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数字的奇妙：素数

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Entries A to Z.
2 i" ^+ Y+ z5 B6 |abc conjecture. : P$ ], Q+ g3 z) N
abundant number. 9 a( W4 F/ _2 F: D
AKS algorithm for primality testing. / P. N k+ E3 b6 V5 m
aliquot sequences (sociable chains). : a, t; d) ^# Q c$ i4 c
almost-primes. : p2 }5 G+ i2 p4 k/ n u$ V" d7 h
amicable numbers.
3 N) I# Y {, u' j2 aamicable curiosities.
$ V4 \: m) Y9 c- o3 g! f. x3 _/ b3 \Andrica’s conjecture.
! X1 R& A1 m. p; Z& l9 rarithmetic progressions, of primes.
8 J/ S( @4 ~, c. |, u, {3 b3 qAurifeuillian factorization. . T& k+ B9 p2 P* L2 s; c5 x
average prime. 0 h7 h1 k. p5 i/ a4 M5 _! n- Z
Bang’s theorem. & ^8 |) W# L! O" v$ C
Bateman’s conjecture. . |, E' z& N3 T* u* w# l# r$ V! B% i
Beal’s conjecture, and prize. 4 w+ N' m- p0 ]
Benford’s law. 7 I1 K& ]0 w8 D; D* [) |' B
Bernoulli numbers. 0 k' g( v7 f4 i6 O
Bernoulli number curiosities.
' r/ s, L, f c* UBertrand’s postulate. & E4 Y; r/ ]2 K
Bonse’s inequality.
- J7 i7 Y' D7 I2 \$ eBrier numbers. ' c* W3 v2 ?* l9 ~& d
Brocard’s conjecture. / G: O4 V# ?$ O% X B7 |
Brun’s constant. 0 q" X* H* s* d- W% n* z2 J c
Buss’s function. ) i p; R8 X& D
Carmichael numbers. 4 a2 }2 [, e! y5 g6 |" d8 z" H
Catalan’s conjecture. $ z9 D; R4 e& B/ r" Y
Catalan’s Mersenne conjecture.
& t; b7 `* U* x7 ^! a4 hChampernowne’s constant.
- k0 n7 U, J d2 U9 }champion numbers. % p* _9 U7 p- o5 C9 t1 G- s
Chinese remainder theorem. ; O& |" Z# x! J5 ]
cicadas and prime periods. 9 H% \8 B- X2 N ?7 y2 g+ X
circle, prime. " ~* P2 K8 \+ ~. ` v' i8 Y
circular prime.
8 z' [3 c5 x* |3 L" j+ [- S& cClay prizes, the. & K$ b5 R! R' s
compositorial.
9 C& f/ X) j0 o/ R zconcatenation of primes. " Q! A# S+ c! u
conjectures.
2 _ O2 O4 ^9 w4 W/ ?consecutive integer sequence.
8 \; g0 E6 a' r3 L2 x- y% Uconsecutive numbers.
1 z$ y3 z- K+ R1 R2 y4 v3 Rconsecutive primes, sums of.
- ]5 }+ I6 r5 B \/ m& PConway’s prime-producing machine. 7 p4 j) c# p/ R; {
cousin primes.
4 ~6 g- m2 ~0 ^; F) J; BCullen primes. , i4 m6 t& l o- y) H5 P
Cunningham project.
; F$ l$ o! J' \4 kCunningham chains. o# R- @1 B0 w( y* ?9 Y
decimals, recurring (periodic). + _$ o% S# Z" v. g) a
the period of 1/13.
" P) ^6 U% [1 J. K8 Icyclic numbers.
& Y7 K: i) V1 r% | j' VArtin’s conjecture. / O, X/ }; `8 D0 k9 g: ]
the repunit connection. * u9 [+ U2 q( m
magic squares.
7 H/ X+ k7 R8 i* wdeficient number.
' W) ]! \, R, s8 k- Pdeletable and truncatable primes.
4 O, n e! c- T% q+ y8 B# b6 uDemlo numbers.
! C$ V8 _+ ]# T+ t6 ddescriptive primes. 3 k" ^/ P* R8 x; z, G
Dickson’s conjecture.
% Z/ l. _7 f; Rdigit properties. 5 ]: z, a& Q& B- r6 S1 H
Diophantus (c. AD 200; d. 284).
; U/ E' _7 Y3 D5 YDirichlet’s theorem and primes in arithmetic series.
/ C3 F0 _/ U' V4 S3 T+ T8 Pprimes in polynomials.
" x; A. U/ F3 [6 K0 F% Ydistributed computing.
( M; ]# |8 ]0 t X+ T ^divisibility tests. . e% m) c7 S3 R @. V% R+ P# i
divisors (factors). 5 Z! V& n. ~$ u6 }% x6 G' N0 M
how many divisors? how big is d(n)? : M \; t" b4 W
record number of divisors.
) {8 z* Z4 Y# t' v m9 }+ R+ _& D' dcuriosities of d(n).
- G. G/ a0 G6 P$ ~6 @; N( {divisors and congruences.
% T1 g F7 f; X3 @& Gthe sum of divisors function. 6 n9 s/ m3 D5 Q/ p, [0 z% f
the size of σ(n).
% o, [% f& A4 _# ~; [a recursive formula. / u2 z5 C. Y/ U
divisors and partitions. 0 @- Y" P2 ~5 [* } T8 |
curiosities of σ(n). : O; e% E. I- N" j
prime factors.
% m* V9 L5 u# M7 C8 n% Jdivisor curiosities.
 W: Q- `' S5 k! O' h: J0 I6 xeconomical numbers.
2 }7 J. H& E+ \ ^4 Z8 lElectronic Frontier Foundation. 8 n% {( j+ g- ^9 ]3 Z" {
elliptic curve primality proving.
) O1 s5 N) d$ @. g# M' hemirp. ! J$ r7 n+ n. [& ~5 g, z" V% \
Eratosthenes of Cyrene, the sieve of.
/ g9 S, o" C" o; GErd?s, Paul (1913–1996). 0 c' t2 u D1 U7 P5 n8 K5 v
his collaborators and Erd?s numbers.
. i" q, H; J3 b; ~errors. : D5 z* {. V3 ~8 Z
Euclid (c. 330–270 BC).
0 K( [* f8 N$ j3 bunique factorization. ) ?4 V" b; ?: ?5 Z! ?: u
&Radic;2 is irrational. & {* |+ ? M5 w: J: o. i
Euclid and the infinity of primes.
: S Q8 Z7 A+ Hconsecutive composite numbers.
 ~7 ]0 E% y4 @. U3 Q. Gprimes of the form 4n +3.
, Y/ \1 t& W' X' aa recursive sequence.
7 O" p& e7 ~: w: x9 G, j4 JEuclid and the first perfect number. / Y# _" d; |$ N# E
Euclidean algorithm. & P3 ~4 F, Q& F& I
Euler, Leonhard (1707–1783). 4 ], K- E. c/ Q& X- _
Euler’s convenient numbers. ! D* I) b7 \$ }3 K
the Basel problem. ) U f% N8 o5 q* `7 l
Euler’s constant.
& ~$ b9 t) p+ [) m: @$ S2 i1 I7 _) LEuler and the reciprocals of the primes.
9 Q5 H. N! S+ |: T3 Z+ SEuler’s totient (phi) function. 9 \' [. d: ~/ J4 N
Carmichael’s totient function conjecture.
6 N3 P5 Z' P9 y5 dcuriosities of φ(n).
* H6 E5 g' e* _4 V" p+ h; EEuler’s quadratic.
# b% l b! X4 p% Uthe Lucky Numbers of Euler.
) g7 I* H% O( O" P4 Rfactorial.
2 S4 u4 |4 C' I/ ~# v! Zfactors of factorials.
9 t m( k% [; U' Ufactorial primes. ' @( a {7 P% K' D/ o) j4 Q1 X
factorial sums.
: }3 ^ \1 P4 F, P' z) ]factorials, double, triple . . . .
$ V. d) ?" q5 A* Z; \factorization, methods of. 4 N H0 @$ y3 s2 t0 ~' ?2 ?$ r
factors of particular forms. 9 c5 {8 _8 S' q' R% n2 o
Fermat’s algorithm.
* }- o/ o8 V y7 Y: ^8 U3 cLegendre’s method.
1 X9 ~) M0 v( {" u9 D. p* Ucongruences and factorization. " S3 g8 T) P) X9 l4 R0 Y, F* O, t
how difficult is it to factor large numbers? + b2 o! r3 _( ?4 L3 p, y3 H
quantum computation. ) b- A' b; h$ C1 V& l4 @( x" o9 d
Feit-Thompson conjecture.
0 \" N1 I' {2 EFermat, Pierre de (1607–1665). 5 ^3 D* r6 f: P; q9 N
Fermat’s Little Theorem.
0 V5 |! x7 t9 Q, k9 X' ^Fermat quotient. # z7 f- [( m! s, k# J& H! w
Fermat and primes of the form x2 + y2. ( Q( f; G! t7 J% @9 Q7 [; X
Fermat’s conjecture, Fermat numbers, and Fermat primes.
 w$ K$ I4 W! c/ l, v: tFermat factorization, from F5 to F30. # F1 m& m2 a" I; T* u8 z
Generalized Fermat numbers. . n% @2 j# }, f5 k1 h
Fermat’s Last Theorem.
6 Z* S/ y3 D, Ithe first case of Fermat’s Last Theorem. 2 l6 Q. E! h* t' m5 d) V6 g! |
Wall-Sun-Sun primes. 2 i: R' ^7 v, M8 ^- G7 ~
Fermat-Catalan equation and conjecture. 2 e* o' w% Z2 f
Fibonacci numbers.
9 {) @8 D4 l& P% [" H$ f/ \divisibility properties. # q7 i8 `$ u, P/ U2 G
Fibonacci curiosities.
7 `( C9 B' N/ \2 c( E. x- {édouard Lucas and the Fibonacci numbers.
$ A1 {' g/ w/ n1 y! }Fibonacci composite sequences. 0 D a. f* m9 I
formulae for primes.
$ Y3 l' f# R- j- _3 j* Q9 e5 RFortunate numbers and Fortune’s conjecture. 2 Y( q$ O7 Q* K" V8 D: i
gaps between primes and composite runs. $ T# F K) k& J7 X/ _+ \
Gauss, Johann Carl Friedrich (1777–1855). ( @0 A) q5 _/ h; i5 r" T
Gauss and the distribution of primes. ) j+ A2 E6 p5 h9 f d$ f
Gaussian primes. 1 @$ `6 `: b6 g$ C# Y2 r% K( `
Gauss’s circle problem. 1 f( z9 H: o) v& x
Gilbreath’s conjecture.
: \+ y7 b; O) ]* u+ y0 ] ^GIMPS—Great Internet Mersenne Prime Search. : _9 L) S& U+ ^& L2 @( X3 x
Giuga’s conjecture. : j, i, N- o6 T5 J" Q7 Y
Giuga numbers.
6 b( f5 V& I+ A8 t* w7 O) zGoldbach’s conjecture. + }( `( R% P' Q, Q/ w; s: A
good primes. ' {4 q- ?1 J6 f. ?# ~
Grimm’s problem.
& n1 v& V/ O! t% E- j& j, FHardy, G. H. (1877–1947). ) J7 ~4 |7 g8 f/ v) ~
Hardy-Littlewood conjectures.
: P9 \* u# ]1 H- d, G4 jheuristic reasoning.
6 X2 T( s7 D9 Y" l9 Y8 t2 Na heuristic argument by George Pólya.
' W7 d( O& ?- K! b5 A9 o$ G/ iHilbert’s 23 problems.
6 @1 d7 S( E- W6 bhome prime. * c1 q7 ]% L9 Y; G0 ?3 s
hypothesis H.
& d& e g( }7 O7 b0 Z% Villegal prime. 7 J u# O* ^7 K& J6 }) e' f% f( Q
inconsummate number. 1 f" m2 i* y% _$ T5 T. f
induction. ) u* t$ g2 g, a; }+ s6 A) q
jumping champion. 4 p' ~- b( W+ `
k-tuples conjecture, prime.
; F. ~8 R- v( S, Tknots, prime and composite.
; B( a4 c2 |; P/ F7 ~' JLandau, Edmund (1877–1938). & B: H8 k4 r: {9 Q" F& m
left-truncatable prime. ' n8 b/ j! h0 I$ g/ v1 N( z
Legendre, A. M. (1752–1833). 8 n- d$ f# n8 |0 K$ e
Lehmer, Derrick Norman (1867–1938).
/ L4 F6 ]! Z& v) f* C2 {' ALehmer, Derrick Henry (1905–1991). 5 L3 e& H T5 E+ G1 p4 Q+ l f" v- R
Linnik’s constant.
 J; a# h" g3 [" I% d6 CLiouville, Joseph (1809–1882). ' Q' @% A! b; Q5 s R" Z" q
Littlewood’s theorem.
- P. L; Q' ]1 Q' R- Xthe prime numbers race. & j: D" }0 l/ L; D' v
Lucas, édouard (1842–1891). 6 ^# v3 [8 {0 t9 O$ y) C+ O( T
the Lucas sequence. x" V, Y2 B4 ~9 i) t+ M
primality testing.
& C0 a$ l+ [6 x0 xLucas’s game of calculation.
( T3 a+ l2 _% L# _2 f! {the Lucas-Lehmer test.
% {* n: S4 h6 x1 `( B1 W1 v- x* I1 Q3 ?lucky numbers. % _* h, h" l2 d
the number of lucky numbers and primes.
# Z! y0 Q( d# p& i% k# Q5 \“random” primes. 6 ?1 e, F% ?1 K
magic squares. ; l, l2 Z( {" F3 e
Matijasevic and Hilbert’s 10th problem. # v. b- [* B" m# y6 ~" q, v! Z8 I
Mersenne numbers and Mersenne primes. / d& s% |! v5 s9 \5 }# b+ W7 X
Mersenne numbers.
* i: d( y" a: H- N4 v. R( Z) whunting for Mersenne primes.
% |- ?5 c0 ?9 w, l- ?the coming of electronic computers. $ i( Q0 R. S' @8 L! j& b
Mersenne prime conjectures. 7 o$ X" L0 n3 }& F
the New Mersenne conjecture.
$ d. k% ~. A& K& K# [2 r, {how many Mersenne primes?
' E' _: Q* {; [/ A' }9 uEberhart’s conjecture.
9 J u# p" i' l% Gfactors of Mersenne numbers. 2 k' e% @: u- Z. L( X' Y/ @
Lucas-Lehmer test for Mersenne primes.
5 }' i9 w2 @; `Mertens constant. 5 l" N4 h) d$ ~, m' O
Mertens theorem.
. s* G Z' d/ |+ w4 mMills’ theorem. & X. E: m# \, T
Wright’s theorem.
' m! ?9 L" r! N8 J3 z. {7 qmixed bag.
& ?8 [5 c+ b! f1 \2 M; {multiplication, fast. % H7 {8 D0 k7 N& k/ s
Niven numbers.
5 s+ E: l- C3 o" x* todd numbers as p + 2a2.
3 o" A7 @* k; ]9 E+ \2 T2 bOpperman’s conjecture. 8 I) K L: K- n9 Y ^# g4 ]
palindromic primes. / C6 C, w4 d# e. x8 X
pandigital primes. ' g" ]$ P+ t- h. B5 E
Pascal’s ** and the binomial coefficients. 4 @5 x$ h3 R( V1 J* ]
Pascal’s ** and Sierpinski’s gasket.
 O# y7 D1 ]* r6 C/ ^Pascal ** curiosities.
. w$ ]/ X: g/ k9 B( E* Apatents on prime numbers. / x, |0 F1 }6 U) c6 \4 ^. x: i
Pépin’s test for Fermat numbers. % i! n! ?4 u' S0 m7 M
perfect numbers. ! |) h* e# [" P1 ^
odd perfect numbers. ) X, N' }9 q5 q- F6 ?
perfect, multiply. 0 C' s- `( b& Q7 t% J F7 ?& K
permutable primes. $ l* A% [, a, m. H) L0 `; l, l4 q t8 l
π, primes in the decimal expansion of. * k) a7 E4 n: x$ M5 h6 ?+ I
Pocklington’s theorem.
" P/ h! N# ~- O4 jPolignac’s conjectures.
/ J# ^( t8 z6 |+ ePolignac or obstinate numbers. + k) M- G: X' _4 x6 Q! h: J
powerful numbers. # D7 e6 m1 j* K( c1 z/ M+ k
primality testing.
8 b/ d$ |/ X6 _1 s* pprobabilistic methods.
) A& g ~/ X$ o/ U7 E( Sprime number graph. " s2 X+ `1 M% o2 l
prime number theorem and the prime counting function.
9 A5 Z8 R: r3 F" Y! Shistory.
/ B5 e% u4 C/ J' F1 g4 Y) u0 Aelementary proof. * z: e6 p5 _% e2 {: G
record calculations.
. ]0 F2 [/ U2 \/ z; \estimating p(n).
8 }6 `+ n9 A% p. y d+ Y8 {calculating p(n).
* d, Q4 ]5 k$ n( ?a curiosity.
& u2 f: z' k# s$ Vprime pretender.
* i O7 b9 G: R( S. qprimitive prime factor.
$ U# j! ^! G$ X/ Wprimitive roots.
% v- H/ h; x0 B2 GArtin’s conjecture.
0 Z" t( N1 A6 O2 i y9 v. w: W3 Na curiosity. ! [6 l" Q; V+ a& v
primordial. ( ~/ o) |. c% N* r* n
primorial primes.
% n) I c* t9 S+ X0 j6 uProth’s theorem.
9 T# \0 x% u/ D0 Q$ T) Q% u8 K/ O' Ipseudoperfect numbers.
, G( J% L/ G7 [7 _2 M0 r8 spseudoprimes.
3 U$ }5 ]4 r. v: @5 Hbases and pseudoprimes.
$ e& ^! Y" i" f# ]4 L$ T$ |pseudoprimes, strong. . s2 s) n+ j2 ~/ R' g
public key encryption. * D( \, c" |1 I; f8 l' a: t
pyramid, prime. 7 ]2 B, E7 P" C) O6 L4 e1 E$ q& [
Pythagorean **s, prime. ! Y. r* X0 b' i' z
quadratic residues.
4 Y; I' h' F5 [& }residual curiosities. : [# l0 _: [* B" D( K
polynomial congruences.
' k, B. p# p$ ~2 g2 s! F3 r, \quadratic reciprocity, law of. + U, |/ ?4 |" H2 y8 e- b
Euler’s criterion. 4 K+ a8 l6 Z% l" s& K! E
Ramanujan, Srinivasa (1887–1920). 0 h% F0 |& m9 n' x- G& Z
highly composite numbers.
. g& a* S8 {. \ H% srandomness, of primes.
. N% W$ f, R* ]& w3 v$ Q/ jVon Sternach and a prime random walk. 1 \; \+ V* A; }+ I
record primes.
4 G h# _4 d9 v4 gsome records.
9 K4 O" ~0 p9 i8 `4 Vrepunits, prime. % m3 N) g4 w" t, |/ J' H! \" r7 G
Rhonda numbers.
/ i0 y, C/ M: @0 yRiemann hypothesis. ) n. K9 C) ?: z
the Farey sequence and the Riemann hypothesis. ) O; { I" e+ `( @
the Riemann hypothesis and σ(n), the sum of divisors function.
" _ b8 ?) ]4 {+ E, H& zsquarefree and blue and red numbers.
- n! d6 s5 @5 [5 n6 Athe Mertens conjecture.
9 v6 C! e* Q- z% o- VRiemann hypothesis curiosities. 3 |" F9 z- \' T% A
Riesel number. 8 q1 Y% y3 q. P p
right-truncatable prime. ; `+ o: Y7 p4 X3 _% I7 b0 K9 V9 j9 O, L
RSA algorithm.
, p Y# ~; V+ V# ]5 {Martin Gardner’s challenge.
+ G( r: n$ S( A0 q2 v" dRSA Factoring Challenge, the New. 8 {* v# z2 F. j' ?2 w0 M% q
Ruth-Aaron numbers.
2 z5 y3 _$ |, r7 x7 SScherk’s conjecture.
9 l; M6 C9 K2 v) d; [6 U8 Xsemi-primes. 9 g; w+ D7 C7 r, H
**y primes.
6 X1 |! v; q5 H/ u5 R) J8 KShank’s conjecture.
, ]' @3 | C& B7 tSiamese primes.
( I* X7 N h' }Sierpinski numbers. , p5 `- Y+ N+ E( a- b
Sierpinski strings.
( i( S* B2 ?) O. w; b; r l) W8 USierpinski’s quadratic. 3 W- U+ ~5 I' Q4 p
Sierpinski’s φ(n) conjecture.
- l4 T5 t% N- t5 P9 G. R2 k4 OSloane’s On-Line Encyclopedia of Integer Sequences.
Smith numbers. : T3 _8 z8 a' H" y, b! s
Smith brothers.
: d4 n- j0 N& Usmooth numbers. ! D6 ?1 L3 _" S6 Z! A7 t1 U
Sophie Germain primes.
$ q O6 N$ {' M* V0 Lsafe primes. 9 N* k0 K+ N; K3 H
squarefree numbers.
& \2 U5 K6 T' z1 L, Q6 M, v1 CStern prime.
 m* ^* z' `) v' }strong law of small numbers.
0 a1 f5 t4 \, \, G3 mtriangular numbers.
' h' j9 }+ B3 P/ ^trivia. : w6 `- _/ O* c0 R
twin primes. , K) K+ h- J4 k% F0 S1 }8 Z* s1 R9 Q
twin curiosities. % n: y0 W0 @ k8 K3 k' @5 @8 p5 A
Ulam spiral. 5 e& V3 l7 ~) H& |6 W8 f: L
unitary divisors.
" I+ z9 k" M) M# @; T1 W% Qunitary perfect.
5 G+ h+ B$ X2 @" G, euntouchable numbers. ( ~3 G! A+ T5 i1 s/ i$ n, R
weird numbers. % Q7 A2 m I& k y; n. Z3 v0 a- D! N
Wieferich primes.
, r# D* U% B; sWilson’s theorem. 5 z9 ^' N4 f% |( S) L6 E8 a8 O5 B3 n
twin primes.
5 s) N$ B7 w) z, z" _ L5 WWilson primes.
/ W# I! d$ S' ~Wolstenholme’s numbers, and theorems.
more factors of Wolstenholme numbers. ) `2 O& b U- ]! K
Woodall primes. 6 M7 n) M; {5 s0 Z
zeta mysteries: the quantum connection.