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数字的奇妙：素数

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Entries A to Z.
1 A9 X B$ U* Z7 u! g. c- mabc conjecture.
8 a6 l- G0 j$ U& h+ sabundant number.
0 ?0 d( t( ^$ K6 o) u3 sAKS algorithm for primality testing.
: h+ ~* a" n7 a7 ?& jaliquot sequences (sociable chains). ' i. H s# m% a" m( I$ k' E! h
almost-primes. 9 e/ v; \$ l" `0 f7 Y; K
amicable numbers.
2 E9 y0 y- w- b: W Eamicable curiosities.
. C8 ^, e U. [+ c! \& hAndrica’s conjecture. `1 U K3 p. e0 V) h* I$ q
arithmetic progressions, of primes.
7 H4 `( H/ t; C# u1 u4 [Aurifeuillian factorization. / i U. p9 }1 \. C2 S
average prime. $ {- S8 _# d6 ?2 O: q6 {( y Z
Bang’s theorem. 1 i: ~( ]4 _4 i* e# R# t
Bateman’s conjecture. ( }+ P; r8 m+ F7 |4 Y* \" i5 ^
Beal’s conjecture, and prize.
2 D* w( v# e0 w# s* KBenford’s law. 0 k' T( Y4 m* o' {/ ~0 l/ x
Bernoulli numbers. 5 A8 r! F( N. R0 h9 H V6 R
Bernoulli number curiosities.
1 _0 ^$ h( `- ?4 yBertrand’s postulate.
$ m9 U' Z7 {% M6 RBonse’s inequality.
1 c/ \. A* O( U9 N/ F3 lBrier numbers.
# E, O4 m: N, u# Z8 n* Q |$ D* _Brocard’s conjecture.
( b/ t" `; P# x/ S; ~! i9 FBrun’s constant. $ s9 d7 r. |, z5 h4 i, f; c& j
Buss’s function.
& z$ ?' U- L; I8 ~Carmichael numbers. : S3 M) g1 L( ?4 W) R* o/ I
Catalan’s conjecture.
* G1 m+ P% s& c" lCatalan’s Mersenne conjecture. 8 g7 r! a- m. O( ?' P
Champernowne’s constant. 3 K0 v8 Y% d6 A
champion numbers. + d6 F% @/ G& `8 p
Chinese remainder theorem. 0 [/ _, _% v; R; Q8 N) o
cicadas and prime periods. 2 h! f3 b* Y3 Y+ c0 g
circle, prime. 9 O3 S3 A! C2 L% ~! D; a3 J6 @
circular prime. 0 o$ c( ]/ r& a
Clay prizes, the.
* T6 V4 m! S" b" m u8 gcompositorial.
7 P, G2 W8 ^! g- ^; G$ [) ?/ ~concatenation of primes. + W3 |3 C6 h4 H4 N: G3 L( v
conjectures. : X- z& ~. Q! H) k B, n) n
consecutive integer sequence. - T7 Z0 p* p V6 e, D
consecutive numbers. # E; K' a6 z6 l6 \
consecutive primes, sums of.
4 X0 C, M4 _$ K, j3 t, CConway’s prime-producing machine.
# T- s- K& M7 S+ v4 Ocousin primes. 8 c( w1 U! P7 r( K/ i
Cullen primes. 9 K! @" d1 S% J
Cunningham project. 8 a2 k6 Z) m6 W9 E6 ]! J
Cunningham chains.
" ]/ \+ X* {* odecimals, recurring (periodic).
' A+ u/ O$ M ?! v" T& qthe period of 1/13. # X0 B" ]7 j: p
cyclic numbers.
- a0 u$ w7 w v/ I9 B8 L7 j3 {Artin’s conjecture. ) s& t( F- g _% R. C, i# ]
the repunit connection.
 d- r7 V) e- d1 e$ ymagic squares.
7 ^2 I! r7 \2 g# c1 `' Cdeficient number. ' S$ ~! c8 L# ]
deletable and truncatable primes. . ?# M& @3 ~) {% l5 B1 C1 W: T
Demlo numbers. 6 m, A# f* U$ I2 F$ b) E. y
descriptive primes.
* K) s, h* q9 J/ z6 K' {Dickson’s conjecture. + `9 Q; n/ j) ~1 c3 \/ C6 c2 s
digit properties.
5 S0 u/ G* J5 r2 ?Diophantus (c. AD 200; d. 284).
) }" `2 q0 M. XDirichlet’s theorem and primes in arithmetic series.
; L p0 I1 t2 S/ x1 u% }$ \primes in polynomials. 6 Z7 H) v* ` q6 ]
distributed computing.
! c9 ?. Y( H+ ^* ?' S4 Pdivisibility tests.
! f* m7 }3 [/ H. t) }divisors (factors). ! M9 Q! i/ O! |2 j3 S+ P
how many divisors? how big is d(n)? 6 {! f# S* W, m, ]4 [
record number of divisors. 3 C+ `) k. t, W1 N- H
curiosities of d(n). & v a1 U- q( Z" Z# a4 @9 F4 o
divisors and congruences. ' [5 {, b" x5 N" ` V; v( Y* a
the sum of divisors function. ; y% U& W: I7 r/ @' \/ _
the size of σ(n). ) f7 L% _& t* k2 R) n* B9 o! O# I5 J
a recursive formula. / ]& n, p; @! ~3 t
divisors and partitions. ! m$ Z. k: r Q2 R# l# S
curiosities of σ(n).
* z6 W% m: x8 k5 {& _7 {; iprime factors. ! B# N6 d" a, q# [/ E+ T/ j: i
divisor curiosities. + l- k4 G9 Z# M( w) {" x& _5 _
economical numbers.
1 f% q- ]( \/ T5 a7 |! V0 vElectronic Frontier Foundation.
7 O* H7 x5 z9 V( _! gelliptic curve primality proving.
7 X% n' Y) u/ eemirp.
! j8 \, }' l' x; t# W. kEratosthenes of Cyrene, the sieve of. ( m8 o( x- E! }& U" w7 n- V
Erd?s, Paul (1913–1996).
8 |. A1 N' L( C5 S. P7 {- h; Lhis collaborators and Erd?s numbers.
5 W) U* K) \" o8 z3 {errors. * C9 J! D4 V' n) J$ b, E8 c$ [
Euclid (c. 330–270 BC). " I' t2 X1 k p& i3 N
unique factorization.
" W: k" K6 |- _2 B&Radic;2 is irrational. * S1 c* `4 ^* |
Euclid and the infinity of primes. 2 D" B9 D J" e% ^$ e" |- E
consecutive composite numbers.
& h7 H O' l9 f- f' v% fprimes of the form 4n +3.
1 z0 o k2 P3 v/ q5 I \9 q* r! da recursive sequence. 1 k2 F9 q+ X1 o4 j% {( Z( D3 f; C: l
Euclid and the first perfect number. - d5 Y& a0 T! C( {
Euclidean algorithm.
' C' }/ m- q s. K/ i) g1 l3 FEuler, Leonhard (1707–1783).
% ?' d- n% r- n0 c3 v: z HEuler’s convenient numbers.
 U [$ T/ B5 H9 a8 h0 K) Uthe Basel problem. " G' Q7 a6 @, X/ i n+ X+ [
Euler’s constant. . L6 B2 A+ _( [5 _, H8 {
Euler and the reciprocals of the primes. ( F9 _0 n y7 e* l
Euler’s totient (phi) function.
 q5 l' F+ \& k4 ~Carmichael’s totient function conjecture.
/ Q4 d1 s8 v8 J5 O* s6 bcuriosities of φ(n). ( W' T8 h! A3 F( d9 u/ X- p% ?
Euler’s quadratic. % F# ?7 r e, m F* C2 H0 g
the Lucky Numbers of Euler.
$ ]1 I m) Z! ]! h- Cfactorial. : ~4 e$ K7 L% y1 T! Y
factors of factorials. 8 C V( a2 J; G7 I3 Q$ A2 A& r
factorial primes.
4 |* L: x! I* B$ W7 Mfactorial sums. 6 n' T' ~: T2 P8 R c
factorials, double, triple . . . .
4 Z3 g+ j* N/ K( x% sfactorization, methods of. / n5 R: B- T4 H
factors of particular forms.
0 b- |% L) R) W2 L9 }8 ]/ {* eFermat’s algorithm.
/ y( t) v) |/ k. y: j9 {Legendre’s method.
: L+ K4 Z; k# O1 kcongruences and factorization. ' b7 r- a+ o' M* _
how difficult is it to factor large numbers? O5 M& L) A6 J" u/ r
quantum computation. , N) e* _1 x' z9 D. E# f
Feit-Thompson conjecture. ) s4 D2 t" G6 V
Fermat, Pierre de (1607–1665).
% @! B1 }& g5 t- \ \9 XFermat’s Little Theorem. % ?+ c9 C# q5 @1 L
Fermat quotient. 0 s- \" p9 J4 @0 | P7 {- |3 n
Fermat and primes of the form x2 + y2.
6 y! m) M: l( A/ i e; g/ hFermat’s conjecture, Fermat numbers, and Fermat primes.
# \! B* S3 z* U g* {. rFermat factorization, from F5 to F30.
8 J7 i# Y" h; X5 g) |1 F; hGeneralized Fermat numbers. 9 B* S( H+ s0 ^- F$ I
Fermat’s Last Theorem. 7 r' \1 m3 ?4 V& B; F; V
the first case of Fermat’s Last Theorem.
9 Q. D( v4 W* ?* L6 j2 ?Wall-Sun-Sun primes.
; |& W1 R" {5 \- v9 p8 k# W) ?Fermat-Catalan equation and conjecture. 6 C' L( o/ c. o
Fibonacci numbers. 1 |, B: T! e" D) m
divisibility properties.
! O$ E% {7 p. y% ?5 B$ BFibonacci curiosities. ) y$ y1 ~7 P+ a3 c
édouard Lucas and the Fibonacci numbers. $ D* u) k3 d9 `
Fibonacci composite sequences. 3 _0 p) w- m5 J8 [* W5 u* m. R
formulae for primes. ' g! ^4 G+ w1 \4 p1 l+ {
Fortunate numbers and Fortune’s conjecture. 0 U; l N& }4 E0 `) u; }; n; c3 n
gaps between primes and composite runs.
9 s) l( y' |) d0 | h+ ~Gauss, Johann Carl Friedrich (1777–1855).
' ?# {2 U& d0 L% X- L( H7 e5 g; jGauss and the distribution of primes.
7 q1 u/ Q! f0 b/ T0 L6 w+ t$ w( GGaussian primes. ! z6 k* j0 p+ K/ u/ ~7 E* P" n$ F
Gauss’s circle problem.
& v5 V: R- s3 iGilbreath’s conjecture. 1 D% y+ k& t8 [, Z
GIMPS—Great Internet Mersenne Prime Search.
2 @- |: }1 n4 C3 E h0 qGiuga’s conjecture. 1 ~* r" X# U. ~) b; r# I
Giuga numbers. % ~; Q) e- w8 G9 p1 s% l
Goldbach’s conjecture.
, I3 Y# w) L$ j7 k/ Lgood primes. c6 a7 _: x, T
Grimm’s problem. 3 }0 Y% n! D4 }6 ~" |! Z: T
Hardy, G. H. (1877–1947). $ X% P. M4 _5 u6 _1 I: X1 S, l
Hardy-Littlewood conjectures.
0 r, `, ?$ a+ K+ s0 z2 b" n$ iheuristic reasoning. : P) m7 a, v6 \+ K, ^ y3 v
a heuristic argument by George Pólya.
7 ~' T1 Q& O, o0 S2 ^Hilbert’s 23 problems.
+ e9 s" D8 T! ]+ ]) Hhome prime.
, `2 P+ H) M/ i8 R7 y3 i$ r+ t" Ehypothesis H. 0 l0 J8 B/ }8 U) z; e+ ~
illegal prime.
' Z) \4 W+ d3 C# e4 Q/ u) Vinconsummate number.
) d7 C( u s/ z- x( k cinduction.
# f' e0 T* I; E! m0 j! ]jumping champion.
) M6 M; I8 `; Q6 V# @2 k5 zk-tuples conjecture, prime.
9 a1 w. S% K( V3 J3 L0 bknots, prime and composite. 5 Y/ n) Q% r y* R" r u
Landau, Edmund (1877–1938). 7 w! \- G! U6 t1 R7 v. l
left-truncatable prime.
9 f5 E7 F2 r, X: J- `/ r. vLegendre, A. M. (1752–1833).
! ~7 \* }( X# _, u4 T2 f! k* }3 ~# ]Lehmer, Derrick Norman (1867–1938). % t* G4 W$ g7 A8 h
Lehmer, Derrick Henry (1905–1991).
/ G6 @ P5 l( ~* [! XLinnik’s constant. 6 t; f/ }3 b( D5 _
Liouville, Joseph (1809–1882). 0 f( r% H( W8 t" c3 c, t5 x
Littlewood’s theorem. 5 t7 k1 w3 t6 ~
the prime numbers race.
4 L3 w, g9 n4 h9 M' X$ F1 I3 p9 ELucas, édouard (1842–1891).
; p/ k; ?( u- ^, e$ l: i: Z7 Uthe Lucas sequence. + N# \8 ]) P" j7 C/ ~% T8 @
primality testing. / k/ e$ m( M0 ?) P( D; |2 _( | e
Lucas’s game of calculation. ' q/ n- i- \2 w* o. v" ]
the Lucas-Lehmer test.
5 h9 P+ \- x6 ^: U& wlucky numbers.
& e* P; W/ c8 s+ M. G) H! xthe number of lucky numbers and primes.
. V, r( A4 i: E: O5 q& ^' Q. `% m$ Q“random” primes.
 l1 u, R5 ?; d7 Emagic squares. - \( N0 v# B) v
Matijasevic and Hilbert’s 10th problem.
! Z2 h1 J- ]& W" _2 E2 N; hMersenne numbers and Mersenne primes. . T# g, L3 v/ q q
Mersenne numbers. [5 u6 G$ a! _/ j
hunting for Mersenne primes.
& y3 I! l, i5 t0 e# qthe coming of electronic computers.
) v) C5 S9 Z, }! A4 c8 o/ q5 p: P$ xMersenne prime conjectures.
: t9 S0 I% Y. V( u! `the New Mersenne conjecture.
9 X" O( G& D/ }, `4 ~! E: g6 Dhow many Mersenne primes? 9 K/ Z P- t: M/ b
Eberhart’s conjecture. . l- h' [9 d0 e( u
factors of Mersenne numbers.
1 G0 A/ @ y x+ jLucas-Lehmer test for Mersenne primes. 0 Y9 F% K/ v# M# X( y
Mertens constant.
0 a L1 @( X7 ~2 x( w TMertens theorem. # l$ |& J i/ e8 n
Mills’ theorem. ' P8 p7 w3 ?! e( k) @5 c r
Wright’s theorem. 9 L. T( b- U+ A7 _6 d
mixed bag.
# b3 v* [- t# c% `/ P2 m. emultiplication, fast.
2 x( m/ W: R0 E4 e4 U, ^1 ?% aNiven numbers. . c% w/ ?; o1 ^
odd numbers as p + 2a2. 9 m5 Y2 p; X! n* ]
Opperman’s conjecture.
2 I& A8 I1 r% h1 hpalindromic primes. ' K( }! v: R/ l) l, w0 ?( ^
pandigital primes.
$ Q% K& h$ d( M0 v8 \+ qPascal’s ** and the binomial coefficients. ! O2 z, t5 J; i2 @- x
Pascal’s ** and Sierpinski’s gasket.
; M* ~9 T$ m0 H2 A( NPascal ** curiosities.
9 s! m9 T, R) l+ t5 w! ?patents on prime numbers. ) ?4 J+ S9 }6 Z5 F% @; [8 r
Pépin’s test for Fermat numbers.
2 i4 N- q+ [/ ]perfect numbers.
) J( \$ R5 m+ A- p, ?odd perfect numbers.
. f% }, h5 Y2 T3 O$ c$ v7 \perfect, multiply. * C0 f0 _$ I* p4 v& G
permutable primes. ' I6 P$ c5 I; c e/ j/ q
π, primes in the decimal expansion of. b1 K# ^3 r- g, ?
Pocklington’s theorem. / s3 f" X$ h- j% d3 z
Polignac’s conjectures.
% L; o+ s& v* K, [, n: F1 a3 `Polignac or obstinate numbers.
7 N( m9 J9 A" V! e7 |4 e1 ppowerful numbers.
- p% K5 t( z# t- F0 Bprimality testing.
6 E" w* w% c$ Y( Yprobabilistic methods. 7 l( g% v+ R2 o7 Z0 |
prime number graph. 2 G8 C. }+ m: Z. C
prime number theorem and the prime counting function. 1 I: ~( F: o; T
history. 8 w8 \: S1 ^/ u5 p. [) y4 B) {" h- s
elementary proof.
3 W9 _* |* D2 @record calculations. " h. g: P% M* B' O9 C
estimating p(n). , l T; Q5 a" z/ i
calculating p(n). ! b- K% z5 v# u
a curiosity. , ?- c/ b% R8 Q3 A
prime pretender.
1 [7 l1 Y& q) @9 X! b' K/ T5 Vprimitive prime factor.
, q6 i4 ?/ }/ l) I# r7 x& Q9 |+ Jprimitive roots.
, O/ v5 }* c' r4 o6 JArtin’s conjecture. ' N/ g5 W* ]+ E: {+ H
a curiosity.
' ?0 S1 D' d" {( ?primordial. ) S7 _9 K" X4 t, [' A @# m% J
primorial primes. " ^' ^( Z# L+ d+ }
Proth’s theorem.
0 F' F! J* ?% ?& n! Bpseudoperfect numbers.
6 J k" J# ?+ Lpseudoprimes. - X# W/ m& q8 C, I7 Y8 g
bases and pseudoprimes.
7 d) h4 p) _* W" j2 w1 zpseudoprimes, strong.
! S9 Z6 W, c! Z- `; c1 epublic key encryption. 8 y* d; E+ n L9 ~! F" y
pyramid, prime. 4 s% M, Y/ [7 Q* G5 M
Pythagorean **s, prime. ; z9 }7 z4 W& u F; ]$ y9 d
quadratic residues. * q2 ^# n. {1 T+ A* G6 f
residual curiosities. . t- \) x6 n; W* J% i
polynomial congruences. ' {9 t7 ?; m& H6 ]
quadratic reciprocity, law of.
$ g4 k0 I7 [7 @, N; G# e+ G& SEuler’s criterion.
! ~( Y, K, |& a0 B* w eRamanujan, Srinivasa (1887–1920).
0 A4 V: Q& x, n5 Yhighly composite numbers.
( j5 |+ T; V6 {; frandomness, of primes. ! ]' L& r9 z0 ~" V4 t' m9 M4 Y
Von Sternach and a prime random walk.
0 e2 X" p7 O, ^- |3 srecord primes. : _. N+ g7 \9 ?9 t6 Y, V
some records. - `; ]6 @1 r6 _2 R* h4 m6 O
repunits, prime.
0 ^& I( L1 k% w; }Rhonda numbers.
3 f c! Q& O3 {0 |2 K# c* U8 M# vRiemann hypothesis. ) ]( F! j# T$ m0 u* ~
the Farey sequence and the Riemann hypothesis. / h) I) T- j) o+ }: H' s! {; F% s7 i
the Riemann hypothesis and σ(n), the sum of divisors function. 2 x! ~' b" e3 `4 r3 X' C
squarefree and blue and red numbers.
the Mertens conjecture.
5 j0 C% G Y% n5 H/ F' fRiemann hypothesis curiosities.
& d; A y* a- t7 A; wRiesel number.
. Z- r# h, g9 x, u, Lright-truncatable prime. 1 ^& k8 ?6 D: Y" G
RSA algorithm.
, S6 F5 j2 N. \Martin Gardner’s challenge. $ r2 y* p( G4 u% S0 Y3 v
RSA Factoring Challenge, the New.
, D4 {1 _: ^; Y; X( ?) o1 qRuth-Aaron numbers.
$ M; G/ V& |- O4 k3 ^Scherk’s conjecture.
( }) r1 _/ t0 a" o; p! t. U/ xsemi-primes.
# j: }; d! S8 a. ^$ H" E**y primes. ! o' w0 L: q- F, {2 ]
Shank’s conjecture.
+ g3 B" b" U$ B! X l% b1 tSiamese primes.
2 S2 t2 F3 K5 r8 } T* e# w4 ESierpinski numbers.
$ F" e) A& h' |1 q8 f% B/ }* oSierpinski strings.
5 F0 D: k- U- zSierpinski’s quadratic.
% d B" X, o z% f/ [Sierpinski’s φ(n) conjecture. ( U7 @; v/ j9 @5 I- c! \ u
Sloane’s On-Line Encyclopedia of Integer Sequences. ! V1 U) J; n0 j9 F- ^" a& J4 m
Smith numbers. 9 u4 b$ x! M- G: d6 \0 b
Smith brothers. , B0 o& C0 y& j4 d" `2 s
smooth numbers.
" H+ r# T5 S7 @7 ZSophie Germain primes. ) ~. C7 q$ r8 ?$ z& B6 v9 T
safe primes. ) Z. D3 S! h. j7 N
squarefree numbers. + Z8 A* e2 W8 @0 o% `! ~
Stern prime.
: z, \- h6 [- D. h, |$ m3 estrong law of small numbers. + R! v- _, b( a
triangular numbers.
2 B1 o r- I& L6 D; itrivia.
 v7 s" m; M* q- K3 y3 ?( qtwin primes. 3 {/ l9 I. v/ b' H! J
twin curiosities. - Z- H3 P9 w8 V) p, u
Ulam spiral.
6 g1 g" m8 V1 R: D, ~, Lunitary divisors. ! T& L3 f4 I- V$ }4 T
unitary perfect. 7 `" W# C2 o) Y2 \% A. }# T
untouchable numbers.
. k9 ]) \) E# P' N0 ]$ Zweird numbers. . i. o$ I3 y/ D9 y
Wieferich primes. 9 }5 R0 A: Y& W; `7 ?! B, Z
Wilson’s theorem.
# d; w) k( @# m# [* o+ W, {5 atwin primes.
# @9 R7 j4 p! o, a% l9 TWilson primes. 9 Y# R h& E9 G2 f0 T1 ~
Wolstenholme’s numbers, and theorems.
8 o: N; [! p8 |. z: W5 l0 z. \1 Zmore factors of Wolstenholme numbers.
0 k. m: {$ @. L7 xWoodall primes. + h+ P/ i! I/ J
zeta mysteries: the quantum connection.