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数字的奇妙：素数

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Entries A to Z.
: c* |3 N5 I- dabc conjecture.
1 M$ M: A* J4 Habundant number. ; ~. A4 s# K& `/ k" |4 v& B
AKS algorithm for primality testing.
& z c& @8 z f! Kaliquot sequences (sociable chains).
; x B- `( W. O r: _# i! T, Falmost-primes. % N9 Z2 C8 ]: V) Y, q' N
amicable numbers. 3 Y: W/ k% r7 E9 s H
amicable curiosities.
$ D+ z+ U' s# @1 a! r V: _/ F0 O# EAndrica’s conjecture. ; O3 {9 J7 R" @! D
arithmetic progressions, of primes.
9 L" ]% `" p9 n( B7 q' M, eAurifeuillian factorization. ! \& A ?0 ^( _$ ? A1 F- E) Y6 p
average prime. + c# _$ a( ]& h2 X! ^
Bang’s theorem.
. l) v! {& }& y6 F& eBateman’s conjecture.
5 I- M9 Z8 P7 q7 @7 ZBeal’s conjecture, and prize.
+ A2 C! H) T8 j [, _) l1 ~/ v" J! XBenford’s law. 2 r. e1 P2 T* l" e2 r" B. q
Bernoulli numbers. 3 H- o7 Y2 z. y# S S. u. y: e
Bernoulli number curiosities.
, [/ o( _/ L# w4 Q. }/ {Bertrand’s postulate. ) G+ o, B) } ^' T6 l5 i
Bonse’s inequality. 9 X$ a/ s/ C# K4 z. L, E; B9 | V
Brier numbers.
7 H3 | |* J) w, }$ sBrocard’s conjecture.
 n* V) P9 {! x, V2 i" f/ MBrun’s constant.
+ q9 A& B# N$ qBuss’s function.
( Q, W7 O5 h4 q- t# s% r1 pCarmichael numbers. 0 A3 S9 y- N+ e/ \
Catalan’s conjecture. % D. g" S4 E7 E; h* l$ i
Catalan’s Mersenne conjecture. - H) o& w2 q3 I; l0 x
Champernowne’s constant. 8 [0 A5 e* M0 |- H5 q2 o
champion numbers. % Z1 O8 Y/ S+ P
Chinese remainder theorem. % l. f0 h# J+ l$ U& l. j8 Z
cicadas and prime periods.
1 W0 G( H! f8 b! K( rcircle, prime.
. M. u+ m+ p1 }0 S4 G" }circular prime. n" n1 O& e. b+ A! x4 Z
Clay prizes, the.
, n1 C5 K$ B0 ?& Ucompositorial. . u! w: Z7 P6 R3 P
concatenation of primes. / L* w8 J) L, V# u! j
conjectures.
' F B1 @8 p# Xconsecutive integer sequence. * z3 |: V( R9 g. e
consecutive numbers.
4 X: ^. Z9 g1 R7 v7 ?+ t- Zconsecutive primes, sums of.
 o' F+ }; ?: J& P0 p( AConway’s prime-producing machine.
' d! B" R( s% B! Gcousin primes. " D4 o4 l# u4 i
Cullen primes. - o9 S; T# q/ [9 K4 J# a; l
Cunningham project.
3 W, |4 b! |% v3 \1 V, vCunningham chains.
7 ^. J5 b7 V! y8 @* zdecimals, recurring (periodic).
+ j* H# A y* t) [" _# e6 Z7 |0 Sthe period of 1/13. ; e( }- q/ C# k- y6 Y, Q9 ^
cyclic numbers.
7 T t- d% v0 t# F( UArtin’s conjecture.
# S' L! c3 B% _% a2 p$ U6 {the repunit connection.
9 W+ Q- g( E( R/ q$ O% d: Q$ `magic squares. 3 K9 Q4 ]5 c/ o9 F
deficient number.
% F+ n! h% M' ndeletable and truncatable primes.
3 t% M8 |' ]" mDemlo numbers. ( C1 I& Q, g9 j- g/ G2 K4 T
descriptive primes. ; [- q! j; M2 G6 T2 h
Dickson’s conjecture. - i9 N, H9 t! v" j3 @. j
digit properties.
3 M: `, n* d0 J$ a& u& aDiophantus (c. AD 200; d. 284).
* E! M& {* t- x' {+ X9 ` h: ?6 _( CDirichlet’s theorem and primes in arithmetic series. : J* j3 m7 |7 X8 E* r
primes in polynomials.
, a% v6 E$ s# _! O0 q+ m& Udistributed computing.
6 d5 _& Z7 R3 \2 t: K! ?, y9 Gdivisibility tests. ; Q6 s; W; k, I7 X3 I" f- Q$ i
divisors (factors). . ~" F$ m- Q5 \/ R& B# m$ e0 k5 i+ `
how many divisors? how big is d(n)? 2 U/ Z3 g$ e/ m( f
record number of divisors. % }: Q V( E' M6 F V$ \% w# Y
curiosities of d(n).
4 j! @- u* {& |, `5 E' Hdivisors and congruences.
8 ~9 R3 c+ a+ c" B( a+ A4 }8 z( a1 @the sum of divisors function.
% q& \' I! D# P- |! R. y `the size of σ(n). 3 e9 j* N# n2 l: B* W+ q' [# K
a recursive formula.
) G% _8 o: ]& bdivisors and partitions.
8 t6 d4 A6 _: G# dcuriosities of σ(n).
2 J+ N1 g* L+ U# Pprime factors.
" F( u( d, c' K) D8 F+ X6 R7 fdivisor curiosities. ( I3 N$ H3 M4 E* O+ X- k
economical numbers.
 R4 L4 `0 g% k0 \Electronic Frontier Foundation.
! M* Y3 z! U N) lelliptic curve primality proving.
- ~! q: c: y- xemirp.
, A2 l9 F' @% G5 N0 ?& ]Eratosthenes of Cyrene, the sieve of. S* a$ [2 D' C) S
Erd?s, Paul (1913–1996). ) P/ D$ u2 f7 W7 `, |
his collaborators and Erd?s numbers.
1 x/ [6 L4 o2 D( d9 ^errors. 7 X& v2 l5 K% w5 y: Z
Euclid (c. 330–270 BC). 8 z% b( M. V* M% } l2 W
unique factorization. 6 j s- p# r1 | H+ {! b' {
&Radic;2 is irrational. 5 W, A5 I' i7 W
Euclid and the infinity of primes. . ^1 @, h+ J& s, B
consecutive composite numbers. - S7 j( w, s6 T: b: p( F
primes of the form 4n +3. ( n9 B1 L, @& m7 {, K5 |; t8 e
a recursive sequence.
# Z8 B/ ]9 k% `) t& y4 PEuclid and the first perfect number.
( ~ ?# L; {- e3 iEuclidean algorithm. / }% i% t; J" I. J! G
Euler, Leonhard (1707–1783). * |! \# S9 N" T" |5 B# K
Euler’s convenient numbers. # z# b* ^ W% c' H; v
the Basel problem. l) F _5 j" b4 r9 `0 ~9 C
Euler’s constant.
- Y' ~. C. m4 a. X$ H. Y1 }0 tEuler and the reciprocals of the primes. 9 ?" K) E+ n- o0 i. l( H
Euler’s totient (phi) function. ( r4 X" {8 b- Z2 Z' o0 M
Carmichael’s totient function conjecture.
" m( ?6 X) i7 D% u" e) N4 o7 ycuriosities of φ(n). 3 W# E+ L. l0 T: X
Euler’s quadratic. & r* j/ ]& C6 U0 l [* g
the Lucky Numbers of Euler. , A$ q3 K) O; s9 P. E6 T7 E( D
factorial. : X: C3 ~# m! X7 a4 v$ B3 M! c0 ^
factors of factorials.
/ K- J: q3 o9 U# T/ Ifactorial primes. # J M/ V6 k" x/ A3 H$ P
factorial sums.
; e$ t& a: |3 pfactorials, double, triple . . . . * s" y. @" k0 J4 x+ ~
factorization, methods of.
* H$ W# a% S, K* \9 r' v5 kfactors of particular forms.
' o$ l3 f J; v, J+ JFermat’s algorithm.
8 r3 C: n! @ K; h% \4 W* FLegendre’s method. & m4 F- w! b4 P. u& M
congruences and factorization.
" U8 H( w! `; \$ r4 P3 r5 Ghow difficult is it to factor large numbers?
3 _# j+ {7 q) ?* i! Kquantum computation.
) ?1 a/ \3 W+ T+ zFeit-Thompson conjecture. % I. H) l7 ]& O- T
Fermat, Pierre de (1607–1665).
' |7 E; q" Q: t O. [! R, j jFermat’s Little Theorem.
) p7 |! H) r4 q' hFermat quotient. 2 q3 T6 C6 t! o' N
Fermat and primes of the form x2 + y2. 6 d/ p8 j1 _# A, T
Fermat’s conjecture, Fermat numbers, and Fermat primes. ) ? ~8 s7 Y; x7 `' F
Fermat factorization, from F5 to F30. ) t/ I3 v, |% h# ~ x
Generalized Fermat numbers.
7 M( M+ w" t- r& p2 }Fermat’s Last Theorem. 3 U6 a* y$ m7 |2 Y. @
the first case of Fermat’s Last Theorem. " }. W9 H: m$ {# Y
Wall-Sun-Sun primes. 2 A, p! [( R0 Z
Fermat-Catalan equation and conjecture. & ~) r; G$ ?. V) G; u: |9 k. J$ I
Fibonacci numbers. - t0 n; G5 L% f1 z7 _9 x3 Q: a" O' P
divisibility properties. 2 m' K6 i7 |4 z; q
Fibonacci curiosities.
, N+ B/ z( P `édouard Lucas and the Fibonacci numbers. / K: l9 J. b# h' p- U6 @
Fibonacci composite sequences.
( Q! J) L T8 b- e! I% kformulae for primes.
8 \9 S, N$ m2 D6 } _' M' fFortunate numbers and Fortune’s conjecture.
6 O" z5 S @. Y. vgaps between primes and composite runs. ; T# X& C; X0 f* X; S& a* c1 M
Gauss, Johann Carl Friedrich (1777–1855).
6 n0 `+ L" R: @# S2 y6 CGauss and the distribution of primes. 2 B0 l% [3 S1 |) q3 O, D
Gaussian primes. : |& Q2 s* h: Y7 s) W. `: c
Gauss’s circle problem. 9 m! a; T; u: J$ c
Gilbreath’s conjecture. ' c2 ?# U& r: g3 {- R
GIMPS—Great Internet Mersenne Prime Search. 4 p& t3 l! w2 r! c; h E7 x' m
Giuga’s conjecture.
1 d1 _3 H7 E: I# F$ F" u+ YGiuga numbers. / ~8 D# H1 z: B2 |
Goldbach’s conjecture.
* L* e$ N/ @& a4 V. l. b7 ^. ?good primes.
5 \; R) H+ t+ q0 Q% |Grimm’s problem.
! `2 }/ ~9 o5 G \: RHardy, G. H. (1877–1947). 6 t! w4 d4 ^5 ?2 K; E) `1 U: f/ j; C
Hardy-Littlewood conjectures.
8 r" O; l" r4 c; ~/ Zheuristic reasoning.
+ ^' C: g/ N( d2 ba heuristic argument by George Pólya.
5 ^; ?; F2 q5 k; gHilbert’s 23 problems. 7 y9 L1 a: Z6 e7 o
home prime. " j* z& |4 m# b
hypothesis H. 8 w/ N: Y3 a. E
illegal prime.
# V' |0 M+ R, `! u5 [inconsummate number. 0 V( \8 ?' R0 o
induction.
2 X$ x( \" N8 \, K* _jumping champion.
# i8 c3 ]: F. m! w0 Z& d5 }5 `k-tuples conjecture, prime.
. M) {% T' h2 u6 S& d- B( [. |* t8 c. Wknots, prime and composite. 0 O5 h D( Z1 |8 |, _% B
Landau, Edmund (1877–1938).
; {# \+ K! R9 V; ]/ o/ I2 aleft-truncatable prime.
; _3 P+ ^: [( V5 RLegendre, A. M. (1752–1833). 7 Z4 z( G: a: t% ^; d0 |+ A+ v3 K
Lehmer, Derrick Norman (1867–1938).
% R' n5 ~/ V/ U7 o: O% r \Lehmer, Derrick Henry (1905–1991).
/ Z: G. K, C% @2 k+ c+ S" tLinnik’s constant. 1 @3 m( \" V, u Z! h
Liouville, Joseph (1809–1882).
: ~; }$ x# A! e* A, LLittlewood’s theorem.
/ R9 Q5 V: }, P' q% Q% mthe prime numbers race.
6 I0 _& d- h* S5 lLucas, édouard (1842–1891).
4 ?" n# P" D- D2 }7 [$ D8 ethe Lucas sequence.
; n, ~ ], O/ Y( `primality testing.
# W! R! |' D* b& H j, lLucas’s game of calculation. # X8 M2 X) r1 I: c. p& n* ^" ?+ h# Z1 }
the Lucas-Lehmer test. ) _% `, P# n* s
lucky numbers. 9 B4 g# r0 x, g; T" f
the number of lucky numbers and primes.
6 R+ S: H8 A- G3 I* v4 O“random” primes.
1 t+ W2 s7 d4 Y0 q% m% R1 q+ |magic squares. 6 M5 ]$ J' t! P# w. T2 `" I
Matijasevic and Hilbert’s 10th problem. 7 R# Q4 _0 O# ?9 O8 v& W, C
Mersenne numbers and Mersenne primes.
2 I2 I! j# d: \8 A# @ K2 ?Mersenne numbers.
" I! h7 }/ [/ k% U! M. @6 J& N- Phunting for Mersenne primes.
5 D- t8 R5 W' pthe coming of electronic computers.
0 N5 S) E* h5 z( u; W4 HMersenne prime conjectures.
2 N; l9 T) _, L) W% dthe New Mersenne conjecture. ; _) J! P {; T) x) q7 r
how many Mersenne primes? " p d4 N6 r2 w
Eberhart’s conjecture. 2 s% q- ]$ N0 @( e
factors of Mersenne numbers.
* |/ ]: ^+ N. V: _) c2 mLucas-Lehmer test for Mersenne primes.
" P; l, S/ l# LMertens constant. * n6 `+ a( }2 V7 n6 u. D0 l! v
Mertens theorem.
2 R+ e! O R9 V0 o6 VMills’ theorem. 2 l1 q) C# ^7 M1 }5 U2 N2 q* p
Wright’s theorem.
4 G7 B3 f$ o1 c; t! O% B) Y- [; [mixed bag.
; d4 y; A* k4 E+ {- N0 x9 u6 Amultiplication, fast.
/ s$ v2 R0 q+ Q# gNiven numbers.
' }" j: L0 \) z' G7 } Wodd numbers as p + 2a2. - i. U6 t. V: w+ q/ }& J2 i
Opperman’s conjecture.
9 b% Z# i8 H% s* G" D8 vpalindromic primes. : O1 D3 Q* g8 X! i4 X
pandigital primes. + U8 L$ m, p3 e
Pascal’s ** and the binomial coefficients.
5 y; l: ?* g; E5 W" w' z; ?- ePascal’s ** and Sierpinski’s gasket.
! x3 ?" L- _, \Pascal ** curiosities.
* L* Z: ]; M& _+ D0 | U( Cpatents on prime numbers. ]. f1 {. Z% L4 n; B) l
Pépin’s test for Fermat numbers. ; R) ~. R+ P/ G3 m
perfect numbers.
1 P6 `9 K+ J# e& S( P) Eodd perfect numbers.
1 A3 n! \& r# T- X+ g! {3 Dperfect, multiply. 3 F4 B7 M/ o& L: J: K3 a" W
permutable primes.
( B2 ?* }5 S& |+ I2 n; fπ, primes in the decimal expansion of. 3 r* N& u8 ?) Q
Pocklington’s theorem. 2 z7 O7 o) h1 }
Polignac’s conjectures.
( M2 ?3 F7 M$ h+ a v8 qPolignac or obstinate numbers. 9 T- S7 ^& k. g1 ?+ _1 D2 z
powerful numbers.
9 U s! H9 k8 @6 K' Kprimality testing.
/ N# g7 W3 L' O3 x9 b* j& V7 nprobabilistic methods. + y: |( I- L4 h$ W5 r p
prime number graph.
8 T$ ]+ R- b/ B4 T# x+ k' d8 g4 Uprime number theorem and the prime counting function.
7 M! ~! f' }& [history. # E. ?8 z* L+ \0 l+ @. h
elementary proof. " j9 Z) O6 M: Y# R, z
record calculations. 2 g. d# B1 J2 \" O" P8 b- A5 R# D. L
estimating p(n).
3 h, P2 v0 w5 W. U7 }calculating p(n).
- ~% _/ K9 `8 n- ba curiosity. % h; c. R& o- ^8 z, p7 S. l4 D
prime pretender.
! c9 v3 N' {1 s1 i, h/ e J2 ~primitive prime factor. 5 X/ Q2 `, k, h5 W
primitive roots.
7 I6 Q" j' T9 P0 XArtin’s conjecture. * A7 x4 ]8 e7 L1 C2 n A
a curiosity. 4 b/ [* ?1 G* w( |7 e
primordial. 2 W# F2 e6 {8 m6 C& A7 j
primorial primes.
- j. B6 I: V% w# N& rProth’s theorem. 2 f0 R9 h2 Z0 u% E" K4 ]4 K2 G
pseudoperfect numbers.
% G8 I* D; c! Ppseudoprimes.
5 I! b; W' E6 P# T) ~# hbases and pseudoprimes. & B9 `! H' r+ ?1 i0 p/ ?
pseudoprimes, strong.
% }& ?: V. ^- C; Y9 l. M0 Opublic key encryption. $ T' h; W+ E' ^0 i( W# e
pyramid, prime. 4 s: c x( K0 w/ H
Pythagorean **s, prime.
 |) v" A+ D7 t7 c2 Cquadratic residues. % {7 O# \8 P }4 ]* R
residual curiosities.
) ~9 H+ J; O; w# Z9 r, H, [$ t& Cpolynomial congruences.
1 k& U, h# ?+ S1 {- P. y$ Kquadratic reciprocity, law of.
, F% g, j! i& {; f, c& a- w% }Euler’s criterion.
* m* {2 l, j* }9 U* J `Ramanujan, Srinivasa (1887–1920). 6 t" S* c9 S1 i% Z6 b
highly composite numbers. . F" d, C( _/ F8 [; t: G4 M( f
randomness, of primes. 6 I9 R1 |4 X8 f' H# f: `" r- f
Von Sternach and a prime random walk. " j1 P1 H' I x& G. ]( n
record primes. . @6 L" x, l3 O4 ]0 K. I" Z
some records. ' |- o" s( H& L9 l3 N% ?
repunits, prime. 6 J1 E" J- B7 b. {& A
Rhonda numbers.
& N9 y( o4 F# N: U0 ^& rRiemann hypothesis.
, A' y# K# U+ p' c, K. G2 f9 Kthe Farey sequence and the Riemann hypothesis.
- Y4 Q) `( \" ?( mthe Riemann hypothesis and σ(n), the sum of divisors function.
# O" K/ Z4 j8 F! T$ Bsquarefree and blue and red numbers. + ?% B+ W: X3 D \
the Mertens conjecture.
) W3 @8 W5 k3 |3 m& u" cRiemann hypothesis curiosities.
" X+ \9 ^8 [$ P: y- w* kRiesel number. 0 d y6 U! ~* k
right-truncatable prime.
* @3 y. X) I7 |' C; E7 i" vRSA algorithm.
" f1 @" P& U4 c h# i% nMartin Gardner’s challenge.
, n/ A$ a8 ]* @- p6 N5 k! o# ?RSA Factoring Challenge, the New. 5 F% v) f3 o( r3 H: K' _
Ruth-Aaron numbers.
& c: J& H: M. e+ x) i! JScherk’s conjecture.
0 A$ Q+ W3 z# S& esemi-primes.
8 n" U: T4 {5 P1 g**y primes. 0 U3 T& ?4 P9 _5 Q
Shank’s conjecture.
: s0 [6 D- w8 b" ~9 Z2 Z- LSiamese primes.
3 _7 R" @; x. V/ L- hSierpinski numbers. ) c0 ]! V& e3 t6 m' w
Sierpinski strings.
# x J+ p7 D* CSierpinski’s quadratic.
# A6 m5 X8 X/ J/ y5 MSierpinski’s φ(n) conjecture.
, ]0 m: A. H. g$ ]4 uSloane’s On-Line Encyclopedia of Integer Sequences. " [; U: i7 Q6 l- F2 V2 W
Smith numbers.
 K0 u# w. F i) Z7 ]Smith brothers.
+ O/ R! B' e# y2 ^/ I( psmooth numbers.
. ~9 _. U( K: d) G" S+ fSophie Germain primes.
1 k# d% z5 L" c, T7 rsafe primes.
( p" Z/ B8 Q& Y, m) R; x* l0 |3 n7 Osquarefree numbers. & [# h2 |- d+ W8 i5 B3 W
Stern prime. 3 S. B6 E" b, y8 Z* A- q+ B
strong law of small numbers. ! }0 ]0 K5 d) f1 R' Y5 M' s% F
triangular numbers. : x- I% O6 Y) c( w3 l/ G& o% x
trivia.
: W0 W: B, u$ T, htwin primes. 1 V' i* f( p7 \; }4 s
twin curiosities. 4 M% ]9 S% N- i3 F, i
Ulam spiral.
- G$ R+ u2 o; Wunitary divisors.
7 i4 v$ i b; w! p2 ?* `; D$ X. l: Qunitary perfect.
2 r. X3 R* A0 h: W9 a% F9 U. K# ?untouchable numbers. : g" x+ H: s9 A' c7 S
weird numbers. 2 S. T. g% l/ x. g6 d; d
Wieferich primes.
" l) K* i# S/ \6 vWilson’s theorem.
6 o. q4 d* H1 w9 P% ?! Ptwin primes. * x l: I x: M! x/ r) Q* ?2 n/ I
Wilson primes. ) [0 ^. q, j" W" k6 S
Wolstenholme’s numbers, and theorems. & \! M) A5 ^6 Z+ O
more factors of Wolstenholme numbers. 2 @2 Y" T, ^8 i+ P3 }4 P: A
Woodall primes.
9 z- Z6 p" F3 f( Z; W! Xzeta mysteries: the quantum connection.