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数字的奇妙：素数

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Entries A to Z. , s/ X. Y, b! |: g3 @
abc conjecture. 1 x/ h. L/ B5 g% l6 T' u6 B* m
abundant number. 5 r5 {" P' O1 n/ {) B* J9 N
AKS algorithm for primality testing.
' q, R% H& d# x9 `0 faliquot sequences (sociable chains).
; A6 X& E, L6 yalmost-primes.
/ m) f$ A' s# ^- x, ramicable numbers.
/ N: G) a1 L5 C6 _: Aamicable curiosities.
# L {* H/ L4 A7 E& |; J* l1 \Andrica’s conjecture. . t/ p5 `- u) y3 x
arithmetic progressions, of primes.
 _2 @* t) T; g/ J$ pAurifeuillian factorization.
3 p) \3 r( t& f" |! N5 d* B. z2 Taverage prime. 9 L$ C* e# Y9 @8 z, D& k, ]
Bang’s theorem.
* z% ~1 f9 [) G1 [0 f" lBateman’s conjecture. 4 h3 y# l! ?0 O: D/ V
Beal’s conjecture, and prize.
7 S" f1 X3 ]+ P' i3 { h. x% ]# xBenford’s law.
. F" i' F; a! fBernoulli numbers. 3 g" |" h/ D1 Z
Bernoulli number curiosities.
/ \; C6 j1 g/ {8 M7 |Bertrand’s postulate.
2 ~/ O$ W. E! Z, dBonse’s inequality. 5 Z1 N2 R/ `& g' C1 @& G# W
Brier numbers. 5 p* H# @: B$ @
Brocard’s conjecture.
' ]; q7 f* }" h8 Q; n) V+ SBrun’s constant. 0 M g9 p X0 t; m7 M. U
Buss’s function.
9 ~! d$ e( [+ e, J7 j8 B4 m+ l, U' WCarmichael numbers.
: ]2 d j3 s+ s1 y7 B' K% H+ A2 hCatalan’s conjecture. ! X# T2 D% Q- _3 k9 C: Q4 W( M" ]* l2 ]
Catalan’s Mersenne conjecture. : j% \7 f3 C' }5 ~
Champernowne’s constant. # Y; ^1 W7 C$ i- N- A6 S8 q& z1 m1 `
champion numbers. # V- t6 U! g$ [0 b
Chinese remainder theorem. - i, g# e7 |# L. D! |* \4 c
cicadas and prime periods.
 J5 J* s! z2 d3 `circle, prime.
8 w; a1 k+ B5 n# b+ |; g) B( `3 [+ v0 hcircular prime. 1 V% Z6 _' O/ m" M6 H
Clay prizes, the.
& U& w( O5 o$ [( z, Pcompositorial.
 s; w S7 X: X+ o7 Rconcatenation of primes.
, V6 I1 o$ \- k+ d0 u; F, vconjectures. 5 A6 e- v5 p2 @
consecutive integer sequence.
4 d. }/ O8 g/ h: v" H4 fconsecutive numbers. : U( a0 |, ]: g( |4 u
consecutive primes, sums of.
/ O% X4 ?, }9 g/ Z0 y2 P& O; J# d. ?( }Conway’s prime-producing machine. . k; Z4 E2 `+ c. K# m. S) r
cousin primes. ; a6 V6 [( |3 q# F" d: M+ n
Cullen primes. 2 d0 L7 z- f, C6 n
Cunningham project.
7 B. n* O5 O& N. ]9 s+ Y8 U9 e! @, `Cunningham chains.
& U2 M3 X4 S( }( wdecimals, recurring (periodic).
1 v4 W% w" }5 f1 y1 f6 `. }# Lthe period of 1/13. 6 U# S0 Z; |; V
cyclic numbers.
$ Z& y- h. L+ H" h' @$ \) GArtin’s conjecture.
% L! I+ }5 o+ D' y& |4 Ethe repunit connection.
! s1 [" i8 {' ^' n: }- E- A H3 Omagic squares. 3 c8 o% ^" E- x
deficient number.
6 y) Q/ |9 s) \- T+ Ideletable and truncatable primes.
. X" u6 E4 }# G% w* XDemlo numbers.
6 p @6 s: P' n* Z2 ]/ p4 a' o+ Edescriptive primes. 3 F9 u5 r5 O4 N7 i7 @9 [: B
Dickson’s conjecture.
; Q$ m' S: [/ g4 V* Q$ zdigit properties.
* n* u/ c, ~2 v/ ADiophantus (c. AD 200; d. 284). $ d7 y$ M# S% X; w, C J
Dirichlet’s theorem and primes in arithmetic series.
* m6 M' \: f3 J1 D! E' _! _7 Q5 Pprimes in polynomials. ) |# U: g: \. I+ p& s7 x
distributed computing. ' f, z, B8 a7 e& Q
divisibility tests.
, C: H! O- h2 s) V5 mdivisors (factors). 9 F4 t" c" w0 @* _8 ^ q. r; j3 D
how many divisors? how big is d(n)? 3 J0 A$ s1 a1 j+ T
record number of divisors.
. Q! R8 w, A0 F% qcuriosities of d(n).
* L" G! ^0 l+ c' ^% k& Zdivisors and congruences. 7 ~# ^& S& i. K3 {) B" \
the sum of divisors function.
& l' c5 K3 L \1 Fthe size of σ(n). + O' C5 {0 `# u0 a0 Y: Y6 b* p
a recursive formula.
8 I+ T- F$ d; S) O" X& Q1 U7 Zdivisors and partitions. $ f5 M2 J; G5 ?% o
curiosities of σ(n).
7 l4 I' d' m& J! ], J. D8 V; c, A$ m: Fprime factors.
& a I/ x: A& t& E+ {6 odivisor curiosities.
' z% e5 u9 C! p2 P4 jeconomical numbers.
. N5 G2 W2 j( _1 R5 J* w4 KElectronic Frontier Foundation. # W1 k3 F1 k& n" W9 o
elliptic curve primality proving. 6 y* a) c* Z/ R) }3 L. F
emirp.
6 ]8 @ p4 ?! h( ~/ h" EEratosthenes of Cyrene, the sieve of. 5 M4 Z6 ] v# a1 x1 j
Erd?s, Paul (1913–1996). ) x& ~- X( [/ q+ g6 u2 @6 }, N, a
his collaborators and Erd?s numbers.
 P3 e/ N; w) l) Z- werrors. + i& o& b4 z7 }' O& Z* N
Euclid (c. 330–270 BC). . P; Z0 R9 V5 I8 V
unique factorization. 1 x' l6 S* {9 u
&Radic;2 is irrational. 8 s7 h/ }2 | N# _- T h
Euclid and the infinity of primes. ) Q$ Y9 ~6 s( t
consecutive composite numbers.
; ?& m" z% ?5 b- H* W) `primes of the form 4n +3.
% U1 j7 [/ _4 ra recursive sequence.
. a7 j7 c* D+ q' S! {Euclid and the first perfect number.
, [7 b, _* f6 R0 _) p5 s- ?Euclidean algorithm.
! i, ^ ^. h, i4 ^6 [) PEuler, Leonhard (1707–1783). ! F2 ~8 S2 s6 g$ a: ?2 o. W
Euler’s convenient numbers.
8 R @3 x. f- Y% K& Y: r; `: H, t4 ]the Basel problem.
0 _" U) g; w/ JEuler’s constant. 5 G! W) ~- `: o" e2 L8 Y" `
Euler and the reciprocals of the primes. 0 C* [" i3 p% K8 n0 u5 f
Euler’s totient (phi) function.
3 _/ O$ _+ r: O- @. P n2 SCarmichael’s totient function conjecture. : {( P" {* ^( a: Z z
curiosities of φ(n).
. U* x. I7 g i+ nEuler’s quadratic. ) G& O' M& F4 P- T' z
the Lucky Numbers of Euler. % x. ?' a' z1 g1 T
factorial.
& T6 ^7 K. |. |, H! K3 q$ g% [% Kfactors of factorials. , S' e' ], [8 S) k
factorial primes.
; A; j5 I- ]: R. {! wfactorial sums. - ^) n7 W- b' k
factorials, double, triple . . . .
. R( {0 v5 s& a. gfactorization, methods of.
' }- o6 V9 j }. U Sfactors of particular forms.
8 P0 \9 n1 W0 {) C. z. OFermat’s algorithm.
# h( U$ e$ N# j1 DLegendre’s method. ' g2 R3 t+ @# _
congruences and factorization.
9 `* V) f& b( `; ?9 d, D2 dhow difficult is it to factor large numbers? 2 K B4 P7 w0 G0 y M$ ?8 Q
quantum computation. ' p( V# n) w' T4 w& j l) z
Feit-Thompson conjecture. " J, ~% ?! K7 W; H9 M9 B) ^! J. S
Fermat, Pierre de (1607–1665). ! B) Y! }: n( P! L' X: }
Fermat’s Little Theorem.
5 z) y2 P& j* nFermat quotient.
Fermat and primes of the form x2 + y2.
2 ^" h& E3 S, m5 Y+ EFermat’s conjecture, Fermat numbers, and Fermat primes.
5 M1 \" G1 H% L T9 e7 B! iFermat factorization, from F5 to F30.
8 W3 x; H* R8 l* B* mGeneralized Fermat numbers.
" g: x9 d: ~' m4 p! f8 @: r# d$ ~Fermat’s Last Theorem. ' I% w0 N9 A/ }5 v2 P
the first case of Fermat’s Last Theorem. P; y, O$ E; _1 a
Wall-Sun-Sun primes.
7 ~2 N" s; Y0 S' O7 j% sFermat-Catalan equation and conjecture.
% J! P# V/ a- n/ D: f! YFibonacci numbers.
0 x+ z5 x: M) Z+ E ?divisibility properties.
, p0 {8 N9 l X& s3 D2 mFibonacci curiosities.
7 P* H# p! e tédouard Lucas and the Fibonacci numbers.
4 o P1 W1 C3 O& j5 |) c7 f! Q' V" VFibonacci composite sequences.
) X7 ]6 [! X$ r. T4 k6 qformulae for primes. & W' V! i9 U5 n) g
Fortunate numbers and Fortune’s conjecture.
 I& }, g3 R9 Z' {# W( ]2 X( y1 ?gaps between primes and composite runs.
' t/ {( x" Z# }) vGauss, Johann Carl Friedrich (1777–1855).
" u! y/ P* `8 J8 xGauss and the distribution of primes. & [/ { w& F) G
Gaussian primes. / `" h* n( [3 ]. s+ h
Gauss’s circle problem.
/ M$ B, A8 ^2 z, I! K: L5 ^$ HGilbreath’s conjecture.
5 W7 T/ D% }7 e6 F H- J# q Z7 GGIMPS—Great Internet Mersenne Prime Search.
, d# K2 X/ V/ F; g! h" tGiuga’s conjecture.
, a& `/ {) U- X) U. r5 l3 @Giuga numbers.
$ Q* T7 c e/ v: NGoldbach’s conjecture. 9 U, E6 O* B2 c# V/ ?
good primes. ; M3 [/ S5 i& T
Grimm’s problem.
/ t( M9 U# H% L$ [6 pHardy, G. H. (1877–1947). . l: V1 d$ z# s0 b* j
Hardy-Littlewood conjectures. ; l) X W3 [* E6 W Z& Q
heuristic reasoning.
; H. S! h2 r( ^5 p0 s- ba heuristic argument by George Pólya. " V) G8 C- X: k* D/ W* [
Hilbert’s 23 problems. # k. @& u7 m' |- d
home prime. 1 d. m8 T g3 g- D% v$ t) H
hypothesis H. # W6 ^' {( a0 _/ P
illegal prime. ! ?6 q: h. ~* R
inconsummate number. ( F2 o+ H) I* e7 f, i6 y/ w
induction.
. P% ^$ D$ J" v* V6 I# P: @6 S) hjumping champion.
( _& x4 y* o4 i+ Z6 ~- b) q& Pk-tuples conjecture, prime.
knots, prime and composite. % k/ o* x* X. t
Landau, Edmund (1877–1938). + q2 q' u1 `" S$ |! d
left-truncatable prime. 5 q! F* h% ]8 s& L! I0 F$ I G
Legendre, A. M. (1752–1833).
 S, W- k* ]1 B F6 \' K# }Lehmer, Derrick Norman (1867–1938).
/ f% G5 M: `7 V1 |Lehmer, Derrick Henry (1905–1991).
# [2 Y+ e$ Q' BLinnik’s constant.
" P( @; f& L9 G2 A. S# @! K8 T" TLiouville, Joseph (1809–1882). 2 `: I+ }8 F/ [( l& o0 i3 L
Littlewood’s theorem. 5 d6 u* q& ]. f% r
the prime numbers race. 0 e5 O% @0 @6 T
Lucas, édouard (1842–1891).
9 p% |+ e. R" f8 cthe Lucas sequence.
) h8 Q" T$ ] b1 s/ N( d1 M2 ]primality testing. # s( D9 t" h# Y7 P/ o
Lucas’s game of calculation.
' Y) N" T0 l* C, d3 o" j6 _the Lucas-Lehmer test. ( i' b6 X: V- f3 F) m
lucky numbers.
) @3 {' y3 b0 V* B9 D4 c; Mthe number of lucky numbers and primes.
4 C5 S: w! c! b“random” primes.
! H+ k3 x9 r/ Ymagic squares. 2 {3 B! s; s3 P. n
Matijasevic and Hilbert’s 10th problem.
0 q) T% j% l! r6 m2 sMersenne numbers and Mersenne primes. 0 D8 Y/ ]; B8 ]$ W* q+ M" L3 y
Mersenne numbers.
hunting for Mersenne primes.
' P* Q3 P T4 Y' k7 Athe coming of electronic computers. 0 z* v R& x, F
Mersenne prime conjectures.
1 y1 {. q- r3 y0 M2 Mthe New Mersenne conjecture. 2 G) Y/ h- W0 _$ ~- F- l) b# G
how many Mersenne primes?
: {/ {1 u3 Z1 c; B: o* z/ f9 oEberhart’s conjecture.
. {) s! P: F6 W- M8 z8 k% x& dfactors of Mersenne numbers.
7 t) R+ H0 B1 z3 q" K$ ULucas-Lehmer test for Mersenne primes.
0 o! K4 ~% @" }. Q% i0 yMertens constant. & c" }& [9 J/ M4 a# s' R0 l' _
Mertens theorem.
8 e9 f! Z* x+ ?4 j/ \Mills’ theorem.
7 s V. I; }7 ]1 [! d: |. ^Wright’s theorem. 4 r7 x0 r1 K5 L( y0 o
mixed bag. . r- w6 l* c) W% i1 @
multiplication, fast. J4 _) P' D4 V4 T0 L8 I( X5 H
Niven numbers.
- O; n: ^" |6 j# L* J! [* b3 Fodd numbers as p + 2a2. / d8 V0 Z* M0 k Q
Opperman’s conjecture. 8 \3 m% B: y' j9 a. S1 N6 d) Z
palindromic primes. ' N# s* l* @" B' Y6 f# c
pandigital primes. % Y: A4 W& O' j4 ^
Pascal’s ** and the binomial coefficients.
 l% s2 w! c" }7 R0 F1 C; [2 TPascal’s ** and Sierpinski’s gasket. 0 O% u2 L0 k4 c" n7 B1 j
Pascal ** curiosities. 4 a# b4 w0 y! G' x0 k# k1 a
patents on prime numbers. 5 C; o; Z$ t* V$ ~' R
Pépin’s test for Fermat numbers.
8 A5 ?. k# ~5 N7 o# K; ^perfect numbers. : F5 G8 ^' B% s1 {" I
odd perfect numbers.
, [" u6 Z! @+ g# Z9 p$ a0 _perfect, multiply.
: k* t* \* }6 [ u' K2 a7 npermutable primes. 5 T0 [0 F: y2 R) \; r# N7 A5 ~
π, primes in the decimal expansion of.
5 z+ g% ~5 q; V$ c8 q3 ?! WPocklington’s theorem.
: N/ z" @7 E2 oPolignac’s conjectures. 8 Z/ n: ~9 g- {, y3 N. o
Polignac or obstinate numbers. ) e- ?# i. F, x9 K o. D
powerful numbers.
% \1 ~/ g+ ?7 e2 v; lprimality testing. & A' P& R9 W9 G- E4 f
probabilistic methods.
$ q& U: r- J7 iprime number graph.
/ S7 L9 H* R/ x' r# Uprime number theorem and the prime counting function. ! }5 p( t3 C5 [1 ^. o
history. . E. {5 m/ [( c; N3 b$ K. r
elementary proof.
- F5 p8 ~# N- n i3 irecord calculations.
& B7 J7 u u; ]3 y7 J0 y( B8 @6 lestimating p(n). " q& X, B2 p: Y$ X: B! D9 r
calculating p(n).
# O/ A# o* D7 j: I0 x5 Ja curiosity.
( K& y' S& L3 O( m `9 u" Pprime pretender.
5 t/ O* y/ V! C+ `* O1 Aprimitive prime factor.
5 m; ]( H9 H& F/ sprimitive roots. ' s) S8 R- I9 f7 c0 |, i
Artin’s conjecture.
4 g9 G! Y% E8 J* z9 d" \1 g0 [a curiosity.
0 l2 v, `4 O6 x# p2 n# E1 H+ kprimordial. ! B, V8 w" t7 {; ]9 z- T: Y
primorial primes. ! ]. b( ?- h7 s
Proth’s theorem.
pseudoperfect numbers. : H: v% P. t |( n' [
pseudoprimes.
 A- }' @$ \0 ]" M2 [9 ?bases and pseudoprimes. $ E7 o/ ~; `1 ?, j h
pseudoprimes, strong. 8 N/ S1 B7 }) _# A$ c* _# ]
public key encryption. 4 l" T+ n% S- A$ }' \' c1 Q- F& A& J
pyramid, prime. % G# V$ Y9 z0 v3 d$ ~
Pythagorean **s, prime. " ?* t( ~7 {1 ~6 G I$ l+ L
quadratic residues.
3 Z, `7 e& O% Eresidual curiosities. . q/ u w+ m% q+ C2 y
polynomial congruences.
1 p' C8 i6 p) lquadratic reciprocity, law of.
, k5 p8 X# I' cEuler’s criterion. 5 {( t/ `8 C5 Z/ B
Ramanujan, Srinivasa (1887–1920).
! z C9 v' }6 w' \$ P, `highly composite numbers.
; [( X3 r. Z0 U: f- `/ k4 q1 ^randomness, of primes. / o) b! x: u% {2 t, Y6 i. A
Von Sternach and a prime random walk.
2 ?/ s, m3 m6 yrecord primes. * e3 O; | w! B3 C; H
some records.
' a* @! R6 S; ]. [# wrepunits, prime. / `9 @6 C: S9 O5 ~" f# Q" ^0 ~
Rhonda numbers. 5 ~/ u9 K9 I9 L9 M- A2 E
Riemann hypothesis. 1 _' z) g/ O `* O
the Farey sequence and the Riemann hypothesis.
, S: A3 B+ m; ]& ~" o' o0 Hthe Riemann hypothesis and σ(n), the sum of divisors function. 4 i3 }- V' V$ J3 _
squarefree and blue and red numbers.
6 V! {; l2 h& H- k7 Bthe Mertens conjecture.
9 B1 g0 l" y/ S! Q$ BRiemann hypothesis curiosities.
2 f3 r; s* O' _) B( `- CRiesel number. 4 v! `" ]; B3 G2 K
right-truncatable prime.
3 M0 b$ U8 j1 T. T) N3 lRSA algorithm. 7 Q% g0 r5 f9 \
Martin Gardner’s challenge.
+ Y$ z& r, A7 e* O9 n" E8 j |5 z& wRSA Factoring Challenge, the New.
, E! q0 s( C$ {Ruth-Aaron numbers.
7 s" ?# Z V0 `$ \% gScherk’s conjecture. ' H2 r3 j. d( _8 e8 H! E" j3 |
semi-primes.
+ C( V# a: |! B7 X9 h7 S& F8 v! K1 {**y primes.
. j: B1 l+ y& U( c+ P& v mShank’s conjecture. + }8 g$ }/ A2 g: A! B6 g- J0 c
Siamese primes.
$ }5 N9 c7 [ ^( J4 xSierpinski numbers.
& @9 l* X- e8 I+ S2 e8 f! b! DSierpinski strings.
$ g9 x7 t# _3 i8 u x: ZSierpinski’s quadratic.
/ P8 [' c- F9 T2 w" S/ gSierpinski’s φ(n) conjecture. ! d7 l$ R- W- i5 v& B6 c2 j+ m
Sloane’s On-Line Encyclopedia of Integer Sequences. [: S. G1 Q6 ? ^
Smith numbers.
% Q, n @7 g$ }/ Q& JSmith brothers.
4 Q, s0 Y, i* W5 v9 Asmooth numbers. $ U2 l& u9 Q% H) I) b7 X/ d( k0 v
Sophie Germain primes.
- F1 l. R. C7 }" w5 P/ j7 s8 [safe primes. 2 @& Z" _6 }' k D$ _6 m+ G
squarefree numbers. % P- m* T+ h+ D& a
Stern prime. * e5 {; `$ H6 b
strong law of small numbers. ! F: z4 k3 ?) u7 f
triangular numbers.
" B" W) q) x! D& Etrivia. ' w; x0 F% }3 o+ z! R# v
twin primes. , a* f# X" ^5 N. f0 g0 c
twin curiosities.
0 N4 n' F |, E, vUlam spiral.
8 x3 {6 A2 w1 k8 o" f& B1 gunitary divisors. ! F. X1 B i( R' p/ K0 m
unitary perfect. 9 C D9 x* A# l) T7 X
untouchable numbers. : F: K( Q% Q- ~
weird numbers. ) Q2 ~+ G7 _# ~- k U! q/ w/ b
Wieferich primes.
2 v$ r1 x3 R' sWilson’s theorem. ! t* ^6 l W. B/ p" O+ U- T1 u) q
twin primes.
9 G! r" t+ y1 w! xWilson primes. 0 X% Q* }5 g5 n( J2 a$ G( m
Wolstenholme’s numbers, and theorems. 2 O) w, A$ n- w) j+ o8 {1 Q
more factors of Wolstenholme numbers.
; d4 f! Q9 O9 ^. `; F1 @ A sWoodall primes.
* L' ^) }" h! L2 `5 E# J- rzeta mysteries: the quantum connection.