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数字的奇妙：素数

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Entries A to Z. 0 B% ]. }+ P2 z2 x$ k
abc conjecture.
- j5 M) d% {, a' @9 [abundant number.
/ S7 W1 w. Q6 ]* ~AKS algorithm for primality testing. ' N5 x6 i2 |* Y$ D/ H! F) L
aliquot sequences (sociable chains). - @% $ I4 R. h* B d7 P4 F
almost-primes. # j# l1 k* _ i( n
amicable numbers. 9 ?: A$ ]5 m& P2 z8 l9 a9 i W
amicable curiosities.
! @6 x+ u9 [" R7 L/ i, N5 VAndrica’s conjecture. $ t% F# j/ _; s
arithmetic progressions, of primes. ! T+ t! D6 C" Q5 x, z7 b% o5 b
Aurifeuillian factorization. + j( O$ F+ S+ [9 {3 \1 v: w/ B
average prime. 3 Y, {' t/ P( |! u$ b' D
Bang’s theorem. : F1 Q6 A. \" R
Bateman’s conjecture. - }- O. K0 I5 f# g( M
Beal’s conjecture, and prize. : Y2 s. |+ H$ s
Benford’s law.
7 ~. U! r0 {. J$ {0 u% {+ cBernoulli numbers.
' C1 G& G- p7 YBernoulli number curiosities. % W0 t7 z( I' E# n# m# i
Bertrand’s postulate. # v8 \6 D; @# d; B3 s; k
Bonse’s inequality. # {8 k# W% _2 $ T" ~
Brier numbers. / T- F- k9 ?: ]/ n8 X
Brocard’s conjecture.
5 ]8 U" m3 j" L# {Brun’s constant.
" C9 ^: b* S' G1 IBuss’s function. / N- n% b- l7 i# Y
Carmichael numbers. $ I5 u- J: d1 \1 ~
Catalan’s conjecture. 5 R" L" T! X6 R7 J- r6 T# J) _
Catalan’s Mersenne conjecture.
# T" o6 R" \4 `* QChampernowne’s constant.
. a, q; o. e* ?champion numbers.
: n% l( D/ s. h* K7 l, |' ]! yChinese remainder theorem.
, K. B7 H( c6 V/ s' gcicadas and prime periods. 6 E* ~( @& h! q5 L
circle, prime. " s' a6 F' w' n
circular prime. 0 H5 e- S/ q9 L4 Q- m3 C
Clay prizes, the. 6 Q2 R1 g3 N* K+ K) b: X
compositorial.
6 H& S) D( y( n6 M, ]( x4 W2 mconcatenation of primes. $ ^9 \, q! b' ^( ?. P
conjectures. " D: k4 k0 [6 o1 ^) m
consecutive integer sequence.
4 m1 I! r* _& ^. j/ w$ nconsecutive numbers.
, j# J5 H. g5 J( |& hconsecutive primes, sums of.
. |! K! u" L8 w+ ^3 ZConway’s prime-producing machine.
: a, S3 A( U/ d& J' u; C7 k8 |cousin primes.
' D, T$ p3 P& M; T9 b/ |Cullen primes.
* D8 B; _" P7 hCunningham project.
9 G! R0 h& Q; y( g ICunningham chains. ! y+ O& t* w# @" ^7 N0 m5 s1 P
decimals, recurring (periodic). - F. F- H2 P# D. S+ {; a. z
the period of 1/13.
' O% q# N# A8 c3 Tcyclic numbers. , {) c" l% s0 t1 k: Q$ ]6 k6 w
Artin’s conjecture. & ~" F; I, |: M; ]* n+ s! V# e
the repunit connection. 5 J% \ m: [1 m) ?! N
magic squares. 7 Y& I9 ^5 X& o) H
deficient number. % W% `- M! G$ T& b7 @) G/ h7 B
deletable and truncatable primes.
3 p( V2 `, |& PDemlo numbers.
! v& D4 s1 O- o8 H5 G2 _. Idescriptive primes.
; X. v- ?) x* x, O+ g4 S8 q W$ d: mDickson’s conjecture. $ C0 ]" k9 O5 C) R! g
digit properties. , t0 h1 k! `) f
Diophantus (c. AD 200; d. 284).
- A; Y6 ^2 ]3 f! uDirichlet’s theorem and primes in arithmetic series.
1 Z. `9 F x# f0 Fprimes in polynomials. + Z7 T! E) A* v/ z9 H! E6 B
distributed computing. 0 g/ _/ H. P% z+ x
divisibility tests.
. K" o `) R$ k7 a- O- U. Odivisors (factors).
2 B0 x. X5 G9 t. Q2 q7 X/ Ahow many divisors? how big is d(n)?
& Q4 i m7 k9 [4 i- `' s, }' urecord number of divisors.
: ^4 m+ O. m2 Q* g% k, zcuriosities of d(n).
% P9 V+ v& H: U7 m' A: A/ Sdivisors and congruences. + f' z. Y" o3 x$ D* O- p
the sum of divisors function.
4 S+ z2 A! U) q7 m# _6 @, c) l. ^the size of σ(n). ; ]) Y6 ~# }9 {. ]. t- a
a recursive formula.
# z: ^& T/ W9 Edivisors and partitions. 4 k% Z+ r7 m) c) Q7 Q/ x/ N
curiosities of σ(n).
& }& N* e0 l! P- }prime factors. 8 B) X2 s% y8 r6 u }$ P
divisor curiosities.
% Q. |7 b1 e& W" Ieconomical numbers. * j& q1 K1 h6 o
Electronic Frontier Foundation. & ?6 D+ E5 I" `1 ]. T% v1 J+ y
elliptic curve primality proving. . |) v" J) L* n& D8 ` u1 o
emirp.
Eratosthenes of Cyrene, the sieve of.
) C. K+ i5 @, F: M @4 W* p) vErd?s, Paul (1913–1996). # J+ _2 ]1 i$ s) g L0 h) \
his collaborators and Erd?s numbers.
+ i% k6 O0 f a3 merrors.
: e& E' w9 r) {+ A" Y) S) zEuclid (c. 330–270 BC).
2 s0 u' K) }+ |1 yunique factorization.
! t& Q0 M7 Q% n&Radic;2 is irrational. # V2 E3 m$ W3 A6 q U8 B
Euclid and the infinity of primes.
4 r( D) v V; H9 {9 c* }consecutive composite numbers.
6 n6 O' k7 S8 H1 T# x0 N! jprimes of the form 4n +3.
) c4 ~+ o0 ~+ I4 @3 wa recursive sequence.
% O4 }9 i: `; VEuclid and the first perfect number. 9 P/ X }5 I2 D9 ~& G* c4 h$ V
Euclidean algorithm.
9 x4 e' {1 Y8 q' ^) N3 d- f! p$ lEuler, Leonhard (1707–1783). . _4 W# K0 b4 K4 [. W& V
Euler’s convenient numbers.
3 l6 A8 O8 \' j" Ithe Basel problem.
 y5 N( D5 h; o4 B4 i4 [Euler’s constant.
* M; {1 p5 ^) N& q5 hEuler and the reciprocals of the primes.
% J- i& q3 q8 v: {" MEuler’s totient (phi) function. ( R" W( S( }. @9 ~* z
Carmichael’s totient function conjecture. + R( X) i7 V5 S: C* K$ }, E
curiosities of φ(n).
8 w5 A3 t" M; nEuler’s quadratic.
$ g" G8 c% b3 bthe Lucky Numbers of Euler.
2 U6 _% f6 Z4 S' y# rfactorial.
5 g0 K! K! n+ [0 g* Y$ d- `, Vfactors of factorials.
, [: {. V' A5 \5 d( C7 B4 A5 ^factorial primes. 7 d) Y! a% E2 o# Z" r4 B- {
factorial sums. . a: g* v' f6 y, c3 w j
factorials, double, triple . . . . # C) ]" s% j2 F6 h
factorization, methods of. - B& B, a) D( D5 V
factors of particular forms.
9 X! Y+ A7 Q6 Q$ HFermat’s algorithm.
4 ~$ U4 x! u8 RLegendre’s method. # L3 ~+ o8 p; i6 b4 `
congruences and factorization. ) g6 j1 P: q9 W2 q: c
how difficult is it to factor large numbers?
. X: c, ]# Z* A7 I: ]quantum computation. 5 `$ h, F5 K8 p, Y. F9 ^/ ^4 w4 D
Feit-Thompson conjecture.
" o( k3 M* v; g3 W0 Y! jFermat, Pierre de (1607–1665). ) e9 Y# ]) ~. U9 G
Fermat’s Little Theorem. 7 s; r. K' R3 i- V$ Q' I9 w
Fermat quotient. 2 d7 M7 _1 D3 B8 _+ o. }
Fermat and primes of the form x2 + y2. + y$ |/ i$ n- d( i
Fermat’s conjecture, Fermat numbers, and Fermat primes. 2 H; Y0 `) }4 T, ?5 Z
Fermat factorization, from F5 to F30. 7 N; E" N) W& t2 N
Generalized Fermat numbers. % B! D! N6 ^- i- w" {$ e1 N2 ^" Q
Fermat’s Last Theorem. 4 q/ A0 c. o' i5 c
the first case of Fermat’s Last Theorem.
( C, r2 F. t3 f' |# ?) }) }5 OWall-Sun-Sun primes. . S! d( |9 h6 H
Fermat-Catalan equation and conjecture. 6 ]( A' a% R V) ]0 l
Fibonacci numbers. / F- b3 D% @# V
divisibility properties. ) l: l$ F: R3 H4 t, V1 ~
Fibonacci curiosities. , t. e# B5 v8 A3 d+ T
édouard Lucas and the Fibonacci numbers. - r( K) d7 S0 [
Fibonacci composite sequences.
9 H5 O) v/ G$ C! h. G' yformulae for primes. S+ o5 a& W. ?& A% |! ]
Fortunate numbers and Fortune’s conjecture. ' G" @6 t: w) j4 Q r% e; M
gaps between primes and composite runs.
; U$ s" ]5 k0 b0 ^& \% Q1 FGauss, Johann Carl Friedrich (1777–1855).
3 r, s' m0 j& l, fGauss and the distribution of primes. 9 g" S8 N5 U; F4 B) ]' i
Gaussian primes. 5 p2 ?5 b) l) M6 i7 ]/ r
Gauss’s circle problem.
7 K" y4 p8 R5 G7 k# A5 P( \5 rGilbreath’s conjecture. 8 j% P! G( S/ ]/ y0 B
GIMPS—Great Internet Mersenne Prime Search.
0 m/ R6 l2 J" L, N- D& f" i( @1 wGiuga’s conjecture.
7 M7 k+ F0 j; W \ @Giuga numbers.
$ g; W3 o; Y }& a9 s% S/ bGoldbach’s conjecture.
2 A7 a# V3 u0 `% k: o# N- kgood primes. ( L8 d" C: v5 x. v0 ^7 u G
Grimm’s problem.
; L1 ]; N- _" `3 Y6 y, J M: OHardy, G. H. (1877–1947).
! B! ?6 b& w# e/ ?$ bHardy-Littlewood conjectures.
3 @# y1 K$ K9 w$ Iheuristic reasoning. ) E8 j" }* W+ ]5 o+ M- H
a heuristic argument by George Pólya.
# ^5 J$ @( l2 S _0 p8 OHilbert’s 23 problems. + ~* x9 k3 u$ Z' m9 v
home prime. / S4 D' K/ ~/ j6 P
hypothesis H. 4 W% q& i; _2 `3 i3 a. c
illegal prime.
% \4 X( i. B2 T* d, binconsummate number. $ w B/ F4 y% Z L% z0 M; q& _0 F
induction. + N+ ~& k) n/ h% }; {
jumping champion. 0 t. S. P ?7 Q2 \4 ~- {
k-tuples conjecture, prime.
5 m% H6 d. _% M3 |- iknots, prime and composite. 2 n. v9 y; {& C: S+ p' {. d
Landau, Edmund (1877–1938).
4 I/ d6 x5 o4 t% {9 Pleft-truncatable prime. 1 V8 D3 j, w) f. [. h. m, ~2 ?
Legendre, A. M. (1752–1833).
) e- o# `* x* x$ }: s SLehmer, Derrick Norman (1867–1938).
9 d* w4 X V5 [. TLehmer, Derrick Henry (1905–1991). - S% a! S9 c" [, S6 a* S
Linnik’s constant. T) h0 u W. d( z' K
Liouville, Joseph (1809–1882).
5 a4 h% B, m- N* ^" E7 X2 D& [& ELittlewood’s theorem. , t: c* Q# L C; l* R N
the prime numbers race. / S7 B$ @& i0 @, e* s+ L& R
Lucas, édouard (1842–1891). 1 L2 U6 m9 C! }! l: _
the Lucas sequence. 0 T' N* B* v4 T3 L0 r' k, {5 C0 t
primality testing. / s: X$ P5 K: d# V: p
Lucas’s game of calculation.
 _ c! W, u: Othe Lucas-Lehmer test.
! l& D, h+ \, K; {2 [, A$ d0 Slucky numbers.
, ?" p7 ~8 }4 L& _1 W4 K8 Y; r* V# m. mthe number of lucky numbers and primes. ( o; t$ y1 k9 S1 [6 ]) a# |9 J
“random” primes.
% }& w* b k; j4 w( w" Nmagic squares. 0 r2 y) i5 A+ }8 j# H) b. Z
Matijasevic and Hilbert’s 10th problem. % N3 N3 y$ t& k3 e; C
Mersenne numbers and Mersenne primes.
7 B$ R+ Y# u' \0 C- yMersenne numbers.
$ @. J: N0 [- Shunting for Mersenne primes.
. b$ M! q, [, ^. bthe coming of electronic computers. " y0 F k5 c# n; e+ }3 ~# O
Mersenne prime conjectures. * k7 w: o! e# a; c c6 E
the New Mersenne conjecture. 5 N% f' p; k: J5 r2 k6 s! F
how many Mersenne primes? ' @5 J0 `8 z5 Z
Eberhart’s conjecture.
0 k/ T9 O7 e: J- {. e, f7 K" `! Y ]factors of Mersenne numbers.
( r- {8 {, D G. ~% j4 _1 t4 u6 mLucas-Lehmer test for Mersenne primes.
, m( K9 B5 b# A* C# M0 pMertens constant. ; b2 M$ n7 ]+ r8 ?' Z: ~
Mertens theorem. 0 S ]( W( o" f3 |" r, T3 O7 F- {+ N; d
Mills’ theorem.
8 X. q/ {, K. K& hWright’s theorem. # D; i, ^7 b2 _9 I. w5 q
mixed bag. 1 J2 x$ ~1 T& O9 ]: T5 f% \
multiplication, fast. , w" u8 D& v6 I
Niven numbers.
( T) J# x2 g N6 Rodd numbers as p + 2a2. , E* l. V. f) e, d
Opperman’s conjecture. 9 U8 O) S2 | M* A* K b
palindromic primes.
. G/ X3 k7 z# c. i5 c$ Rpandigital primes.
5 a8 L- H/ r4 @8 i9 {- oPascal’s ** and the binomial coefficients. 7 ]; t5 P! S* F" j$ l3 i
Pascal’s ** and Sierpinski’s gasket. . S5 W8 s6 Q9 F/ q
Pascal ** curiosities. 5 W5 [; G1 }& D' _1 U5 V9 R7 O
patents on prime numbers. % j- g/ Q2 E: U3 F
Pépin’s test for Fermat numbers.
! ]' o, ~' C, i: G0 S0 ?perfect numbers.
! g. L* b1 p! J: l+ ~1 uodd perfect numbers.
0 v8 X# q a( mperfect, multiply.
9 G. E( v. l: jpermutable primes.
. f; A& ~' G6 U# T8 F: N" sπ, primes in the decimal expansion of. 3 b" a) w6 T. A+ x2 W b; J: N
Pocklington’s theorem. ' Y. w, ~+ r; u' T
Polignac’s conjectures.
- O" p" e( {3 c% }Polignac or obstinate numbers. . M) }/ j3 s# P' e. w
powerful numbers.
7 ?, O/ P. ~! l4 r# r; tprimality testing.
. [# [4 m2 z$ q/ X, i, {probabilistic methods.
' \+ W3 o% [5 N6 g5 xprime number graph. ( }! ~4 r- F+ [% W0 P w4 [3 S+ u
prime number theorem and the prime counting function.
7 q9 n! {4 G1 ] A) e+ chistory.
 V% a' a' A0 D( gelementary proof. 2 B" |- i! M Z
record calculations.
4 x9 v4 n+ B1 q- F! t3 Q, f. eestimating p(n). ! d! `# p6 G: G) U4 t
calculating p(n). : Y% G. ?( W& J0 m* i) Y
a curiosity.
- q0 `/ h1 a) \prime pretender. 3 d. y" k" W) l/ z1 z4 Z
primitive prime factor. 3 n n$ Z/ X2 k4 t3 g! F' \
primitive roots. 8 o' z4 x/ s6 b! o" k
Artin’s conjecture.
/ i. _) }6 g5 `/ b1 g* Q3 Ga curiosity.
* |/ b# _' q( \/ t; [" iprimordial. 3 \0 M. C" G. k
primorial primes.
, ]. N# a: _( @, I4 S8 f5 NProth’s theorem. . J W/ \* V# S" S8 d0 G& N
pseudoperfect numbers. 6 F5 h% P l% B* [9 s8 a( C5 m
pseudoprimes.
6 E- S. k- C, N. Zbases and pseudoprimes. 7 H$ b$ a2 p! Z
pseudoprimes, strong.
4 T( g+ A5 k7 \" Opublic key encryption. 9 w4 q) y7 G, T) z
pyramid, prime. 0 i& F/ W+ v& b/ K! l! v" L- i
Pythagorean **s, prime. }4 I7 B. i" P, [. i$ M& P4 U" r
quadratic residues. ( v: j3 i' F5 @: q. ^3 y
residual curiosities.
8 D; j. A' Z- J: ], b5 y7 Jpolynomial congruences. 8 N2 r9 s8 o; {- f
quadratic reciprocity, law of.
1 i6 y6 V _ ~7 U6 v; _$ Z3 H7 `Euler’s criterion. 0 ~' R" V7 C( M8 g
Ramanujan, Srinivasa (1887–1920). 7 L2 c8 j# H, R0 y: F& }
highly composite numbers. " \" M* ?5 b% o4 b
randomness, of primes. $ K5 x9 f; B4 X6 v9 X" m
Von Sternach and a prime random walk. # u0 G* c& ]+ `9 d0 O% q
record primes.
9 o; R( K/ o( l8 hsome records.
; ~) U' B. _) q# Srepunits, prime.
4 ^+ N4 R, k, }Rhonda numbers. ! a) T" R& u. `) C! P
Riemann hypothesis.
2 ~! F3 Z9 q0 o* E+ G; Lthe Farey sequence and the Riemann hypothesis. 4 _- y! Q: T0 \1 J# ?
the Riemann hypothesis and σ(n), the sum of divisors function.
0 H1 s+ U5 W U6 O4 Msquarefree and blue and red numbers.
4 G" M3 I( V. e7 t6 _% X6 f9 ~the Mertens conjecture. 9 J! ]) b( [7 X8 k; ^7 b: w3 I
Riemann hypothesis curiosities.
6 ^& Z, S3 E& W2 K& u1 R* B# YRiesel number. $ u" X# I8 z7 ]8 I5 }+ ?" V& g1 D
right-truncatable prime. + i" r" Y9 J( K8 `
RSA algorithm. 0 `- e H' |& H g, h0 ]6 C
Martin Gardner’s challenge.
+ | b. {5 L7 w) Y4 r7 pRSA Factoring Challenge, the New.
$ X. K4 V: {2 h( ^8 s9 C8 B; n. Q. eRuth-Aaron numbers.
( n. ]; X* @4 v$ {Scherk’s conjecture.
8 g, e8 v2 M6 L$ e+ Ysemi-primes.
 t# O& _5 z1 D- Z**y primes. ! O! k( f6 u/ V- P. E/ z' c
Shank’s conjecture. - b3 K, T8 Y! o4 U
Siamese primes.
/ U( j; e# m2 h2 }0 qSierpinski numbers. . C0 v3 F2 B1 Y+ S0 b# `4 c( [& D
Sierpinski strings.
2 `2 m8 j4 M- }) w7 \Sierpinski’s quadratic.
: _0 m2 Y+ \, `) M" ^! J& i9 _/ lSierpinski’s φ(n) conjecture.
) I, h8 b: B5 S$ v& W) KSloane’s On-Line Encyclopedia of Integer Sequences. 7 [# X$ N' z0 }2 a C% t
Smith numbers.
, Q' t; r0 P3 k2 ?Smith brothers.
7 U' _ O' r2 z! P+ Dsmooth numbers. 1 w, g! W: j% U7 ^
Sophie Germain primes. & q; ]& a) V: N% i
safe primes. ) b1 x W+ \4 I4 l2 f
squarefree numbers.
! U2 |8 y8 S6 }- Y; D) V9 y5 Q4 ^! g+ DStern prime. & b3 |9 U2 Q# | ^ B
strong law of small numbers.
; l2 _$ P( l- o, K: `: |( ^6 wtriangular numbers.
5 _: ^+ c0 `' |; M+ S6 k9 rtrivia.
; G' Z! l L$ M1 Y- ~$ Itwin primes. * b C( @5 d8 C2 S
twin curiosities.
, D; o& i* h) H9 IUlam spiral.
3 G3 n1 C. H- Yunitary divisors. , k% X$ p3 k3 ]7 e1 y5 V2 ~8 b
unitary perfect.
3 I6 o) W; N* @/ \0 {untouchable numbers.
" u" _8 d" s6 P* ?, _weird numbers. ' T: s ^' h2 |
Wieferich primes.
8 R/ y" W" |3 o) QWilson’s theorem.
: b2 _% U( S/ T3 p% k' Mtwin primes.
, S9 C9 q+ M3 {' E0 F8 ]. ] r* ~Wilson primes.
# d* A0 k1 c0 bWolstenholme’s numbers, and theorems. ( g% B, g) \8 O" _ ?9 r2 |
more factors of Wolstenholme numbers.
( p7 s+ c7 N. J, eWoodall primes.
4 }& n/ B- ?! U: lzeta mysteries: the quantum connection.