eberhart’s conjecture. 6 _- F+ l# k; X, t R: K9 H
factors of Mersenne numbers.
1 p7 E q/ U6 _1 h# n* WLucas-Lehmer test for Mersenne primes. ( {6 H' }" [3 G( o/ Z2 e' K
Mertens constant.
& k$ Q) Q( [& q/ `+ ^7 \Mertens theorem. : y2 g& f4 P5 L0 G5 ~" K# }
Mills’ theorem.
- G0 h. l% |$ v/ G$ ?6 r* K7 \4 SWright’s theorem.
; h H5 u& c) |* x$ w- y5 o8 i2 Pmixed bag. $ S$ w6 {- e# f- `
multiplication, fast. 3 f. ]: g, g2 q1 i
Niven numbers.
! ]/ G! T' l1 v$ B, eodd numbers as p + 2a2.
3 t; ? |# T; e2 R4 r! M9 mOpperman’s conjecture.
5 D' [9 {' H" ], B, ~6 Y3 s! upalindromic primes. $ s* a2 ]1 R- s( u
pandigital primes.
9 m( i1 d4 x5 y: u& i3 |' ^* SPascal’s ** and the binomial coefficients. ! U% a6 D; V/ o% S: ?
Pascal’s ** and Sierpinski’s gasket.
1 a, }7 t5 Q" d5 N6 X: R- `& TPascal ** curiosities. - ~; M4 _6 \. s1 y* }7 F
patents on prime numbers. : e& w- h x' m$ K/ C9 [ \
Pépin’s test for Fermat numbers.
/ f, P1 b& X7 E- c0 bperfect numbers.
1 _ ^# n# }+ y7 Z, i! @odd perfect numbers. / @/ B6 ]; z6 @
perfect, multiply. - o7 J, y) ~( y
permutable primes. 3 @9 t, w& B- a
π, primes in the decimal expansion of. 7 c3 u% W; N2 j8 x I& g
Pocklington’s theorem. 1 F0 W* q- e0 r. H7 u& ?% R
Polignac’s conjectures. 7 S( A C5 Q* D4 K: |
Polignac or obstinate numbers. 4 g, @, z! h% j1 Y
powerful numbers.
9 j. A, `0 Z+ _: ?/ \primality testing. & C1 t0 y* I9 v8 t/ a
probabilistic methods.
! o1 u: a4 I- e8 Y0 I% Q# r( ^! Zprime number graph. , H+ L1 F7 [# N% Q- U' g8 [: R7 @# M
prime number theorem and the prime counting function. # Y% t/ k; d* m* v2 @3 [/ f4 g
history. * K! O1 w8 z" D, k: ~
elementary proof.
* n- r& p) h z# @, h+ Orecord calculations. & u0 w3 ?( `+ I) P9 p; T
estimating p(n).
% b. y2 d' b- b+ m1 acalculating p(n). 2 Z! i0 M" Z7 |* O
a curiosity.
3 D: u7 g- A2 w; k8 q' @ oprime pretender.
0 X. o; a' i! L3 h& v! zprimitive prime factor.
" s" b2 b) r- l4 v% K: Mprimitive roots. 4 H7 f) R2 ^# s5 Y% ^# f. S
Artin’s conjecture.
 n2 v2 m" K$ d ~) E9 L! ?a curiosity.
! z$ ~1 L& E% r7 Lprimordial. : n0 k Z/ S$ W
primorial primes.
, V0 C- `# n f! ?$ EProth’s theorem.
6 {0 a- C1 S7 |9 ?pseudoperfect numbers. 2 I: u/ S1 }7 v
pseudoprimes. $ T4 F3 L) b1 h( S+ n, { S
bases and pseudoprimes. , g0 Q- {3 r) d+ }5 g, N v9 ?5 S: I
pseudoprimes, strong. * g s% M! U6 b% t3 ]3 y
public key encryption.
1 w7 G6 B( O6 L! [pyramid, prime.
/ y8 Q3 U2 d' C1 ]9 f& w gPythagorean **s, prime.
2 K; e/ @: x" I9 d/ F2 o* equadratic residues. ! B: k3 G' ^7 Q& I7 F. H
residual curiosities. 4 Z. J* E$ q: \
polynomial congruences. % n$ W* {! n) {% R
quadratic reciprocity, law of. 2 Q! }; N' v! F) g6 x9 k
Euler’s criterion. H; n7 H# o% E* M: a; d" i- q. E
Ramanujan, Srinivasa (1887–1920).
( P0 o. c: E0 K& {1 r. fhighly composite numbers. * T7 R2 N+ N$ K7 f* P
randomness, of primes.
# o/ N' q) ]3 OVon Sternach and a prime random walk.
5 l# R0 y' b/ Q% ]/ brecord primes.
, q0 J2 [1 K4 ]* R9 V# U1 f. @7 Csome records. 9 J( Y% l: h7 F& B9 M
repunits, prime.
) z( y; ?8 m' Z |: IRhonda numbers.
8 E2 }1 H2 w) q5 lRiemann hypothesis.
, M7 l$ G6 w# \* F7 l$ g+ `; I6 X5 ethe Farey sequence and the Riemann hypothesis. ! B2 ^7 G5 t* R' R( V# `
the Riemann hypothesis and σ(n), the sum of divisors function.
# O0 U% N" ?, h0 `6 I/ Psquarefree and blue and red numbers. % F* [ j- n F
the Mertens conjecture. ( T- I. k% r8 x% p! y) H
Riemann hypothesis curiosities. # S J$ g* I% d
Riesel number. 7 O# O1 h+ g9 P$ E, w
right-truncatable prime.
" {2 W- L/ R; z- eRSA algorithm.
5 H. J7 g4 ]6 E T7 eMartin Gardner’s challenge.
" |; R% q8 [5 C" d4 ^5 |/ X# IRSA Factoring Challenge, the New.
/ ~ Z. M/ C& tRuth-Aaron numbers. " o% f, u5 R" A6 P
Scherk’s conjecture. . f1 a! s# o- @5 ^! D
semi-primes. 5 r2 `6 q) X) @; ^) X# G/ c
**y primes.
6 _5 `3 t1 l8 r. K3 L7 cShank’s conjecture. 0 E* E2 y/ K0 ^6 X' ^: w
Siamese primes.
2 M" Y( s9 b/ Z+ x* YSierpinski numbers.
. L! K6 q! {6 d) ~( BSierpinski strings. # p( w0 C% D, a9 Y. H
Sierpinski’s quadratic.
! A, U! \2 P5 \7 V0 DSierpinski’s φ(n) conjecture. 6 S! g; S3 [4 Q5 Z+ E
Sloane’s On-Line Encyclopedia of Integer Sequences. / t/ Z2 K# b4 l! m; |& {
Smith numbers.
! t, H' w6 o0 `$ f5 y0 ESmith brothers.
0 N! }- w# g, x" i- ?! ?smooth numbers. - h Y) }$ ^* m1 s6 d
Sophie Germain primes.
- j) H( U$ M' C/ s3 R3 Usafe primes.
2 b% p0 M) i' l4 \2 b& m. ^# S8 Msquarefree numbers. ( D% Y( Q, l+ w7 x$ G
Stern prime. & o4 a& u. v2 ~1 w9 a: x) ^
strong law of small numbers. 4 @& \$ B3 g) J% ~9 {: }( S7 h
triangular numbers.
1 A B `8 a$ S8 B' Xtrivia. & i' _; b* H8 d+ k# f% ^# ?8 z
twin primes.
# B# _# M+ h- ~8 h, J4 M; E" \twin curiosities. 5 J: |5 b' i4 `2 T- {& L
Ulam spiral.
+ n% l ^% Q" [unitary divisors.
) B e- V& b5 o6 ^8 hunitary perfect.
9 P# R' J m& k& h9 Y/ buntouchable numbers. : y4 Q' E: f {: p7 R3 }% h, C5 u. y
weird numbers. : ~' l* s5 c* p9 G' q: \5 S; i# v0 r
Wieferich primes. , @. T1 d/ e! c) Z" j) H
Wilson’s theorem.
. L5 j9 F4 B# i- j# T8 ^! Ztwin primes. & b& Q, t% _8 I( V. o, k* j. x9 \
Wilson primes. 1 S: C$ ^0 x; s% Q+ V
Wolstenholme’s numbers, and theorems.
! G' r n! u6 v$ C" Cmore factors of Wolstenholme numbers.
5 l# R5 M/ T. [% a: z2 \6 @Woodall primes. 1 U- M4 y7 z! V2 p" f# V [; V
zeta mysteries: the quantum connection.