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数字的奇妙：素数

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Entries A to Z.
1 m$ v8 I% ]8 f# E. o: S/ habc conjecture. " P5 u$ W- \" a. J
abundant number.
8 R9 m3 i$ x2 g" I4 b+ @( iAKS algorithm for primality testing. 6 k& H, t! y) |9 ?7 J+ ~
aliquot sequences (sociable chains).
$ ?& p: T3 o, ^: ]/ Y. Ialmost-primes.
5 \! O$ K2 j' E2 Camicable numbers. $ V1 `' i) F; Z+ \# H$ Z: y
amicable curiosities. 5 d7 t$ d9 E x$ M# ]2 J9 j1 v$ v
Andrica’s conjecture. 0 k5 V5 O& N+ h" v
arithmetic progressions, of primes.
0 X; _9 R7 P" L: uAurifeuillian factorization.
, p6 T6 `; G7 d9 |3 @" ?8 K& Zaverage prime.
- L% {. L, G1 N. kBang’s theorem.
* z5 U' W- V5 k# l1 K5 ?Bateman’s conjecture.
# h& u G% H! h6 Q, h/ GBeal’s conjecture, and prize. . C$ p; z( N$ }. x9 d2 {9 Y6 }- L
Benford’s law. 1 u$ z H& P% l. [" V6 G
Bernoulli numbers.
# y: g/ y& {1 }4 N- CBernoulli number curiosities.
% c ?3 Q6 m. uBertrand’s postulate. # H) j' M' Q3 m. \
Bonse’s inequality.
2 ~' M! a, n. _3 U9 M tBrier numbers. ' A9 i: l$ o' k' L' L7 @4 W. P
Brocard’s conjecture. 7 ^$ o4 Q4 g6 X/ I2 _5 t/ f" ?7 s8 f
Brun’s constant. / Y) S$ ?: b, }" k( [" V
Buss’s function. " w' c- v0 A/ u. y4 a7 O+ E& f o
Carmichael numbers.
* x2 [% e/ ~3 }! T: TCatalan’s conjecture.
 J: h9 K/ h4 nCatalan’s Mersenne conjecture.
. W# h$ k3 a1 h$ hChampernowne’s constant. - i) }. p, k0 {6 l* d9 ^
champion numbers.
) ^5 J; E! S' Q* `, rChinese remainder theorem.
+ i& G9 `1 p ocicadas and prime periods. . y: I1 l+ i* B3 k$ K: ~ m
circle, prime. # Q7 X8 K4 P& A' P) x; E
circular prime.
, @% w4 Z$ ~3 Y8 T; c# u- S9 BClay prizes, the. & `- w) q I, p& y
compositorial.
3 J- X' S! @ ~ uconcatenation of primes.
+ P1 h: N2 r8 c6 zconjectures.
6 o6 x3 T6 s# Pconsecutive integer sequence. , j i# M0 { U
consecutive numbers.
9 L7 m# B/ n3 N) J4 P: Z' Pconsecutive primes, sums of. ) X. _' W6 L. ?7 U* Z( M# h
Conway’s prime-producing machine.
; u4 A" ]# N7 I" S, U0 j8 gcousin primes.
' Z6 Z* t6 K& {Cullen primes.
/ z0 a+ ? h; P' MCunningham project. 2 X" `, y# q R# N+ n, ]5 L8 ~
Cunningham chains. . J+ w5 F* D; F8 @- S
decimals, recurring (periodic). 9 L& t9 i7 n1 l9 i# R3 j
the period of 1/13. # X, Y1 P9 t* G8 b7 T; f3 s5 |
cyclic numbers. / s& H0 _& G; P. b( F( v, d3 x( }
Artin’s conjecture.
+ D3 y8 p; K T. U/ O6 f3 F3 tthe repunit connection.
) K2 y( c- a* ~% q% J* b8 Jmagic squares.
" g) Y! w" e$ m- \3 q7 d0 _5 W( ]deficient number.
5 u3 ^5 p- o- ydeletable and truncatable primes.
3 M, q T. T- J: v2 } ADemlo numbers.
% H+ R$ C! F1 y: W& \descriptive primes.
8 W4 q5 t% F& |) j7 C( G$ i, uDickson’s conjecture.
( v' V7 K( C& Y2 I) odigit properties. ! S/ _' e; |% i2 N" X8 V' `
Diophantus (c. AD 200; d. 284).
. N3 [7 I4 A$ h- j6 sDirichlet’s theorem and primes in arithmetic series. 1 \" [; [! r6 t* g4 M
primes in polynomials.
6 S( f2 Y# d: V1 [8 ?7 v Xdistributed computing. 8 Z+ W. Q+ T0 G0 w4 T. o
divisibility tests.
$ q2 _6 m- {# Edivisors (factors).
6 `# J' `2 M: j+ Lhow many divisors? how big is d(n)?
/ p$ a5 ]0 c' S5 rrecord number of divisors. ( A* a1 | H% j2 i8 H: ^8 B
curiosities of d(n).
+ `# p0 z# x7 xdivisors and congruences.
5 f7 N! ?5 J% P" F) d, `" ethe sum of divisors function.
5 p/ T. e% w' u8 Y1 h/ Fthe size of σ(n). & v/ J- O, v6 |5 H
a recursive formula. ! q1 l# z% g. F0 H2 w/ i
divisors and partitions.
! d' X ^8 r* @' ycuriosities of σ(n).
+ |% j# U1 |( Y" b% \prime factors. 9 }( @ S! t* c/ v9 Q" N; [
divisor curiosities.
6 @9 T) v5 V* W, N: k5 reconomical numbers.
" \& ~( p* ~8 e7 Z e# ^/ FElectronic Frontier Foundation.
( j' P( S3 @9 E9 {, c3 Welliptic curve primality proving. : n% y; ^1 @/ K0 k" }1 a5 I
emirp.
) |( b$ T7 ]5 D& @) i3 `Eratosthenes of Cyrene, the sieve of. ) k0 _7 h8 C U$ v
Erd?s, Paul (1913–1996).
7 O, ^' n' _. q% ?# ?3 E' R. \his collaborators and Erd?s numbers.
9 y" A+ H9 Q" U+ Qerrors. ; {' L; j3 c) o& ]0 b
Euclid (c. 330–270 BC). 5 I1 g H/ ~1 f# V. ]& s
unique factorization. 8 Z0 P, u' V( O" ]% f
&Radic;2 is irrational. 6 @4 V$ U' k# H- d, v* ~
Euclid and the infinity of primes. ; M# g2 }# Z% x. H; E
consecutive composite numbers.
' O% m8 o0 g( w! I6 \2 C+ zprimes of the form 4n +3. 2 Q: s+ s: [2 J
a recursive sequence.
: k) d4 {, |$ x& @: f5 CEuclid and the first perfect number.
. Q0 e9 }0 c, K+ f; _# g; U# xEuclidean algorithm. 7 \ h0 k" i* x# j# |: `2 n) n
Euler, Leonhard (1707–1783).
' }& M$ H5 m7 V6 w$ S. AEuler’s convenient numbers.
: e( ^1 ~9 x7 H; Vthe Basel problem. ) R. L, m; W+ [* b
Euler’s constant.
" B( @: D N6 L" R8 nEuler and the reciprocals of the primes. ; p# m/ x2 @5 Y9 q! }; Z1 d
Euler’s totient (phi) function.
' R* n0 b7 F0 X/ E% }Carmichael’s totient function conjecture. ( T: z e/ p& p( v# L, Y
curiosities of φ(n). ; K+ n1 ~! o+ G3 d: N! q# V- `
Euler’s quadratic. ' c1 D' U3 `: e2 G$ x
the Lucky Numbers of Euler.
; z3 z( U/ K; b9 l) mfactorial. : b. Q' D6 @7 s% [0 p. O/ M
factors of factorials.
0 d/ f- U+ }1 [' b6 d- Ffactorial primes.
8 W" I# I* o" C) Gfactorial sums. 6 R% A5 E. T! z! d# g6 k( J
factorials, double, triple . . . .
: R1 p1 c: G5 t4 D! Mfactorization, methods of.
 Q, h6 T. ^9 i( H8 j+ @" |factors of particular forms. " R6 o( x. K8 E* N* T8 ~" n
Fermat’s algorithm. 3 w; ^6 h& {4 ~. y5 X; o
Legendre’s method. 2 q% @6 `6 C2 C
congruences and factorization. / [/ S$ S& D: q: E" H- g
how difficult is it to factor large numbers? ) j* q+ J( S* r' D# G( W" ?" V
quantum computation. 6 e- a# m* L# g- f0 E {
Feit-Thompson conjecture. . j/ D' k8 t9 f% B; Y) b3 h
Fermat, Pierre de (1607–1665).
# W( ~+ s* R- W* N+ `5 `! k, xFermat’s Little Theorem.
. r7 M; B; J8 }8 L0 BFermat quotient. / {4 e% c& R( }
Fermat and primes of the form x2 + y2.
7 S9 y, j1 U" K8 wFermat’s conjecture, Fermat numbers, and Fermat primes.
" \6 D4 H; V( p7 s; I4 yFermat factorization, from F5 to F30. $ j2 O9 {. i. c! w* X* r
Generalized Fermat numbers.
: W m9 O( c) I4 U6 w9 bFermat’s Last Theorem.
# U: ?! G: j7 f$ J2 ]3 ~the first case of Fermat’s Last Theorem. 1 v% Y& o# G4 B- K3 Q* y
Wall-Sun-Sun primes.
. _6 N- a( G6 Q, N% f4 J% VFermat-Catalan equation and conjecture.
! s) z# b% ^& M& W6 _) ~: ^Fibonacci numbers. ! Z# ]# R% l* u# u
divisibility properties. . c9 a2 I5 I' {+ s5 H6 F' j9 i
Fibonacci curiosities. " E! i' h) x3 h6 q
édouard Lucas and the Fibonacci numbers.
* o7 E' C2 h6 EFibonacci composite sequences. ; O3 F( p' h+ s" J( k( t1 a
formulae for primes. 7 h0 T& F, J$ {8 O% F; ^2 \
Fortunate numbers and Fortune’s conjecture. 7 u8 d% x8 X- p
gaps between primes and composite runs.
% g3 m1 r. Y/ U2 HGauss, Johann Carl Friedrich (1777–1855). ; q6 v J) M: h' h
Gauss and the distribution of primes.
0 p! {) e6 g* f+ W. d) A7 t: XGaussian primes. 4 I7 [( {" z9 q% r2 Y
Gauss’s circle problem.
0 E1 T- @, h" ?7 Z! m. uGilbreath’s conjecture.
- q- ]4 R: N' s. ^4 j% |0 k: B5 ~GIMPS—Great Internet Mersenne Prime Search.
% [4 B: z) {! ?, _Giuga’s conjecture. # ?; i5 U* F: ?* z4 K; {7 T2 I2 D5 v
Giuga numbers. 7 P% q( m- w. D. ^* s, J% e
Goldbach’s conjecture.
' o M% T, y2 p0 d A. t3 Wgood primes. 0 y$ S' N6 ?8 _5 y" F7 P
Grimm’s problem.
4 N+ @ o- V# G3 Z1 ^+ W/ YHardy, G. H. (1877–1947).
' \: J, U( Y' h- [* ^& Z- w4 ?0 kHardy-Littlewood conjectures. . N) g7 Q0 `4 U% u
heuristic reasoning.
) ]' j" S/ a' v7 v8 ca heuristic argument by George Pólya.
4 a. c% | l, I* T" J4 ^Hilbert’s 23 problems. ( @) T2 q) P7 K y
home prime.
# r0 `* y* a2 `( ihypothesis H. . r2 w# {7 q. \1 K( c- d2 j
illegal prime. % R: @& y# |" r) g
inconsummate number.
* i( H; Y/ d; F0 `! d* `induction. 1 A1 Q1 S2 J5 I( F
jumping champion.
! e1 A' ~5 R. h0 Rk-tuples conjecture, prime.
1 S- l1 ]( i8 |5 {knots, prime and composite. # m7 k2 T2 r6 U4 D' g* n
Landau, Edmund (1877–1938). ) B$ A0 c8 t1 s. t5 G
left-truncatable prime.
& y3 m0 u* ?+ W, N% ?, {0 ILegendre, A. M. (1752–1833).
& M2 A5 M/ T' c# M: i. zLehmer, Derrick Norman (1867–1938).
 x) ~/ {' A& G1 p; xLehmer, Derrick Henry (1905–1991).
) |6 i- [( s: o- \) ULinnik’s constant. 7 c* D& h; O3 \2 m2 }
Liouville, Joseph (1809–1882). * i- w; I( M( h' s% C4 O$ V
Littlewood’s theorem. * e/ }2 J0 D1 f8 u
the prime numbers race.
" {3 x% O* e1 J: ?. s0 q' P* iLucas, édouard (1842–1891).
5 J4 ^/ V$ c; V6 @0 Xthe Lucas sequence.
4 \: V0 L0 \" J9 C% f y/ @primality testing.
# o* D: f# [" k3 E9 cLucas’s game of calculation.
7 H9 m% T# J4 |0 U9 Hthe Lucas-Lehmer test.
; B+ `2 S2 o2 flucky numbers.
7 {8 \( G/ k1 {; uthe number of lucky numbers and primes. $ c9 w, o" ]2 V& r5 e
“random” primes. " E) A3 l; Y# T' t3 C0 ]/ j
magic squares. + t7 J' h/ \! g& f! K
Matijasevic and Hilbert’s 10th problem.
. r* ^# a7 K+ J- [, Q' j# @9 UMersenne numbers and Mersenne primes. 5 D8 T# R- P( J) Q# m
Mersenne numbers.
/ p( R( y! m" W; t3 M1 s/ chunting for Mersenne primes. 3 W X" ^- e( c8 u
the coming of electronic computers.
4 ]; S; W: k' g' q5 WMersenne prime conjectures.
+ ]( D4 l/ j& F Qthe New Mersenne conjecture. $ P2 |9 W+ o6 ^' N$ `
how many Mersenne primes? - z. |4 z" H; Q3 p: [: k
Eberhart’s conjecture. ; J' l$ I8 {1 [- U) s; s4 T
factors of Mersenne numbers.
( }6 |- v- o* u. b2 MLucas-Lehmer test for Mersenne primes. % k: T1 g, j! c& r" Y
Mertens constant.
6 ]/ ^/ p3 w! f/ cMertens theorem. 3 @' H. ]9 i) v
Mills’ theorem. / X. S0 N' c0 i( F2 [& d
Wright’s theorem. " N1 p7 |: ^5 n7 n3 h. n
mixed bag.
$ G [9 K& x# `! R% d" Gmultiplication, fast.
6 w( v* C2 x5 {& f! o: hNiven numbers. : w$ l3 O n% w9 V2 H/ r
odd numbers as p + 2a2. 7 Y7 ?: G4 A. T' n; S5 j. h- _
Opperman’s conjecture.
7 f( ?9 i' O2 x X! N- O! J1 ~( }palindromic primes.
2 Q) q( i) `5 @! c$ m0 l+ opandigital primes.
" |* S& \ I( X5 u' w: bPascal’s ** and the binomial coefficients.
9 { C, }2 M h! \Pascal’s ** and Sierpinski’s gasket. 0 G @( A; l! F6 D
Pascal ** curiosities. + _) Y# S3 X0 M
patents on prime numbers. 0 L% a" P" D+ b5 K y; ^& C
Pépin’s test for Fermat numbers. & B' L, `- [5 S5 T+ l
perfect numbers.
8 f( n% A& I% o+ B6 z# hodd perfect numbers. ' x% q5 h6 `7 s
perfect, multiply.
5 s; }, P, |! V- w% N; n0 qpermutable primes. 6 z! T! z# \ k3 c1 u
π, primes in the decimal expansion of. $ \9 ]0 m- i, U
Pocklington’s theorem.
" [9 U1 a% d( O, z5 A4 wPolignac’s conjectures.
) r: j6 _; K1 ?) o8 _Polignac or obstinate numbers.
% q9 s( }1 o. F7 {powerful numbers. * O8 [# r5 P( k) H6 W9 |" a
primality testing. " l3 ?) l' Z% i2 f
probabilistic methods.
/ c2 ]7 c: T Z; zprime number graph. 0 t& n r" B5 U5 S1 I" S% s( v, @$ `, m
prime number theorem and the prime counting function. / {5 Q# v! ?; j/ ]( ]
history. ! ]6 z% @# d& @: e# D2 ^+ _0 ^
elementary proof.
6 P+ z8 G6 j$ Rrecord calculations.
5 ?, B3 w5 j; Lestimating p(n). & G3 d4 [& D" f% T+ L: u4 ^
calculating p(n). 0 {1 {7 n) n0 Z
a curiosity. 5 X. P1 }, s1 s n; y* ~
prime pretender.
8 ^. G8 [! h& ]. z6 Hprimitive prime factor. - R2 I" W6 h( }4 {, O2 Z
primitive roots.
; {. D6 N( s8 J; c7 M8 }8 v2 YArtin’s conjecture. ; ^! c9 i; G# q9 C8 y
a curiosity.
' H( V! [8 P8 ?$ e% ]$ cprimordial.
. n! D. c: W6 \) t9 A- Aprimorial primes.
; H5 r. y* y+ w r! MProth’s theorem. - v# ` c) y- }$ \) a5 F; i
pseudoperfect numbers. 2 C9 I& X- R+ o- b; r1 s$ C8 p
pseudoprimes. * s) @' X& S! M
bases and pseudoprimes.
4 S$ F8 g, q0 Y! e9 b' `$ Lpseudoprimes, strong. ( M3 J5 ^- L- n& Z- x3 P
public key encryption. # ~& e) d4 r, j' p: z% Y, Z" H
pyramid, prime. / |3 p9 n4 `/ p% ]+ C. w
Pythagorean **s, prime. 3 u- Q4 r- u6 h5 j
quadratic residues. $ W3 F; {' M( a) {
residual curiosities.
( k) k; i* S5 r7 A5 vpolynomial congruences. " Q; k: H: X/ A: R( M* v9 A( @# l
quadratic reciprocity, law of. 8 ^: A. w( {3 i) H" i# D4 [' L
Euler’s criterion. : e* }( {! o) Q1 b- T( L
Ramanujan, Srinivasa (1887–1920).
 V$ C3 w6 L0 z, A& w- S% Ihighly composite numbers.
* I) T1 m( n9 U! ~randomness, of primes.
. x R3 g7 b, Z6 p0 ?! q' HVon Sternach and a prime random walk. ) r* K6 i* r$ t# M4 m4 ]. J
record primes.
 x8 ] l5 w$ P# ksome records.
 U% X7 a/ W8 ]* Wrepunits, prime. 1 j' x3 Y# F" o* P# O) {6 q
Rhonda numbers. 3 J! n( R; e( b2 F( d; W
Riemann hypothesis.
2 W/ c. s4 J( }; Sthe Farey sequence and the Riemann hypothesis. * `. g; Q( f) H+ a$ {+ E
the Riemann hypothesis and σ(n), the sum of divisors function. ) H- o* {. j% K. N, k
squarefree and blue and red numbers. % ^. Y( d; X' S+ H a; N3 q
the Mertens conjecture.
8 W) H- }+ c0 W g, yRiemann hypothesis curiosities. ( W1 w/ ?) h7 j/ y/ _
Riesel number.
9 c1 O; C! c, |: V. Iright-truncatable prime. ! s# Y. W1 V8 ?! e. K3 _, ]
RSA algorithm.
; p) O8 i5 v5 Z. a8 W$ ZMartin Gardner’s challenge.
6 Y( ?. @' R% H# m3 W* D: ^& @RSA Factoring Challenge, the New. ! Q Z5 s7 T5 y5 ]% v
Ruth-Aaron numbers.
+ {! g; {# u3 g4 A% [7 nScherk’s conjecture. 6 c* }8 D7 |/ K( j8 v
semi-primes. " S$ G6 i# z7 N) i# X8 u" Z
**y primes. " t% q8 U7 c6 |0 b, y
Shank’s conjecture. ( x7 R/ Y* {, F( g M
Siamese primes. 7 d4 `$ u9 u8 ]: T3 m4 t
Sierpinski numbers. % R& I- H! \2 @2 i
Sierpinski strings.
9 y! C- U# [: h$ @! m; K B1 u `Sierpinski’s quadratic. 6 n7 i, N! w. _1 h1 K
Sierpinski’s φ(n) conjecture.
" @# D9 r+ ^# C% O" O9 VSloane’s On-Line Encyclopedia of Integer Sequences. 4 Y! J E: b9 ^" s: | U
Smith numbers. ( P# s V$ r$ k
Smith brothers.
 C, Y1 L" F N% S lsmooth numbers. * Y0 `* B3 _, E* d: X
Sophie Germain primes. - Q1 r" @0 b& d. j0 [& U
safe primes. & |5 K5 d5 @( x; l6 d$ C
squarefree numbers. " B- h* Y1 f- m: n: v, s% Z
Stern prime.
 O' G. L& \+ Y4 H9 V( o9 Istrong law of small numbers. 2 B' S2 Y; S, u
triangular numbers.
$ t" M' U3 q- a( Y2 P$ i9 d4 Ftrivia.
" @, ^- a8 S# v5 l7 itwin primes. & q: H+ Y9 b/ u
twin curiosities. ; U: @ c! o6 F# i+ ~1 O
Ulam spiral. 3 m; h' v/ w4 h: ^
unitary divisors. 3 z* e8 W# S) E n/ i
unitary perfect. . M, j/ r$ ]* T0 @) [: S/ r2 x
untouchable numbers.
0 U0 l g1 d0 d+ Eweird numbers.
% h4 S4 b% _8 BWieferich primes. ) b! ]. [; S4 Q1 [8 B/ [( s+ M0 ^+ _
Wilson’s theorem.
( a9 Q- |3 w Ctwin primes. 1 ^1 j! g9 b+ Y1 C, Q- Q* \* S
Wilson primes.
6 B8 e. v! w2 |4 G5 |$ J& M: X0 p1 bWolstenholme’s numbers, and theorems.
# W, }7 F/ ]% k) J" w/ a9 H M! xmore factors of Wolstenholme numbers.
; R' C" J5 _1 J2 L4 TWoodall primes. 2 \* Z$ w$ J, r/ r' g& L
zeta mysteries: the quantum connection.