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数字的奇妙：素数

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Entries A to Z.
- L( [. N" V" E2 Oabc conjecture.
: [4 H1 y0 S5 A9 D1 aabundant number.
AKS algorithm for primality testing. / w! Z2 H1 B- d9 T6 ]4 Y+ {% T" ^
aliquot sequences (sociable chains). ' o, s5 y0 z" F" t/ O. Q
almost-primes. & k" o7 d) J: @) t- H0 w
amicable numbers. 7 l2 ]/ Q) x3 i$ e
amicable curiosities.
; x- y; V# `8 G- m R! B5 Y$ sAndrica’s conjecture.
- I3 L W- r* j* @! y! g5 Rarithmetic progressions, of primes. ; Y% q! p/ H' R" H. Q X
Aurifeuillian factorization. 2 l9 b# P! o* A4 D X
average prime.
* \5 J- y4 s! h. ^; RBang’s theorem. # P( C5 n+ {. u5 C
Bateman’s conjecture.
6 E+ u9 [. V- M! O sBeal’s conjecture, and prize.
' g1 d1 ]4 j. j% E7 LBenford’s law.
# a+ m4 w) G" |" y7 _Bernoulli numbers.
) r; I0 h8 A( `. o9 p7 h: q( c) GBernoulli number curiosities. : ~4 n9 D6 [4 |5 B9 d& M* r/ f
Bertrand’s postulate.
9 l& M- i* X/ V4 yBonse’s inequality. " h) k# L. h3 m- x- v" M7 F0 u
Brier numbers. * A+ k4 r$ X9 H* S
Brocard’s conjecture. 5 l" P B4 @: Q
Brun’s constant. # r' S. ~% L. O3 P
Buss’s function. : e/ K( U* F2 \# s
Carmichael numbers.
: u' p8 d6 F" `) B# PCatalan’s conjecture.
" ^( F9 i! W# T& L" D1 U0 HCatalan’s Mersenne conjecture. F2 D( x! E- _4 o5 X y) N
Champernowne’s constant. $ g7 N2 {) L4 H$ ]
champion numbers.
; [0 G- Z+ \$ R6 r/ w- TChinese remainder theorem. # A7 @$ N7 V7 X' p; U
cicadas and prime periods. ( o3 G- Z" v( [
circle, prime. 7 ^( p3 a: G3 L+ A
circular prime.
( r+ x7 ]& e1 z4 g" U! ~Clay prizes, the.
" d$ v. D8 Y, ]6 J' i7 i0 s' ?+ Bcompositorial.
9 H/ @$ j* r9 f# W$ @2 nconcatenation of primes.
& ?0 V- N% W. a( x7 @conjectures. ) Y2 [4 y W3 A/ q/ I. g7 [
consecutive integer sequence.
4 B) u5 U" v9 _+ x3 v- econsecutive numbers.
 b0 e5 o/ N- }* M( w/ j, n6 fconsecutive primes, sums of. ) P4 G% J6 X% Q0 r+ x
Conway’s prime-producing machine.
2 R; J' E; [$ }cousin primes.
 K0 O G. Z- k! ?- s1 q" ^' WCullen primes.
 a. z# ]7 g. r) g. V2 v8 C" CCunningham project.
2 c z7 a- [: a( T9 F( mCunningham chains. / \5 z3 V) L7 i/ Z- T7 J% R
decimals, recurring (periodic).
6 {& B% _/ m: }- }8 G' s2 d4 ]5 ]: `the period of 1/13.
cyclic numbers.
3 q K& c8 O! v% `9 j1 SArtin’s conjecture. 4 P- E4 N: O7 h" x, x5 P4 a# m
the repunit connection.
. j1 r1 a8 u( ?magic squares. 5 F+ Q- B8 |& ~% F1 U/ Z
deficient number.
; R- @ L# O( F5 k1 K! X; Kdeletable and truncatable primes.
; {' v! N5 l6 ?- Y3 ^7 ADemlo numbers. 8 U) p4 q( H) ?# |
descriptive primes. ; c4 K4 n/ b9 G# y V9 j* d
Dickson’s conjecture. 8 V) f& { t2 w! W2 @- {
digit properties.
5 V' d8 R* n' O, n, {Diophantus (c. AD 200; d. 284).
- }' V* h3 p0 a. `" d/ O }Dirichlet’s theorem and primes in arithmetic series.
: e" ^" S; `& N c9 {4 cprimes in polynomials.
3 C" ~) w/ o. @' b" odistributed computing.
1 k7 C2 u; e8 K5 V$ f4 R* X% Qdivisibility tests. f) a; i! t) k+ @4 I
divisors (factors).
2 Q+ _, y+ r: W/ B6 Ohow many divisors? how big is d(n)? 0 X% w3 L9 j, C0 M
record number of divisors. $ Q8 g* f! y$ r t: |
curiosities of d(n).
' c8 C/ t; P2 U7 I `: `divisors and congruences. U) U- u/ k0 f* [8 A
the sum of divisors function. , f; N: o6 i$ z& ]/ W9 |
the size of σ(n). 7 N' q0 x& P* _. h
a recursive formula. 0 o" X3 o: }+ n G1 d$ y/ r
divisors and partitions. : \: }9 l3 x D1 y% ~
curiosities of σ(n).
! V' @; c; p4 j' h8 J: V: Qprime factors. 5 f9 n5 r& j. S/ v) [4 r3 S
divisor curiosities.
0 h5 g) B Q/ ieconomical numbers.
& O# E: z4 \5 Y' q$ f0 wElectronic Frontier Foundation. : F( C1 f* Z; [6 q$ v P: Z- }8 T
elliptic curve primality proving. . P4 Y+ t* q3 n8 {
emirp. 1 D2 s, J8 a( V+ g7 q
Eratosthenes of Cyrene, the sieve of.
" s" u+ I2 L1 l- b/ zErd?s, Paul (1913–1996). 2 c0 f) j1 _0 i* S5 F+ e
his collaborators and Erd?s numbers. j, Y2 g# x$ V0 K9 y6 L1 z c; I& R& J
errors. 6 y; Z, v& l% p0 ]" p, ?- \
Euclid (c. 330–270 BC). 4 N m3 z/ [: E8 s# j
unique factorization. + S6 ~; E: ~5 j( |3 R8 V2 b" `5 p
&Radic;2 is irrational. & T# f! Q. R7 k5 C- f
Euclid and the infinity of primes. - [1 W* m' M$ g4 `1 M
consecutive composite numbers. 1 i1 D6 F* o+ K- d( J
primes of the form 4n +3. 4 G; Q5 p: L D( Z8 ]- g! Y$ e
a recursive sequence. + S( b) {( ] P' t) \
Euclid and the first perfect number.
6 |. {( M9 h7 g. [( ]! YEuclidean algorithm. - p) z8 w, T2 T @$ o9 Q
Euler, Leonhard (1707–1783).
 }& A5 M5 e# T- j9 NEuler’s convenient numbers. ! k6 W4 t- T% K' r% w
the Basel problem. $ \6 A: k% C7 a' A2 F- v' d
Euler’s constant.
) p3 e6 _: F, ^: E$ l, X1 BEuler and the reciprocals of the primes. 7 ^2 Y; U0 m; J0 Z# M0 {; z+ z/ D. }
Euler’s totient (phi) function.
- @ |! C3 _" n% I8 X. FCarmichael’s totient function conjecture. " H- c( p: R+ M9 p, h* W1 G
curiosities of φ(n). 4 |1 l1 |0 z4 B3 J7 R4 h1 E
Euler’s quadratic.
8 M3 w2 N2 N! P0 G7 u& ythe Lucky Numbers of Euler.
' ^$ ?; @ s% c9 A9 { V2 Ufactorial.
$ S; |0 K, K3 O$ l* vfactors of factorials.
0 u0 b5 `. f& Q/ Y- E) h, `factorial primes. ' y0 K2 s: G C4 w
factorial sums. % D: b+ \" g" z' g0 ?6 l
factorials, double, triple . . . .
0 B1 y: ]7 t+ gfactorization, methods of. 5 C5 C+ H; u4 J- \) ?
factors of particular forms. $ }1 n5 p0 y J( E$ c: A8 G1 R
Fermat’s algorithm. ) T9 c! h9 v) Q4 g# B# m' _
Legendre’s method. t* }6 z( y0 B# m% [: m \2 z
congruences and factorization.
$ |) u$ @# ?5 Z+ I# Nhow difficult is it to factor large numbers?
* a# w B0 ^5 x6 Y9 r* Cquantum computation. 4 q& S" ~* _% }% {, g
Feit-Thompson conjecture.
( X% J1 y7 _+ k C9 jFermat, Pierre de (1607–1665). * p" y" |" i8 c, u0 B8 r1 u
Fermat’s Little Theorem. - l+ q7 H! X4 V. v$ A( g
Fermat quotient. $ }& U9 e. w0 V1 Y
Fermat and primes of the form x2 + y2. ; i- f% ?( k6 ^
Fermat’s conjecture, Fermat numbers, and Fermat primes. # @. G0 k* t# G7 w3 |; @
Fermat factorization, from F5 to F30.
# i7 w2 u3 U9 K- A2 y& c& `Generalized Fermat numbers. ! |3 x9 ]/ L4 G3 k) O% Y8 q! {8 t
Fermat’s Last Theorem.
6 o6 t* _( A, G; y' v7 _& Ithe first case of Fermat’s Last Theorem. * z! a9 D6 c2 d7 x' k8 i5 j4 b5 |
Wall-Sun-Sun primes.
% L' i b) B X3 RFermat-Catalan equation and conjecture.
9 ~$ M1 @$ Q' L4 H; cFibonacci numbers.
' A3 d4 p; O9 p, Odivisibility properties. 9 x3 ~" ^0 H4 i, q' M0 Z: a. X
Fibonacci curiosities.
9 S5 D: {9 S" Tédouard Lucas and the Fibonacci numbers.
" P" l2 _3 \8 dFibonacci composite sequences.
9 u3 _$ g9 y8 \# b" Rformulae for primes. 1 N: I* a6 @; u2 f4 R2 ?
Fortunate numbers and Fortune’s conjecture. 6 j5 U* F0 v( N( Q+ t$ ~ ]1 ?
gaps between primes and composite runs.
4 L; N+ d9 t9 T. ~9 G2 m S8 ?( `Gauss, Johann Carl Friedrich (1777–1855). # n. e o% K: q3 M( i+ y
Gauss and the distribution of primes.
; D/ E. m0 $ ~. i* nGaussian primes. 1 V1 I/ n5 R, R$ h, |# h. Z
Gauss’s circle problem.
 J" k% w* q3 k( o0 X2 u3 F$ iGilbreath’s conjecture. + a! v r! o1 ]7 w" `' I
GIMPS—Great Internet Mersenne Prime Search. 7 @! I6 I; w) P- ?8 w+ P. c
Giuga’s conjecture. & \. ?8 `$ u3 B
Giuga numbers. $ \* t+ }- e) a
Goldbach’s conjecture.
' I* r. W' r8 c, Zgood primes.
- V- C) i, k* W, \9 q9 lGrimm’s problem.
/ F' @( w( d: [ DHardy, G. H. (1877–1947).
4 G N) E) }7 G( THardy-Littlewood conjectures.
! O) f7 I6 g, d- `1 y& Eheuristic reasoning.
+ F( F8 W' q' _1 G* va heuristic argument by George Pólya. ' B' q7 ]" ?! ]6 q7 B. O( ?- }) J( z2 j$ F) T
Hilbert’s 23 problems.
home prime. / Y6 d3 f& N, j Z: a2 K
hypothesis H. ) C m1 W) ^0 c0 D( ? Y0 P
illegal prime.
 c% g* r3 Q+ s. b* hinconsummate number.
! J% H3 b. T2 z( o' dinduction. # f% l% D: y* D. }" H# b
jumping champion.
 }; t2 P* p3 lk-tuples conjecture, prime.
) q) _7 B: \) x3 Nknots, prime and composite.
5 d1 x1 }2 P( {: wLandau, Edmund (1877–1938).
3 q5 M# A& ]5 Rleft-truncatable prime.
! g! c$ D3 E) H) U+ TLegendre, A. M. (1752–1833).
8 A7 X6 w$ |1 U" s. q7 mLehmer, Derrick Norman (1867–1938). " S1 y/ K8 _. \" o" V$ L
Lehmer, Derrick Henry (1905–1991).
, h% t R# T/ {) N& a' zLinnik’s constant. - S4 ]" Y" H( B( v0 D& K5 J: A
Liouville, Joseph (1809–1882). 3 i l" e! h" N+ ?/ Z
Littlewood’s theorem.
# `3 W& D1 }: F, Dthe prime numbers race. " n8 @* K2 P% y+ i2 d
Lucas, édouard (1842–1891).
5 _; L. `3 S% Y, l+ [2 V5 L% [the Lucas sequence.
) T+ v4 ?6 c+ {" z) qprimality testing. 5 M* ]% |2 l, y3 l H! |0 {
Lucas’s game of calculation.
6 k R- D0 `* E3 j9 F9 Kthe Lucas-Lehmer test.
4 a7 p4 \5 @8 O% ~' }, flucky numbers. ( h$ P) r1 ?" ]- o
the number of lucky numbers and primes.
 L& r+ ^# G- k' G5 t; b“random” primes. $ T$ L% u1 x- t! u- g# \
magic squares. 0 W4 U2 x) o" R* U5 }2 |, M
Matijasevic and Hilbert’s 10th problem. 1 a- y" m3 N, P9 j! ]+ R
Mersenne numbers and Mersenne primes. % V# k0 k8 x+ _; n# r& P0 ]
Mersenne numbers. . a9 V, }6 [6 k: R
hunting for Mersenne primes. 6 r! i+ r% F# P3 t
the coming of electronic computers.
, h) \; H B, h5 V9 K9 x3 hMersenne prime conjectures.
 v- }1 O0 W3 k9 M2 M7 h. Dthe New Mersenne conjecture. : ?, \8 r8 A( R4 ^2 t
how many Mersenne primes? , S, y& p$ F9 B6 G2 d
Eberhart’s conjecture. . L8 H# T- o8 k$ A
factors of Mersenne numbers.
7 @, @0 @9 v8 J; |. ELucas-Lehmer test for Mersenne primes.
5 w1 m% a8 ]) s" O: @6 x, ^Mertens constant. # P4 ]1 E& w7 {6 a
Mertens theorem. * E: o* W) \; X8 [
Mills’ theorem.
7 c1 g; s2 G" Q6 r/ e( _, bWright’s theorem. 8 @3 }% P4 z- B q, h. e
mixed bag.
- H- N1 L9 @1 {multiplication, fast.
' [. M2 B6 C$ S& e9 m# n0 X* ]2 jNiven numbers. 9 p. V7 a; }8 g" M0 q2 f
odd numbers as p + 2a2.
 L/ E' Q4 ]/ y1 F7 q- j* cOpperman’s conjecture.
# ]* c& l3 Z& Q- W* r' \palindromic primes. % v, V; e# P* V: |$ T
pandigital primes.
; V" v, O7 h7 ~& P$ k$ h, r2 iPascal’s ** and the binomial coefficients.
3 \. k3 L) i: E4 P, tPascal’s ** and Sierpinski’s gasket.
0 N4 ]4 E: x* e9 u! h- ZPascal ** curiosities. 5 g! y) n3 g9 t- J( w7 B0 @
patents on prime numbers.
/ l) J% B7 W4 n! K; H# e! @Pépin’s test for Fermat numbers. ; R) T! s5 t. f! R& {) u- y
perfect numbers.
8 {0 ]. u1 z. @( x! Y- kodd perfect numbers.
. x" A- W0 x: T$ Bperfect, multiply. $ C5 j" G+ Z9 k! j- g; T- x
permutable primes.
3 z/ b4 H' A6 z0 L* M" Lπ, primes in the decimal expansion of.
1 t) x( [# z! O4 z* ~2 ?Pocklington’s theorem. % c v) C6 Q8 ?; z# x# S
Polignac’s conjectures.
 B V6 [4 r. wPolignac or obstinate numbers. + J0 t. O# b h- H1 k) c, X
powerful numbers.
5 |, B% e! `: @) K7 @% T; d/ r" i0 {primality testing. 8 D- t( q1 B( X, X
probabilistic methods. ! s8 a7 F2 Q. M% ^9 I$ z
prime number graph. + A. Z; e! c {; @ F! K/ N8 `
prime number theorem and the prime counting function.
! u9 m& t+ v! t! r7 R) mhistory. % s2 k8 u2 |4 O4 {
elementary proof.
/ T. u" Z& ]& }& U% r4 zrecord calculations. + m: P" _3 z" x8 i$ v% P
estimating p(n). 5 J. T+ e$ t4 q8 P, n8 V; Q4 M
calculating p(n). $ S# H1 u: S2 Z' Y) V) [7 q2 a
a curiosity.
; N# ?# @2 ], g/ Q4 eprime pretender. ( O1 ?& s) B: C9 r
primitive prime factor.
3 j3 S7 v s# Xprimitive roots.
' D! d; N$ R9 U5 g$ o% sArtin’s conjecture. 9 z2 @$ e. Z' q1 ?% N
a curiosity. . d. M8 b# R* i0 e5 q
primordial.
 s4 R _# G# w/ D( E# Eprimorial primes. ! y: G- V r4 G; p9 R( T! @
Proth’s theorem. : d* ?1 j7 N: o% ?) E6 M& g
pseudoperfect numbers. % q. F( ~! \' G0 Q6 p) Z1 e
pseudoprimes.
, p& c2 b8 D$ T, nbases and pseudoprimes. ) ^* ?: \0 l9 C H9 j8 ~4 {
pseudoprimes, strong.
4 H: j* r( E; k I# }) K7 Fpublic key encryption. Y1 [) U& N4 j% m* W3 h- o
pyramid, prime. ! e4 N; m* G( `3 y# i1 `% p$ ~8 r
Pythagorean **s, prime.
6 C0 `7 L. M, @: Xquadratic residues. : ]' u3 _8 ^, f6 H, K4 t# T
residual curiosities. ( M5 |8 l$ w) G! n V
polynomial congruences. ' h5 |0 f( B, A4 n5 Q) w
quadratic reciprocity, law of. # G- d n/ e m. H( t! N4 U% }# y
Euler’s criterion. . w4 F; `5 _8 y+ ]# a* m
Ramanujan, Srinivasa (1887–1920).
: q3 t1 u& U4 n# j" s _/ n) @& Fhighly composite numbers.
! e* n: r5 r1 f" S9 lrandomness, of primes. : x) `: j4 s9 n6 N
Von Sternach and a prime random walk.
( }0 o* o/ E& x* u7 n( z+ hrecord primes.
0 a. L* F/ y2 Y, m" \: m2 W3 Vsome records.
: G( d5 c- @) s# _/ o# v/ B4 z8 Crepunits, prime. 4 ~/ t# F9 G# O
Rhonda numbers. ( |, Q! N" Q; }( n( R" z
Riemann hypothesis.
) v- ~2 s k. M3 ^% r0 S% g P0 ]the Farey sequence and the Riemann hypothesis.
5 I, y# v. f) Mthe Riemann hypothesis and σ(n), the sum of divisors function. . P% [2 x7 }/ q2 F, n E
squarefree and blue and red numbers. . Y0 j# @& n& g" h: T3 p, l
the Mertens conjecture. 7 d$ `! V m& Y
Riemann hypothesis curiosities. ) ~, p5 y3 p4 y" B9 X! S8 |% k5 E" W
Riesel number. + E, m; P$ w3 F
right-truncatable prime. 4 n3 v3 O% j0 F" O1 B5 ^6 ?* v
RSA algorithm. . w. X- Q5 v9 K
Martin Gardner’s challenge. ( {8 Z1 D+ Q/ G5 ~! r- d
RSA Factoring Challenge, the New.
, U& C4 d( c5 \$ v( L" tRuth-Aaron numbers.
) e& \% G; V! `; WScherk’s conjecture. 1 Q7 q- F, z$ t
semi-primes.
! d" g4 o6 |! @% q: j1 A**y primes.
) U9 a0 Y; _4 d8 lShank’s conjecture.
- x( R4 e" v0 K; a9 f# A; M* \* R& kSiamese primes.
. J3 S U2 q6 x2 NSierpinski numbers.
) q. j: s" O6 k4 O, lSierpinski strings.
" a& T- ?3 `3 k N& \6 c4 ] E& ASierpinski’s quadratic. 7 K5 v+ W, u% B. E( l
Sierpinski’s φ(n) conjecture. 2 z9 L8 j# A7 c4 h* ]$ U
Sloane’s On-Line Encyclopedia of Integer Sequences.
8 n4 Y0 D7 t9 G' G$ z) T8 C& hSmith numbers. % Y# v- C1 h6 n i% \9 n4 e: }
Smith brothers.
! h# y: G& N0 i R/ j7 \smooth numbers.
! d( _' Q2 U1 J$ K' B9 E1 p: ~Sophie Germain primes.
; o, f1 I" K3 a1 hsafe primes. 2 S" V/ @* Q, |9 t8 ]# T- j
squarefree numbers. / R* o u/ A: u* \5 b4 [ d
Stern prime.
, d. m4 M' c# M! X1 ?% f& Astrong law of small numbers. ' w' Y9 `- [4 l3 P
triangular numbers. " J1 B: q# N0 P( D6 w, \
trivia.
* o+ Z( y6 I9 [ n' Itwin primes. 0 f4 j$ _- _! I# D1 [( I
twin curiosities.
/ a7 `) a+ b+ c i6 J% j. YUlam spiral. 9 n! r+ F" s- q& ?
unitary divisors. 7 k6 Q& D: x/ V& D# v/ G1 m* ]
unitary perfect. ( x: g2 F( \) E4 _0 N7 U
untouchable numbers.
 Y( g$ E3 Q8 T- Z7 P8 Y: O- [weird numbers. t) f8 q# ~7 P/ v/ Z- K& K
Wieferich primes. 2 l$ G) f: x9 i% T( O
Wilson’s theorem. - z) R& g2 y2 Z% q
twin primes. 1 D: `+ D% U) T9 x% `: s
Wilson primes. : @& i L) e# @' a5 T
Wolstenholme’s numbers, and theorems.
; F8 q+ o1 D9 M! qmore factors of Wolstenholme numbers. 4 }4 ]4 x8 ?9 j. a' C6 G
Woodall primes.
% G+ n1 h3 E% U0 L/ u! d5 \) lzeta mysteries: the quantum connection.