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数字的奇妙：素数

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Entries A to Z. 7 Q4 E. G$ T4 z% k3 M) ~4 I& l/ S
abc conjecture. # Z) g' \6 r8 O
abundant number.
$ L9 i) H8 ^" R, t- @1 t& f) J1 KAKS algorithm for primality testing. Q* p( ]9 e4 T( r5 F7 C3 M4 t
aliquot sequences (sociable chains). 0 V. d0 @: V0 X
almost-primes. ! I0 u1 A. ~6 e8 I1 B0 z9 k
amicable numbers. 9 e3 G4 L9 V# f2 B1 p! u
amicable curiosities.
* E( A0 w7 c uAndrica’s conjecture. + V! P* R: R# w) O9 {% k* ]5 o
arithmetic progressions, of primes. $ C# o# Y; w7 ^/ M2 y0 P. H0 m w5 G t
Aurifeuillian factorization.
* Y8 y& K' b( G. Z" oaverage prime.
% k2 p% p$ b. u6 z7 p5 ^1 b! ~Bang’s theorem.
 H4 J: _, u5 bBateman’s conjecture. 6 ^& [6 V/ i. z3 z" c. ?9 w- r
Beal’s conjecture, and prize. . y2 G/ \6 [$ u N) u
Benford’s law.
& C I8 h- n9 E' D# O/ n: hBernoulli numbers. 5 j p! C1 [" e" f8 n* y9 c# a
Bernoulli number curiosities.
/ {' D0 f0 E6 v4 n( Q# C/ iBertrand’s postulate. 7 z! i. N `% T2 I
Bonse’s inequality. + c6 E& ~5 A: g5 Y) B
Brier numbers. , b# j% [ D9 d, M
Brocard’s conjecture.
$ V2 V. E9 G" d* A7 D9 L! RBrun’s constant.
0 f# N" U+ e( j" L v) jBuss’s function. + \1 C" K ^3 i
Carmichael numbers. ) l% N8 U/ y0 R5 M; o3 ?
Catalan’s conjecture. 9 c5 u9 O( i( Z" Y
Catalan’s Mersenne conjecture.
& Z* |& V6 W' kChampernowne’s constant. * Z2 ]3 [7 o- W' X" q3 l/ l- n
champion numbers. & m+ g3 _& k5 }8 {+ l% f) }+ g b
Chinese remainder theorem. 5 H. X' h2 ~/ v/ ?& j% S- a
cicadas and prime periods. % ^* @7 r3 B7 N, z- I
circle, prime. ) T, B" e1 F3 f% L; z8 h D
circular prime. ; k j% k: X7 p! C1 r& _! @8 g$ S
Clay prizes, the. 3 b! t9 i _- a( |
compositorial. ; y8 ~4 ^0 X: j( @1 q
concatenation of primes. 1 Z1 u8 y% ?# J. p+ X6 Q$ F) i# U
conjectures.
3 M$ }- T1 u0 a z+ Qconsecutive integer sequence.
 F: U) V1 z$ ^3 Lconsecutive numbers. 7 w" Z8 _# b( J, `
consecutive primes, sums of. . X: |9 z. S& r, v
Conway’s prime-producing machine. + F, B; ?" X3 m
cousin primes. " M3 |" t1 j! t4 m
Cullen primes. : v/ g1 G- @( Z; @
Cunningham project. . d1 b, l0 |9 c. {4 B2 o- l
Cunningham chains.
 l, _3 H7 M/ C4 h% ?$ r0 [decimals, recurring (periodic).
" E4 I. Q, T; R* u6 T$ }* Vthe period of 1/13.
% M# r3 T' Y/ v2 Wcyclic numbers. % I" c; T9 p9 t* M( e6 L# T" Y
Artin’s conjecture. ) R! m6 d8 ~3 e5 X7 t2 h* O/ @
the repunit connection.
3 m; D8 Y7 a: \9 |2 j; H' [" X. Rmagic squares. 8 B' S& } t5 a E0 Y
deficient number.
' V9 x* z2 Q& ~; d# d) P& ydeletable and truncatable primes. ; r3 I$ I V! T0 ~7 c8 p
Demlo numbers.
6 D) O! c$ M8 E/ P" wdescriptive primes. - F6 e( v( I1 ?/ A% z
Dickson’s conjecture. + Z5 k4 k3 t% B5 z1 }! l8 X
digit properties.
2 {) B, h, `: G# N1 c4 BDiophantus (c. AD 200; d. 284).
- v6 g2 k$ C" V6 j5 z* _5 eDirichlet’s theorem and primes in arithmetic series.
! _0 H( [& o& E1 g6 o" P9 B+ ^primes in polynomials. 4 v3 j: P9 q1 i8 R! l: ^
distributed computing. / i* @7 J- n! q3 C
divisibility tests. $ t1 V7 W4 L" d& Q
divisors (factors). 3 t# X+ v2 p. x5 u# p9 }
how many divisors? how big is d(n)? ) I4 b* o |1 |% ? {
record number of divisors.
( O: p4 G! b. E3 j+ Y3 @3 Rcuriosities of d(n). 5 n5 n. `" f( W8 u
divisors and congruences.
8 _5 c: ~! N& [! d( W& y9 Fthe sum of divisors function.
: `# e. c; x. P9 b+ xthe size of σ(n). " m) j# O- Q3 c! p* e
a recursive formula.
7 [9 g# N/ h v& z( L/ ndivisors and partitions.
9 v s8 T1 m# y" Ocuriosities of σ(n).
% N1 t* _/ _7 |6 [* M6 L7 _% hprime factors.
/ n% W' t9 U" i8 U& w2 @8 U; idivisor curiosities.
" T3 `. \. M2 t# x" Zeconomical numbers.
% t: G+ P: D- y& e; _3 UElectronic Frontier Foundation. 1 U/ d9 r0 `7 I
elliptic curve primality proving.
emirp. 6 o4 {- f* B& [7 A: S
Eratosthenes of Cyrene, the sieve of.
$ z$ @$ k" ?$ M6 v: I8 _5 z+ @% |Erd?s, Paul (1913–1996).
' j* \: l2 |- S, [his collaborators and Erd?s numbers. ~4 ` i' J% r
errors.
- J, ]. g d- w" hEuclid (c. 330–270 BC).
' F; Y: p, T2 O: D% ?% f" Gunique factorization. * f" I7 B6 F7 R% c, m1 Y9 e
&Radic;2 is irrational. : V% s6 ~% M- E5 s* M& P
Euclid and the infinity of primes.
, ]/ _: v& E8 K# ?& econsecutive composite numbers.
2 Y2 U+ H. L0 |1 J: [& ?primes of the form 4n +3.
. Y( j% ]3 h9 U1 e( Oa recursive sequence.
, g, t! }8 U ]& B- X, pEuclid and the first perfect number.
9 t3 A8 f1 H# H& x/ xEuclidean algorithm. ) ^* V6 M9 x9 A9 L' ~# d) Y
Euler, Leonhard (1707–1783).
" E4 g2 z/ q. q1 wEuler’s convenient numbers. 9 `" i8 @9 H0 G# c
the Basel problem.
. v9 H% Z/ ~/ _7 _, A* LEuler’s constant. # @8 w6 z! b, j3 g8 X
Euler and the reciprocals of the primes. / W1 D( s# G e
Euler’s totient (phi) function. " z0 I+ X# h" E' H
Carmichael’s totient function conjecture. 3 U, \, z9 F/ Z0 _- [; R6 E: e; V
curiosities of φ(n).
6 c& j% V8 @4 \! n7 X# hEuler’s quadratic.
1 F8 T* X. j- J4 ?& V+ bthe Lucky Numbers of Euler.
) }' }" y" j5 g# sfactorial. 5 S- k3 e: [$ e+ J. S
factors of factorials.
5 w g# G) m I8 @factorial primes.
' _' B p6 o; ifactorial sums. % s( w, z* _+ D3 x) b- p/ ^( e1 r
factorials, double, triple . . . . & j& u2 ?: S; y" j
factorization, methods of.
) A8 V8 d$ N+ o% y, Q% H( rfactors of particular forms.
% X( g2 L' C* l0 F7 |: {Fermat’s algorithm.
4 S! `7 p3 ]4 ~6 v. BLegendre’s method.
; B; T3 Z$ s8 O" e, c9 T# Scongruences and factorization.
 `* Z& Z7 [3 I4 O; \. I" Uhow difficult is it to factor large numbers?
0 T: o1 R' I6 A5 u5 j% M2 n- squantum computation.
7 a3 s# t: }7 v! { hFeit-Thompson conjecture.
# l0 ^" T$ @4 m3 j. C3 qFermat, Pierre de (1607–1665). J4 C+ j& h. W
Fermat’s Little Theorem. 6 \. S( x/ f3 U3 |1 J* |3 _
Fermat quotient. : h: }9 Z1 P/ z" i+ B+ P# ~: w
Fermat and primes of the form x2 + y2.
Fermat’s conjecture, Fermat numbers, and Fermat primes. * m5 p6 M+ |: C, r9 P- q5 Z
Fermat factorization, from F5 to F30.
9 N, U, m9 F9 \# @+ dGeneralized Fermat numbers.
4 o3 p! [; L7 k3 L2 J; k3 [# nFermat’s Last Theorem.
; v, f: b; T; tthe first case of Fermat’s Last Theorem.
7 Z5 x* ~+ ^8 k J" [. t5 _, @Wall-Sun-Sun primes. 9 x* k$ N3 L2 G
Fermat-Catalan equation and conjecture. : \; X# ^2 R, o6 f) y6 h' d# A7 `# ^# y
Fibonacci numbers.
& w: ]0 i0 d# q. Edivisibility properties. 2 W% U6 U" a; p* C$ Q
Fibonacci curiosities.
- k& U1 j: i% Q3 D- nédouard Lucas and the Fibonacci numbers. 7 Q* E- M2 I/ r' Q6 U$ ?
Fibonacci composite sequences.
4 _7 k" Y$ f! I& n- m/ x" i1 k8 aformulae for primes. . V$ r- H5 F4 Q( B* u |! i5 l
Fortunate numbers and Fortune’s conjecture. , L; R, S y/ d
gaps between primes and composite runs.
* f! s6 D! i6 DGauss, Johann Carl Friedrich (1777–1855). # T. y" m, \+ ~ o6 m6 z1 v
Gauss and the distribution of primes. 7 V* K. Q# g$ R; k- L
Gaussian primes. 7 k) P# Z# _) z/ D2 V) S$ q
Gauss’s circle problem.
4 z% o2 s; C$ _& y. ]$ g9 oGilbreath’s conjecture.
0 N5 V, g4 @ {. I; cGIMPS—Great Internet Mersenne Prime Search.
) P& v$ o# h9 `# ?, O4 S$ e6 MGiuga’s conjecture. 8 P; |+ F4 x) }/ O( B! E
Giuga numbers.
8 c# H/ h! R1 VGoldbach’s conjecture.
& t5 j4 g$ @$ I* g) S9 Pgood primes.
2 \8 g3 x0 R% e, v4 [Grimm’s problem. 2 @; x) r1 U- Q- ]$ s: S
Hardy, G. H. (1877–1947).
: K6 h. g; `0 R( n R( `) vHardy-Littlewood conjectures. 5 P% y5 R( ]6 J
heuristic reasoning. ! a" m q# q/ Y! V$ h
a heuristic argument by George Pólya.
$ [ w+ ]* X; I' E8 d- [Hilbert’s 23 problems. * i7 @! C) r% Q* J; [
home prime.
! P5 S2 K' ~1 r$ fhypothesis H.
2 G2 x$ m: e5 p' R) `illegal prime.
# k2 a0 i+ @0 T( Q! H: c- h: _inconsummate number. # x* n2 G+ s& |% m: }2 X8 M* ~
induction. S, P7 ^6 G* w$ c3 |! j
jumping champion.
9 B- E4 m( t# L& C/ l( g+ l$ }k-tuples conjecture, prime.
& o$ J: P6 S O4 `$ `& Wknots, prime and composite. 6 U! w8 W4 R7 |0 `" ?
Landau, Edmund (1877–1938). , v& }( l: e8 j
left-truncatable prime. # W1 g/ |5 Z9 \7 J. L( A
Legendre, A. M. (1752–1833).
& D; m6 M4 L6 {5 W* lLehmer, Derrick Norman (1867–1938). . y/ l6 h% J, t1 b: h) l/ Z
Lehmer, Derrick Henry (1905–1991).
6 i$ y9 f# C; b% A" O& lLinnik’s constant. 0 u: Z+ Y6 H% @, w( `( R& c; z
Liouville, Joseph (1809–1882). 0 h4 q" v7 M4 c/ n- Z, A5 X4 d
Littlewood’s theorem. 5 H4 M/ n; \9 J; _: a1 w# t
the prime numbers race. " f) x7 k9 m, w. j
Lucas, édouard (1842–1891). ( a2 k6 p6 P4 H m) I
the Lucas sequence.
6 P0 V! M( ]! u! P- G5 Bprimality testing. ' G7 Z% ]! z5 U# l
Lucas’s game of calculation. 9 {9 k# a% G& |* P1 t7 k2 X% F
the Lucas-Lehmer test. ; r1 a- \ H, J) [8 x
lucky numbers. 4 t- l' n* t+ B5 d T
the number of lucky numbers and primes. & C% I) P' v1 n3 h. i# ]( a, w+ p# s
“random” primes. + w3 {4 {) V( d0 [
magic squares. . [5 _6 h* d# I/ w! ~* o. }
Matijasevic and Hilbert’s 10th problem. |( ~/ l7 V9 X
Mersenne numbers and Mersenne primes.
7 j& m- P, B% tMersenne numbers.
" n! {. t E: e* t/ Ehunting for Mersenne primes.
6 |: S. P- G2 Z# i0 o6 c8 Ythe coming of electronic computers. / s6 H& Q8 u; k+ T
Mersenne prime conjectures. # m3 [# J W+ @7 C
the New Mersenne conjecture. ' K. Y1 i, g* P, \
how many Mersenne primes? 4 R& o5 K, n" w! A
Eberhart’s conjecture.
 H# ?: R9 S0 Y2 y' [2 q' Wfactors of Mersenne numbers. 6 K Z Z: K" T. y4 J
Lucas-Lehmer test for Mersenne primes. 0 b0 K3 u+ _ w7 U( o( o9 _! J
Mertens constant. . c* T6 h) C/ o! |
Mertens theorem. ! P( h' y" D' F6 v: j
Mills’ theorem. ! |, d# r; D& S2 J N# E W
Wright’s theorem.
4 N' r5 ]$ x' z2 Y+ R) Y2 {mixed bag. & e% e/ q ~, ]. `4 x1 S+ ^1 K
multiplication, fast. 1 }: P$ L# h5 s! Y7 s' ?
Niven numbers.
6 Q. D$ `: a* u% w X: S- @odd numbers as p + 2a2.
7 k7 G9 ~; @6 V' |' X4 Z3 tOpperman’s conjecture.
: a8 x. I; m% C3 Y; ~) V! t! [palindromic primes.
& V' q. P m0 w* r. c$ qpandigital primes.
. L. H! {. D3 Q0 G0 g6 h' bPascal’s ** and the binomial coefficients. & f& @8 [# y; E/ ]
Pascal’s ** and Sierpinski’s gasket.
1 L) o& T: q% ?9 G& w3 ~) x9 V9 d( uPascal ** curiosities. 7 b& @% q0 i. y
patents on prime numbers. * `& x# F$ c6 o4 T, ^- A
Pépin’s test for Fermat numbers.
/ F6 Q9 e4 t/ r7 d! Tperfect numbers.
& O/ m5 ? ]5 e% fodd perfect numbers.
9 x! c9 Y5 C* G5 j( P. x6 y8 fperfect, multiply.
* n8 s* |4 n" b) |2 @permutable primes. 7 m: x1 i; ]+ E) |1 m+ J) Q
π, primes in the decimal expansion of. ) j3 s: U2 M) J9 u
Pocklington’s theorem. 2 O( b. f7 f; K: M
Polignac’s conjectures. . h( N0 [2 y$ i- K( E
Polignac or obstinate numbers. $ ~* A" l1 g3 M! g- X a
powerful numbers.
1 y: V6 k0 |& k$ }) Yprimality testing. 7 b+ G3 t7 s* w0 P3 ]) X
probabilistic methods. . @% C" ~0 ~8 Q
prime number graph. 4 [* i. f6 G* R0 j8 n6 n- \
prime number theorem and the prime counting function.
% z- E( x! Q! y" s3 ~- Nhistory.
7 o0 W/ u( y) d2 [elementary proof. . S4 K7 y9 W* K) c+ f
record calculations. {; e/ h: g5 `: U6 h' b
estimating p(n). ( q e6 y. R5 \" X c5 ]
calculating p(n). . [+ r/ p- o: @1 H$ c+ ?
a curiosity. 8 m0 W) G0 u* s2 J& i" y8 l0 U
prime pretender. 0 d$ S8 S: V$ _2 {) v/ b; k( `
primitive prime factor.
% O! ]- B: P( Wprimitive roots.
% `2 U& s# j$ |, Z0 ~Artin’s conjecture. 4 U. w( Z# u2 F2 g7 D
a curiosity. 1 [- E0 m* j8 `3 a. k4 r* r" S
primordial.
 u6 k% {) U0 ~* @" wprimorial primes.
2 K1 a k1 @# T0 Y) iProth’s theorem. 0 D2 P+ M8 d h" e6 O$ q/ O
pseudoperfect numbers. ' w4 ]/ R0 V8 T1 N! Z. g
pseudoprimes.
8 ^9 T) D1 _. i8 p, abases and pseudoprimes.
* a9 M' L5 \* L: [& rpseudoprimes, strong.
" ^) F' j$ z; M4 R2 z/ |public key encryption. 3 o( ?. d& l5 _* q& v
pyramid, prime.
7 u4 K' s3 ]) `" APythagorean **s, prime.
- e0 {6 u/ M, A+ l9 Q xquadratic residues. ; m" c# A- f Q& H, S6 {' g
residual curiosities.
4 M- s6 n5 I; H0 z/ W: hpolynomial congruences.
( B! d3 \# X: Q7 v y: u: U3 ]quadratic reciprocity, law of. " m; ]5 Q7 Z/ M8 m0 e
Euler’s criterion. & d! g$ Y% [$ W# E
Ramanujan, Srinivasa (1887–1920).
) P) y' O' V9 Chighly composite numbers.
2 x7 s2 y3 U7 ~9 R5 ~: _9 arandomness, of primes.
) s. T& A' P! |) eVon Sternach and a prime random walk. ) b3 A, j" t& i; N# q0 t
record primes. 6 m" G; X0 F: d6 v0 F
some records. ; }% `9 k/ J4 L
repunits, prime. ! @; s5 D9 ]$ l
Rhonda numbers.
' _: J4 N1 I/ K' P/ ZRiemann hypothesis. " ]- ^4 L" T6 t' `; b9 c
the Farey sequence and the Riemann hypothesis. f6 n$ o* N, ~6 Z
the Riemann hypothesis and σ(n), the sum of divisors function. 6 r( _* K1 j% E" ]% E
squarefree and blue and red numbers.
' `. e4 ]8 I# }; s+ Kthe Mertens conjecture.
$ p6 Y. |7 Y5 y* {. `Riemann hypothesis curiosities. 3 ?# C) N1 e- `8 ?1 m. {
Riesel number. ' d) @% L' h/ r! E: r
right-truncatable prime. 8 l- v7 ?4 L! o2 K H$ a
RSA algorithm. 6 K- Z, f. ?# p ^% D
Martin Gardner’s challenge.
4 n3 X" X9 O' S! x$ ~+ L, hRSA Factoring Challenge, the New.
$ v4 m7 y, p0 K6 NRuth-Aaron numbers.
: V3 B, S4 ~$ j. Y) CScherk’s conjecture.
; h, i0 h6 x: ~+ U$ {- f8 Ksemi-primes. 9 m7 `7 [* Z; f( z g
**y primes.
) S4 J8 Y% a9 Z- qShank’s conjecture.
2 j) R. F/ D4 S) fSiamese primes.
* B5 H: Y: z5 m. `2 O6 k& xSierpinski numbers.
4 Z0 S( @, ~- S( gSierpinski strings.
$ i4 x3 w' G9 s/ cSierpinski’s quadratic. g- ?, ~0 d1 z4 M9 @; H
Sierpinski’s φ(n) conjecture.
) {2 P' J& `/ oSloane’s On-Line Encyclopedia of Integer Sequences.
; C4 V% \( N& x- YSmith numbers.
+ ?" H, X+ {8 _2 {: p4 @Smith brothers.
: t5 c Q8 a$ ]: |$ n& B/ j; i# gsmooth numbers. ' g( z& n! k# w2 {+ w; d) ?
Sophie Germain primes. - z; A q% T( R
safe primes. 3 w% i1 Z: Y# a9 |, j
squarefree numbers. ; r8 `* r& B2 k/ D( k% l
Stern prime.
! b D$ F( ?- {$ A A2 x9 Kstrong law of small numbers. ) J X9 ]9 A2 I$ w2 x/ x
triangular numbers.
0 l: I! K9 n1 }$ O/ O. ^; Vtrivia. : K) s* ]( U1 ~8 h- i
twin primes.
7 \3 v" o& Y' v% y' }& b9 Q1 e! Otwin curiosities.
5 |5 ~$ L2 M4 Q$ |3 fUlam spiral. 6 S0 ]7 S1 \5 { ~2 F
unitary divisors. 0 @! H1 E6 M; p( X
unitary perfect.
* C" Z j$ X" }$ funtouchable numbers.
2 X& M ]+ B8 E0 F1 qweird numbers.
- L. R+ H# y; `% S- `4 lWieferich primes. 3 s. c7 S; A; v; N
Wilson’s theorem.
2 I- x3 w+ R' F: i. f% q I2 Y5 v1 ktwin primes.
9 d% L, V0 m& B9 \Wilson primes. 8 |3 s% [/ V- J' S
Wolstenholme’s numbers, and theorems. 4 x- f& C2 M, Y
more factors of Wolstenholme numbers. 0 q. q$ o$ U1 C5 `, H
Woodall primes. + a8 G* _3 b( h' u5 J8 |
zeta mysteries: the quantum connection.