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数字的奇妙：素数

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Entries A to Z.
$ o% K! s. z2 rabc conjecture. % A1 u- m. X! y
abundant number. ; A% [, W/ c0 i% T, E6 O3 v3 c9 A
AKS algorithm for primality testing. 9 ^; o, Q& J& k/ ]6 w }" T6 E
aliquot sequences (sociable chains).
4 l! V+ N6 x2 S0 Kalmost-primes.
6 A. h/ U: z' d$ L* F$ m5 L0 Ramicable numbers.
) L3 e! h6 `5 U! Pamicable curiosities. # l& s: |% q7 e& L
Andrica’s conjecture. 3 o0 \' z2 k$ O$ f
arithmetic progressions, of primes. $ x) g. v% ^% b
Aurifeuillian factorization. % T7 n- Y( j5 b. R& t
average prime. ) @1 Q, _( U/ ]) K9 B3 t9 p; j3 j
Bang’s theorem.
) l' t/ } d' N% iBateman’s conjecture.
! b, ?. V; m* b6 {0 k8 z- }Beal’s conjecture, and prize.
5 b+ C, D3 H" W/ F% \Benford’s law.
! U& `/ X9 |$ A# g9 IBernoulli numbers.
7 b2 {2 @9 |8 L2 ^7 W! J- eBernoulli number curiosities. + C* g1 O. H+ c7 j
Bertrand’s postulate.
- c/ O8 g8 d0 [9 \0 Q. E7 d: oBonse’s inequality. 6 q( R6 G( h. V% `) T7 d
Brier numbers.
/ _% [, X% M4 m1 _* ]" M+ |$ |/ ~Brocard’s conjecture. $ g& b5 L' i" X: _+ v. r) l# |. L
Brun’s constant.
7 @( Q G" w4 x$ iBuss’s function. 4 q9 E1 \: |1 y3 E$ n# z# {4 C2 j
Carmichael numbers. / v: C; f; L7 l1 v
Catalan’s conjecture. % ?2 I& B" b, o$ ]
Catalan’s Mersenne conjecture.
4 @3 p' |! b! ]5 k6 kChampernowne’s constant.
 ]% x9 Y1 ~9 Q4 [- U1 Z5 Mchampion numbers.
% O1 A+ n" ?' S# R- sChinese remainder theorem.
; ]0 s: x/ \$ a% K! Ncicadas and prime periods. # J) a2 h6 X9 x- d
circle, prime.
. N5 q! `1 m8 Ecircular prime.
7 Z! i; J& z% l+ a' G6 J+ z @Clay prizes, the.
1 H* J! [' T" V7 f8 ?" M: ~& gcompositorial. + n. z* j7 l, Z! |9 q0 T
concatenation of primes.
! W! G5 m* w, Y, Z3 t' B. T& `9 bconjectures.
% G e' W' T, Lconsecutive integer sequence.
0 y- Q; z; _4 U2 aconsecutive numbers. ( B8 ^. C% w4 X& R/ x4 a+ z K
consecutive primes, sums of.
6 W2 f6 `. q- g# IConway’s prime-producing machine.
7 X4 |. i+ {+ P/ |, b) {cousin primes.
9 \9 M( O7 s. {/ c0 K; sCullen primes. 9 y8 a6 o5 d* M" l% \# S3 o( _9 q
Cunningham project. * P/ v' F' q2 W! d: a) j; y0 e& }% U
Cunningham chains. ; Q6 M- ^3 R, b8 _7 o
decimals, recurring (periodic). $ G7 D6 ~$ W4 E8 Y' s0 H
the period of 1/13. 9 k' B/ H7 t! o& H
cyclic numbers.
$ p( V$ p- K' M) [/ x+ }Artin’s conjecture. - y4 Q6 b. D: f3 s+ m' h* B- M
the repunit connection.
: n/ T- `5 B5 k2 nmagic squares. ( d X6 c; I+ K
deficient number.
1 ]- r( S& {: J" kdeletable and truncatable primes. . L( U2 P! o) H; i. B; `
Demlo numbers. # h4 a) o/ @# X7 V! t- [9 {' C! o
descriptive primes.
' f' c* E1 s0 {% T xDickson’s conjecture.
+ Y/ b- [8 Z% o) rdigit properties.
) F; U8 s: e4 U, ~9 Q5 _Diophantus (c. AD 200; d. 284). 7 |' J( f/ n$ W) O9 n$ Y
Dirichlet’s theorem and primes in arithmetic series. 3 e3 a5 }2 ^" P/ e0 W9 \+ R7 d
primes in polynomials. 8 s/ i1 K3 _8 ~; S$ p& x( a
distributed computing.
5 X }. @; T" [/ s% O$ W+ wdivisibility tests.
. Z0 l+ {$ z+ T7 X4 Q/ v* J; m$ edivisors (factors). $ `8 k" X1 Z7 z1 Y
how many divisors? how big is d(n)? 7 f3 y- K2 b# {. m
record number of divisors.
- q6 X% r/ A1 [/ A. f; L( lcuriosities of d(n).
0 ?4 n! h! Z5 P5 Sdivisors and congruences. $ B6 ?2 j F* R) H
the sum of divisors function.
9 v" }1 y" b% D) [- U z, cthe size of σ(n). 8 v0 w" P- V4 k& r' [
a recursive formula. : ~3 K4 |( W# Y
divisors and partitions. 8 I' [8 y; t- p8 S+ x4 o
curiosities of σ(n). 9 F5 k2 e8 e: r
prime factors. , k7 [' E3 r2 u2 |2 k* n* A8 W
divisor curiosities. 6 D# c3 u# m' {. t* ?: v6 Y7 {
economical numbers. 4 i0 ?' T) Q3 r' w$ u: |1 R
Electronic Frontier Foundation.
4 N/ I+ D# A8 celliptic curve primality proving. + s" A% T1 c6 ~3 \4 x4 E- G
emirp. % l" i2 T2 A4 y# h" D
Eratosthenes of Cyrene, the sieve of.
4 U0 ~4 I* L( }1 q) R2 ~8 ^0 MErd?s, Paul (1913–1996). ' J6 Q! V: T# r ^
his collaborators and Erd?s numbers.
/ f4 L/ F* U0 ?4 K, i7 Merrors. # J/ F+ e9 p( i( l1 E/ Q
Euclid (c. 330–270 BC). 8 S3 m& j+ k: b4 D
unique factorization.
, p. P7 Y2 T# q; U5 Y% r&Radic;2 is irrational. , P8 a% X8 Y" `. W2 y. Q
Euclid and the infinity of primes. 1 E0 u9 {% P! J0 X+ u4 Y
consecutive composite numbers. 9 C2 W8 f* \; M8 s+ C
primes of the form 4n +3. 7 t) O" h e2 \) x O' ^
a recursive sequence. $ i2 |0 j. s( X, n6 g& P
Euclid and the first perfect number.
, z7 i6 R' j' Z7 jEuclidean algorithm.
9 f8 l: z) T& \$ g: x- w0 [Euler, Leonhard (1707–1783). - n0 r: A" y0 i+ E
Euler’s convenient numbers.
& m5 F. s3 L( N1 Y# h4 fthe Basel problem.
: U4 `# v$ z: {) i$ jEuler’s constant. / C, s: l! d: A1 H/ s
Euler and the reciprocals of the primes.
" n# h/ p$ I" e- zEuler’s totient (phi) function. " H# `, i2 c% I8 p( R7 t
Carmichael’s totient function conjecture.
3 W- O; I& d( X0 A: Qcuriosities of φ(n).
$ \9 @* L3 |; n& R% d: OEuler’s quadratic. ; ]) ~% }, ?* r
the Lucky Numbers of Euler. ' r, M( o# r7 t# Q! J! c
factorial.
6 m5 ` Y6 Z0 |1 d, F# sfactors of factorials.
1 F' `& Q w1 C: D+ @; r5 K; f4 {factorial primes.
- J: Z7 G0 c' q0 H [factorial sums.
* b8 C; ]7 ?/ n/ V/ g# kfactorials, double, triple . . . . $ ]' |0 m( u6 g Q
factorization, methods of.
+ U' F1 ?5 z& S4 Y2 I9 Xfactors of particular forms. 9 L; E6 ~$ E( g q+ l: ^( Z
Fermat’s algorithm. 6 A4 B' g8 ~" T- M4 v3 G( C
Legendre’s method.
. U' S8 `. _) h! M! r rcongruences and factorization. j! }* I r! I2 F! k
how difficult is it to factor large numbers? % r1 G% [1 A5 h. T% i
quantum computation. 9 h7 g+ c, |6 |- {( _, `' U
Feit-Thompson conjecture.
% i Z }9 w; y" w4 i$ M2 qFermat, Pierre de (1607–1665).
+ B: [/ H9 i. UFermat’s Little Theorem. ; k0 H5 ]8 o \( z3 m( S
Fermat quotient.
+ H1 X$ ?7 |1 o' ^: lFermat and primes of the form x2 + y2.
9 I5 |, @/ I0 s) BFermat’s conjecture, Fermat numbers, and Fermat primes.
* b. G5 K. f6 N0 }: mFermat factorization, from F5 to F30.
6 ~" }, n7 t. dGeneralized Fermat numbers.
/ N/ H7 K+ Q& s% y N1 d" EFermat’s Last Theorem. 5 _, z7 p6 X) ?2 O* h; v
the first case of Fermat’s Last Theorem. ( V3 E8 k; A& J( R
Wall-Sun-Sun primes.
, P) D* Z- |. w) L0 u6 B1 jFermat-Catalan equation and conjecture. + D, B, E$ [- K
Fibonacci numbers. - e0 g: n% N4 [$ u
divisibility properties. . d4 s. u" l! o1 K8 f
Fibonacci curiosities.
8 j9 ]: T I! r9 @édouard Lucas and the Fibonacci numbers.
+ G& P; D) |! _1 f7 J6 W- eFibonacci composite sequences. 8 ^( }$ F% `0 R) ^% C9 ]4 U
formulae for primes.
! b5 O4 O' P, `Fortunate numbers and Fortune’s conjecture.
; s+ F! _) |0 d1 \, Ggaps between primes and composite runs.
$ P5 F9 E( ?1 a, b- Y. [! f6 a+ B" d$ WGauss, Johann Carl Friedrich (1777–1855).
$ ^& q. I O+ a# W! _0 JGauss and the distribution of primes.
( {$ a! t8 Q7 x8 fGaussian primes.
" w; G( O+ P. W5 eGauss’s circle problem.
3 r/ z+ i2 A4 kGilbreath’s conjecture. # A0 o* c! A7 ~, n1 u0 y m5 i% [
GIMPS—Great Internet Mersenne Prime Search. * ?, F/ {( [' T$ F9 n
Giuga’s conjecture.
/ U8 C2 n' m- I# G7 C) P) uGiuga numbers. 0 I. c1 a. [+ l# {: p6 a
Goldbach’s conjecture. - ^! n# D& L/ r% C! R* K% j) D
good primes.
& @3 ^# h9 s, }Grimm’s problem. + T/ f; i* S- ~2 y9 R9 _+ a
Hardy, G. H. (1877–1947). 3 U8 q9 ^! y8 A; |: f+ E0 Z; m$ D
Hardy-Littlewood conjectures. ) ?) y4 Y$ q* s& i+ W( {% G7 d" W
heuristic reasoning.
, P/ j2 ?. F# }: A& w1 h' ?2 T! f* na heuristic argument by George Pólya. 8 a& f. s" b2 u& d) {/ s1 v
Hilbert’s 23 problems. & Q5 ^; g1 R- C9 u
home prime. 8 V. M1 d3 ?/ T% x- o9 Z) R
hypothesis H.
$ k5 T o3 g, S: g1 xillegal prime.
, n, u2 e( C6 _inconsummate number. 6 | z6 H- j; S8 D
induction. , Y/ ]1 s+ D6 p. l
jumping champion.
* p! M( {; p1 j5 k# |1 K- Tk-tuples conjecture, prime. , B! V. z6 R, D; m) e5 r
knots, prime and composite.
! e/ f* F+ O. S$ ^' I; kLandau, Edmund (1877–1938).
4 D5 E5 L0 D. `* d! H& |1 `$ fleft-truncatable prime. $ y" ]+ q% N2 l' p1 x
Legendre, A. M. (1752–1833).
; q: t$ ~. p7 w) }% e; @Lehmer, Derrick Norman (1867–1938). 7 }, \- w b) @ S% v. B- W
Lehmer, Derrick Henry (1905–1991). 7 R. G5 E. S, j7 G. _% I# r
Linnik’s constant. 1 r6 d) u, m J, e7 j
Liouville, Joseph (1809–1882). * q* W, v ^8 g! o5 ?5 Q. b
Littlewood’s theorem.
7 U; ^6 l) b% A+ K+ qthe prime numbers race. 8 a+ s' V$ v$ l# y" O3 \3 g
Lucas, édouard (1842–1891).
. D/ j, h! j3 a: Q% S Jthe Lucas sequence. 5 z' n( U: F: H% c1 R
primality testing.
+ _2 Q H* I# V) LLucas’s game of calculation.
5 |% B6 U( W) |$ w$ V0 K6 `the Lucas-Lehmer test. 6 d, D6 L+ d7 \
lucky numbers.
$ b8 q9 p! z( Z0 [the number of lucky numbers and primes.
7 O( R) p. |& z4 x; y, ~/ |“random” primes.
$ ?( C5 m* A. B/ rmagic squares. - \, l! Q& u4 Y' c
Matijasevic and Hilbert’s 10th problem.
$ B# x5 @ e# z1 {" IMersenne numbers and Mersenne primes.
1 t$ Q% B/ x+ oMersenne numbers.
, }" t1 |4 h" g$ u' _7 @7 ~hunting for Mersenne primes.
: w) ~) p7 I) f4 D4 Dthe coming of electronic computers.
0 R8 A) W. A, `; T# kMersenne prime conjectures.
' k; Z2 v# a3 Q3 ~. X8 s: v5 ^0 zthe New Mersenne conjecture.
) y8 {# K* K$ _: n7 W: R! | [how many Mersenne primes?
. v2 d" s$ N( D' X# Q4 C( ]( c* wEberhart’s conjecture.
4 G' j8 i7 f# u: Wfactors of Mersenne numbers. ) R6 _0 I, b3 q" o5 H
Lucas-Lehmer test for Mersenne primes. / ^) m& T$ F( `& s6 Z8 F1 T
Mertens constant.
5 O# n$ l4 A- {& m% \0 K fMertens theorem. ! }/ F- F+ L1 F3 o( k% |
Mills’ theorem. 9 u5 h( S! ?: l: J; x* x
Wright’s theorem.
; \# J- n8 R7 }$ C& z1 Umixed bag.
0 a* o1 ~) J! L' W, ^multiplication, fast. ; ? o: l4 b4 A q# S) f
Niven numbers.
/ A/ b/ A. p* Iodd numbers as p + 2a2.
, P( g# B. ?, T& S' t: a7 h3 ~, g' _Opperman’s conjecture. 0 \9 X* ]3 M( X% _+ `
palindromic primes.
9 \" w) m( a0 D9 ~. o# Zpandigital primes. . A/ @' @4 }9 g" Y
Pascal’s ** and the binomial coefficients. 7 g; s0 F7 {& o, u+ v4 S8 N, A
Pascal’s ** and Sierpinski’s gasket. 6 W/ ~: G2 _5 N- [0 p* P
Pascal ** curiosities. 0 @$ B3 c2 A) N4 ?0 ]$ Y, |3 l+ v
patents on prime numbers.
6 |) E( {! L* F* D0 p) DPépin’s test for Fermat numbers. 8 k' G- s" D; j6 j0 V7 s
perfect numbers.
; u; u! H' z' X" z4 A+ ?odd perfect numbers. - w* f- l3 g% b* z; l# D! A& a( K
perfect, multiply. / ?+ g% Y, n. b& ~7 H* |$ X
permutable primes. $ ]- a6 H9 l. C6 P4 U
π, primes in the decimal expansion of.
8 j+ ^& Z5 y) u- j* G ]! b9 W' WPocklington’s theorem.
7 o7 m% e3 O1 U3 C1 u" K( ?Polignac’s conjectures. 6 {, A0 D4 A% E" `
Polignac or obstinate numbers. 0 R; M" ?. c3 ]. n1 }5 C$ L
powerful numbers.
4 S6 \, B) O7 k5 \3 w3 m6 y4 y$ Q5 Fprimality testing.
& u1 y' m8 S6 H, R1 a3 {probabilistic methods. # S6 N; x9 l5 D; |: ~" [
prime number graph.
4 _: A1 h9 e' `prime number theorem and the prime counting function. 0 X% G, [8 e3 y ^1 j
history. $ _6 m; o( C0 K; J
elementary proof. + P; w y8 w! E* l% s4 p3 g) y' ^
record calculations.
, M1 b) z5 j$ A2 C0 D) Oestimating p(n). ' @8 w" a( v' }0 k) J, \
calculating p(n).
7 \% G. j, ? D) ]" B5 ra curiosity. " K: F* V6 J* i! G+ [8 w: Q. {
prime pretender. 7 t) D' C$ N+ {9 ]4 g/ g
primitive prime factor.
3 x2 J$ U _+ h! I( u3 h. Xprimitive roots.
9 e8 k3 s) \7 h& t1 ^/ lArtin’s conjecture. ; X$ e$ i+ l0 J
a curiosity.
8 u( i1 V8 m& c% L- aprimordial. 3 a% a ^$ Q4 L; m; @
primorial primes.
0 b: z9 l# a+ _Proth’s theorem. 5 ?* M3 R/ ` C$ c+ o7 z# @
pseudoperfect numbers.
2 Y+ a& i! S" bpseudoprimes.
2 C6 R _" G$ }0 }bases and pseudoprimes. 5 E4 j: V+ x+ s" c2 [( w: f
pseudoprimes, strong.
# K- f$ n( f/ n0 L( s5 _$ S! fpublic key encryption.
. h5 F2 A: k5 C* G3 Q. L, ^3 ypyramid, prime.
" k5 h7 o, M' {! I+ W* N) iPythagorean **s, prime. * D+ Y4 V# _& S E- U3 |7 z$ ]
quadratic residues. 5 c7 R* l8 E. I0 O1 r1 ?6 Q* V+ y3 y
residual curiosities. 5 |' W" r/ r5 X- N J& _
polynomial congruences.
4 O( l1 @7 T9 p9 H9 vquadratic reciprocity, law of. 4 E" p2 Q9 F6 o3 c) ~, k" X+ Q7 k
Euler’s criterion. - d& s1 C' p3 x
Ramanujan, Srinivasa (1887–1920).
4 Q( q! }3 h: V4 C$ j6 a3 ?4 }highly composite numbers. 0 f; Y$ u: ~1 d. i1 M
randomness, of primes. % w+ I1 f/ T+ H/ o
Von Sternach and a prime random walk.
. d% [" p/ t5 y/ p' Grecord primes. 6 \" m$ L2 S+ l* K8 ~# \
some records. . E+ W7 e1 v0 n; S# n7 c" N
repunits, prime. 4 R0 R: x7 ^+ i$ D
Rhonda numbers. 2 {- E! l3 s" ^ X
Riemann hypothesis. [; v2 }( |% \$ G' m6 p
the Farey sequence and the Riemann hypothesis.
& f/ Y) @- I' E: P+ V5 Vthe Riemann hypothesis and σ(n), the sum of divisors function. ; a, t& N6 z' f2 f- V7 @3 `8 U1 {
squarefree and blue and red numbers. 3 M: F3 Q* f& S+ M
the Mertens conjecture.
) \! |( i/ a4 yRiemann hypothesis curiosities.
2 i7 ~ l: v! A' fRiesel number.
# ~9 k/ O* l8 Yright-truncatable prime.
, T# b4 t" U1 o! w: qRSA algorithm. * j& K* ]/ q& ~1 m) ?+ b
Martin Gardner’s challenge.
8 m' r! p" e. |0 [RSA Factoring Challenge, the New. 9 S e- ^6 v# \# p3 |: B$ p& \
Ruth-Aaron numbers. $ a; B: q! ]+ a, V1 L! X) |' g
Scherk’s conjecture.
$ }# I h$ ^8 N1 d tsemi-primes.
' |2 n+ s8 H0 U* p**y primes.
; l# W8 S4 H- W8 cShank’s conjecture.
& c |1 q y7 |3 [, oSiamese primes.
" F8 [# N0 E6 h8 `+ TSierpinski numbers.
7 b* Q3 Z" x# T; Y H" d, g$ {Sierpinski strings.
+ t+ G0 L+ d4 d V; ySierpinski’s quadratic. ' m5 M( v8 e4 J
Sierpinski’s φ(n) conjecture. 0 C- k0 E! n! u9 c8 z9 N
Sloane’s On-Line Encyclopedia of Integer Sequences. + Y4 a3 B( g* ]) M: J( F/ S
Smith numbers. 7 d& P" q ]. }
Smith brothers. " M) \/ O) h9 L7 e2 K0 O
smooth numbers.
' F* _- u0 R9 `9 r! x: R* ASophie Germain primes. ' o0 n0 } w t' N$ C
safe primes.
# E! C* t3 g# }squarefree numbers.
; H: I3 ]2 f V* pStern prime. / \$ ?1 A1 a2 u0 H+ b0 b
strong law of small numbers. ; W6 o7 K- s0 x# o
triangular numbers.
7 a6 h0 ]0 [2 Q6 Z$ V( I4 ptrivia.
/ m1 ?5 r- z- i/ \4 `5 G8 q) Btwin primes.
9 x1 _5 F) a0 x2 |# {twin curiosities.
 d _) n" m/ B1 ]Ulam spiral.
: L+ Z: H p1 @+ h( Eunitary divisors. ) a1 @' ^2 }0 I, R Y) E0 }
unitary perfect.
/ z5 {! F- `7 M! `' Funtouchable numbers.
 R+ T2 k% Q0 ^weird numbers. 1 G7 R% l- j" J; x5 L
Wieferich primes. 3 z9 [; ~. c( t+ F3 ~# @
Wilson’s theorem. ) o/ p, M/ m$ g
twin primes.
0 H$ I) F; S" \" l' ?Wilson primes. % P7 x% H4 q! n9 v
Wolstenholme’s numbers, and theorems. : G! l' U, ^, Z- t& v/ Z; O/ z @
more factors of Wolstenholme numbers.
, r) @' ^4 X2 j" ]5 v: cWoodall primes.
, a( }9 ~! d( Y# W- T2 y; hzeta mysteries: the quantum connection.