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数字的奇妙：素数

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以下是目录，如果觉得合你胃口，可以在后面直接下载附件。

Entries A to Z. 5 E% s" t& J8 Q; N0 U
abc conjecture.
4 d0 s1 |1 f) O E$ I2 aabundant number. # P$ [, c& i; L) j r% _+ i4 k
AKS algorithm for primality testing.
5 f9 A/ l& b( ?0 Daliquot sequences (sociable chains).
; `9 W" U, b; D; xalmost-primes.
) r' W! v- V- }1 |( H2 pamicable numbers. 6 C* ]/ A* Z% a z7 E
amicable curiosities.
- n- Y% X9 n) R# |* qAndrica’s conjecture. + `) @! v2 d9 U) R' k8 y
arithmetic progressions, of primes.
& a$ u- ]) W' ^8 Q% JAurifeuillian factorization.
" s. n9 B9 V8 D" H. j; Faverage prime. / V2 @( U. E g; k" L
Bang’s theorem. 3 T$ @- q% p4 ^% ]! y9 x( \# j
Bateman’s conjecture. * t3 K. S2 W5 S, H+ A+ G3 K* a
Beal’s conjecture, and prize.
4 }6 e5 ?, U1 z' J4 ^1 fBenford’s law.
2 y9 T3 L" ^5 n! JBernoulli numbers. % u+ m0 }6 Y+ @9 @( m8 W
Bernoulli number curiosities. & n8 g+ S/ H5 P8 j9 l$ r
Bertrand’s postulate. , x/ S% K+ G( ~' [3 N0 V" t- u
Bonse’s inequality.
! d0 Q" F2 p f( \( X. RBrier numbers. + y1 p4 g2 i1 _
Brocard’s conjecture.
- W+ X g, ?3 M; \; a, cBrun’s constant.
% {9 [2 K9 U+ W2 d5 BBuss’s function. 9 g- Y6 g. M. y* m J. E! v4 [, l
Carmichael numbers.
0 O7 d& Y) h& f+ ]Catalan’s conjecture.
0 C$ ^* z( M% N" i! cCatalan’s Mersenne conjecture. 4 g# X+ F, E3 e% v
Champernowne’s constant.
$ z: w& V6 s: T% c, dchampion numbers. 3 e+ D8 R; r9 U o+ W
Chinese remainder theorem.
7 y2 H* Q8 m( v, x- l# ecicadas and prime periods.
6 ^" u8 @# u2 N$ i- r7 G! Fcircle, prime.
9 K4 D/ j1 u+ Zcircular prime.
- a( ?/ {5 v% i# iClay prizes, the.
* B! c/ J# i3 V, zcompositorial.
3 A' s9 P# E$ O8 E9 T, pconcatenation of primes. ; Y% M4 v3 d7 w4 t
conjectures.
1 M: O2 u4 x/ \. Q$ a$ Oconsecutive integer sequence. + `$ a5 M3 V" A
consecutive numbers. 1 s( i* Q: N( X0 g! W" v; a
consecutive primes, sums of.
- n d8 J0 ^' R9 B( K0 BConway’s prime-producing machine. # @- V5 T, G" S2 [1 o& a4 |
cousin primes. + m, J0 p4 r" u. j0 N
Cullen primes.
) s- R9 w4 J- x8 ?9 RCunningham project. ' X2 l! E) F5 y3 L: O9 z/ g
Cunningham chains. ) V1 [5 U: x4 [. r1 ^
decimals, recurring (periodic). 8 `9 U% N. z. m/ j' s( U
the period of 1/13.
' L0 N7 Q z2 T3 |" }' r7 o0 B! {/ gcyclic numbers.
% v" j9 N1 {" Q* T! pArtin’s conjecture. + a, |( F/ h0 |1 k; E
the repunit connection. " ~5 {! [+ ]' G1 i
magic squares. $ I2 g1 F* `& l1 z
deficient number. 7 y& |7 ~0 [4 J# ?7 L( Q, ~) F( }
deletable and truncatable primes.
! m) s7 t- x6 P$ \) w5 `. tDemlo numbers. , m( h! |/ `* K' Z# m
descriptive primes.
! K/ S& K4 f8 D& `# r' y9 nDickson’s conjecture. 2 Z# ~$ s8 R0 p( v0 I
digit properties. % f e0 |& p/ g, v. ]6 C
Diophantus (c. AD 200; d. 284).
$ \7 t# F* L6 Q' r _! K( wDirichlet’s theorem and primes in arithmetic series. ' f- V4 ~) b/ d* \1 d
primes in polynomials.
0 S$ K1 Y# o, b. H2 Mdistributed computing.
/ N# r: S' c$ m5 ?! {: gdivisibility tests.
& e- P8 b: v- y4 h. e1 S4 Edivisors (factors). 0 Z6 T# ^9 {+ n# |* i
how many divisors? how big is d(n)?
8 u" ~# K S- v- ~9 Z* arecord number of divisors.
4 V' n! k2 Y6 i' A- {curiosities of d(n). + i9 l& U. x- B1 c3 n
divisors and congruences. ) ^, m! y( L7 ^1 T; c+ G5 m/ G
the sum of divisors function. $ v# b" w0 B# ~% g; I' Y
the size of σ(n).
0 D9 k$ F0 a1 T0 Aa recursive formula. , x+ D( L' R M
divisors and partitions.
! H& F8 ~5 T+ Q8 |curiosities of σ(n).
, H& U, ^% S7 C3 s( sprime factors. $ P3 C% a8 t* y3 {. r9 u
divisor curiosities.
! C1 p! h4 L+ s, x1 geconomical numbers.
0 ~" d2 g/ g; h) @9 GElectronic Frontier Foundation.
3 p1 y* z$ {& g7 R7 X9 ielliptic curve primality proving. Z1 Y5 A5 L5 y& X. Y$ Q
emirp.
' e& G8 L' O# [% s5 r6 B- }+ LEratosthenes of Cyrene, the sieve of. ; s- X4 L! [/ Q* \* y" C3 U
Erd?s, Paul (1913–1996).
' ~) I! u$ |5 e! g& @! z fhis collaborators and Erd?s numbers. 6 S0 p$ B! k }1 J% O
errors. % K+ [" c5 x! B+ {" t% q; n) d9 }7 o0 R
Euclid (c. 330–270 BC). " M& B4 `% w1 Z0 t! Q
unique factorization. $ o5 z0 j. p7 V
&Radic;2 is irrational.
# S2 z3 b/ w/ c6 }- XEuclid and the infinity of primes.
* d/ Q: P+ i& y+ Wconsecutive composite numbers. . |- b' c6 N3 m6 j
primes of the form 4n +3.
8 g8 E* J. z1 J3 [; s% ua recursive sequence. ! K. V& y2 C! A/ I6 `
Euclid and the first perfect number. % s" o: k9 x9 \
Euclidean algorithm. ' Y- X. t! G% @7 N* H
Euler, Leonhard (1707–1783).
$ R7 S* Q/ Z$ m% yEuler’s convenient numbers. - \4 @' N& Y$ Y4 v7 t
the Basel problem.
9 F- o% u( b, pEuler’s constant.
7 K, _7 O) a$ X# q8 zEuler and the reciprocals of the primes.
+ L9 T9 q) l, c7 Q5 tEuler’s totient (phi) function.
5 T5 J( o: d: _$ {% UCarmichael’s totient function conjecture.
( {& h j( o/ F8 t+ _curiosities of φ(n).
* e* t0 r, d: y- T7 jEuler’s quadratic.
5 M! y0 g" b; Y6 o5 _the Lucky Numbers of Euler. ; X+ F7 ]* Q4 c( }4 q6 K
factorial. * \# G9 I& a# }% F: V3 C* G
factors of factorials. 0 j+ k+ y. i) [ v0 W% p7 d
factorial primes.
6 A" b6 R. s* ~factorial sums.
! C8 O, |4 M3 o) F7 tfactorials, double, triple . . . . / V7 L" E7 b$ ]6 R6 }0 z. E* b
factorization, methods of. + U% v! _) g1 C0 {8 D8 c }
factors of particular forms.
 g1 J" ~' E' s5 KFermat’s algorithm. 3 \$ m. r2 r) G4 u0 }
Legendre’s method. $ w* p; `+ h( ^/ v% G' g
congruences and factorization. ! O! j4 b( Q5 _' |( |
how difficult is it to factor large numbers? ) E8 v. _9 f, L, K4 Y3 U
quantum computation.
1 Z3 t0 ~8 s! b. m- G+ w) ~Feit-Thompson conjecture.
, D# Q* H0 p# l2 E4 h7 d& uFermat, Pierre de (1607–1665). - u' P7 O: P3 u% H7 R7 W- Z. s; O1 X
Fermat’s Little Theorem. - c3 \6 ~" E' |$ O/ s' J
Fermat quotient.
+ @3 T4 x7 I# m4 H7 K3 HFermat and primes of the form x2 + y2.
4 @; u& ^2 T. }2 p* v/ T# }) _5 nFermat’s conjecture, Fermat numbers, and Fermat primes.
5 @& S. O+ m5 |0 S0 EFermat factorization, from F5 to F30. 2 w: v M8 v# c& V+ t; x1 J8 @
Generalized Fermat numbers. 6 x9 i) I3 \( L7 Q! d
Fermat’s Last Theorem.
) K# g. |/ s# H: `the first case of Fermat’s Last Theorem. 4 p- Q y7 c4 i, q- g
Wall-Sun-Sun primes. 2 i ~8 E$ l, [0 U
Fermat-Catalan equation and conjecture.
: R; P. {/ U# kFibonacci numbers. + k2 V" E/ P; u& J( o L6 I) U2 D9 Y& A
divisibility properties.
2 `) ^, R4 F+ ^1 l9 g, Z) vFibonacci curiosities. 3 P0 V: X6 ?- ^2 C' y6 G! F
édouard Lucas and the Fibonacci numbers.
8 ?7 C9 U- J$ }. C. q% GFibonacci composite sequences.
. N' t3 c d# G4 f/ x2 N2 t' fformulae for primes.
: v. C# E z. bFortunate numbers and Fortune’s conjecture.
7 d# M! N1 p( c: Egaps between primes and composite runs.
/ |4 p, @/ J' RGauss, Johann Carl Friedrich (1777–1855). u* {1 Z6 m: L
Gauss and the distribution of primes.
; W3 ~4 d$ D: _' [Gaussian primes. ' ?6 I& J- |/ v( T& L( ?5 X0 X$ H4 M
Gauss’s circle problem.
* q# m. a! E$ X% a# PGilbreath’s conjecture. : r/ w7 ^7 P% k2 n. g- s0 C' }
GIMPS—Great Internet Mersenne Prime Search.
4 K }, W+ k$ ?Giuga’s conjecture.
0 }9 ^9 }9 E2 d# ]1 i5 lGiuga numbers.
6 D; _" d5 [ b# x7 w( TGoldbach’s conjecture.
% u8 \0 z+ q$ `* B/ g& ngood primes. ' S1 p- u7 l/ |8 t* Z2 P* w- L" Z
Grimm’s problem. 1 U! E2 |! a* x- c. O
Hardy, G. H. (1877–1947).
! J2 c3 A" }6 N3 c7 u. O$ jHardy-Littlewood conjectures. 4 |. z2 [/ Z8 U3 j6 ^& Y+ L/ }. m2 ^, a
heuristic reasoning. ( l h: Y2 V1 S5 J8 H$ W; X
a heuristic argument by George Pólya.
* v0 I" \0 S5 {& V1 O7 p. S" g6 n# {Hilbert’s 23 problems. ; b; M4 @! l9 Y7 c9 T5 i# I' q. w# D
home prime. 8 M/ C# I F4 R w; A
hypothesis H.
' m1 e: f3 }& E1 _- M1 Uillegal prime. ! J" c% b! j; P0 U5 \# g' F: H
inconsummate number.
6 q9 ~) e& P+ |7 {induction.
% S8 k7 [7 k6 i# r9 g/ L$ V0 P" w% J9 ojumping champion.
9 E3 S# _7 i5 |+ B6 t( }" ], ^k-tuples conjecture, prime. 7 a" b1 l! s* K8 p9 `$ D
knots, prime and composite. ' n2 g, b' \- l6 m9 Q) f* S1 B
Landau, Edmund (1877–1938).
) Q5 T: i" `" B6 T$ m$ oleft-truncatable prime.
/ w3 d# X7 y' v9 H! j8 pLegendre, A. M. (1752–1833). , O2 M" r2 |1 V4 G/ K" l
Lehmer, Derrick Norman (1867–1938). 3 H) X* J) g: ~) t. ~% z0 |
Lehmer, Derrick Henry (1905–1991).
' Y' U/ R& x- ?1 HLinnik’s constant.
0 X4 c; |( X2 `$ V( K: T' N3 yLiouville, Joseph (1809–1882).
3 O2 y# T. l3 g4 OLittlewood’s theorem. 8 r7 \6 i& J% s" @7 P& g( F
the prime numbers race. : X) g. |5 r5 R& X3 u) ~
Lucas, édouard (1842–1891). & y0 P$ Q3 h. S% C! |8 J4 Z
the Lucas sequence. 3 |0 W" q6 C6 E) A- A1 r$ a; }
primality testing. 9 L8 d6 w H7 x. O; ]
Lucas’s game of calculation.
; i" u6 R( R/ l0 u' k$ g2 y" F* F' athe Lucas-Lehmer test.
 N7 X, z2 r; blucky numbers.
- K: E7 T# o- d7 _0 G" f `the number of lucky numbers and primes.
/ N* {" O+ I% A* M“random” primes. B' Q% e/ t0 x* ^6 ^: d+ S7 |. k
magic squares. ( i! x' d1 _* c7 a
Matijasevic and Hilbert’s 10th problem. : }1 l) H5 P8 m1 p& P0 k& m" X; C
Mersenne numbers and Mersenne primes. 2 |6 A9 q4 d7 v4 _, U7 a: N2 p* v
Mersenne numbers. % W. ^6 a$ u% H0 I
hunting for Mersenne primes. 9 L+ u/ X+ k) f
the coming of electronic computers.
1 i# i7 F0 d: q$ [8 m8 a# CMersenne prime conjectures.
- ~% K6 ~1 t# M1 |) l7 x- N8 ]the New Mersenne conjecture.
. e' U8 {- _! d3 J2 Vhow many Mersenne primes? . j' R4 }8 t0 w3 A
Eberhart’s conjecture. 2 [' F* B; x' w5 s
factors of Mersenne numbers. & j" y3 c. j3 \9 P
Lucas-Lehmer test for Mersenne primes.
1 z6 w9 Z+ ?2 |2 lMertens constant. " ^. V d; i( X- z$ y
Mertens theorem. % ?7 D3 r* Z5 V3 ^
Mills’ theorem. 3 f8 f0 @% H3 K5 U% \/ e; F
Wright’s theorem. * O1 B5 C C, @0 A& ~+ g
mixed bag.
+ N; A; b0 r9 z7 amultiplication, fast.
7 X6 ?3 }- X# W" |0 bNiven numbers.
7 Z+ C- q+ x( H' Yodd numbers as p + 2a2.
0 m5 N7 ]5 @" e) w, COpperman’s conjecture.
# k# C) v- a: Dpalindromic primes.
9 S6 U9 n' ~% W1 L' X; c& K) zpandigital primes.
' n8 p+ W+ i6 F; pPascal’s ** and the binomial coefficients.
) f$ v7 N; {# Z5 HPascal’s ** and Sierpinski’s gasket. ! X( N, s; I# t+ ^
Pascal ** curiosities. ' X+ ~, Y4 J- t: ~5 p2 L
patents on prime numbers. - G2 j6 j( G; _6 L4 h
Pépin’s test for Fermat numbers. : x8 I1 N, a" ? [9 k) H
perfect numbers.
0 R: I9 r+ b* i, dodd perfect numbers. 4 T& a9 L5 m# |2 T! c- m5 O8 K
perfect, multiply.
6 r( K: W. C4 R3 m4 v: y7 Gpermutable primes.
0 ^8 k* @# O/ K' l0 ]9 ^3 R; lπ, primes in the decimal expansion of.
7 T! j/ M) M$ n, [+ g8 mPocklington’s theorem. 6 U) P' Z7 I( E% J! _1 |# R
Polignac’s conjectures.
1 h. e$ W; {& C$ D5 jPolignac or obstinate numbers.
3 @3 K$ y: S! @2 j! D! }/ G+ \. A ppowerful numbers.
$ k7 }& b# B& ~4 V$ u0 F* O l6 ]) lprimality testing. ; n8 i& `* J/ D9 ~- e
probabilistic methods. # {) U5 j$ ]' P2 C" Q* _
prime number graph. + y# |# } y. T. @1 K
prime number theorem and the prime counting function.
( \+ U4 P8 m: s; v) |9 s/ i) qhistory. 3 [# Y2 O. k" W; }% K* R+ ^
elementary proof.
* n/ T& B+ N3 N: N j4 krecord calculations. l/ j/ R+ Z8 h* D( V7 N6 J
estimating p(n). & l8 w' G7 |1 A0 O; k0 e
calculating p(n). & Z8 V6 [ _! ?, I3 I
a curiosity.
( }8 x& r( g+ G0 Z# x6 v" M2 hprime pretender.
; p, B+ [8 o$ Sprimitive prime factor.
6 M# V3 M0 A, Y4 sprimitive roots.
) w0 W4 i! _7 J V7 [: KArtin’s conjecture.
( P8 l/ T) c( B1 k7 za curiosity.
9 A: Q- i W5 Y# S/ r6 xprimordial. 1 t" n* v3 E9 a8 X. l9 @7 z
primorial primes. & j, f. {" x( n) i9 `7 @2 ? ^
Proth’s theorem.
( y# ~7 s5 i) X8 _pseudoperfect numbers. 2 \: n. `) [1 z
pseudoprimes.
 e, w) ]! n9 h. @bases and pseudoprimes. ; \5 u7 l6 Y A! M* ~ ^
pseudoprimes, strong.
; g! V0 ^) D& \. i* Q' f) `) ~public key encryption.
/ D9 F8 m' J9 P0 d2 D. }) Opyramid, prime.
. v1 @3 k2 _0 W8 BPythagorean **s, prime. 0 a! [% a. v( p W* ^
quadratic residues.
! q1 }# r3 M9 m; nresidual curiosities.
1 B& f7 j$ ~2 Z. n [ y+ Z( k0 |polynomial congruences. 4 P# u0 r5 q9 Q1 r* t% ^
quadratic reciprocity, law of. 5 }4 g M4 M2 c0 x: \0 W5 M% O
Euler’s criterion. . o3 w- ]% Z3 m" t9 N4 I j
Ramanujan, Srinivasa (1887–1920).
$ |% a3 C8 ?, O$ U' |highly composite numbers.
/ c7 f% v1 [1 B) i/ |6 m$ N5 Urandomness, of primes. ) C* _; N6 u, f" Q9 }) z
Von Sternach and a prime random walk. : H" {, }. W' } j6 l) Q4 C
record primes. & x; \! G N/ j9 S. d+ w
some records. 0 i; F; v3 K* V$ {" \
repunits, prime. + q; ]8 n8 X9 |: j& k( O
Rhonda numbers.
8 a% W. a+ I/ M% IRiemann hypothesis.
( ^# t" b% T7 y; m2 A U1 e2 Fthe Farey sequence and the Riemann hypothesis.
 b! [0 [. y9 r$ ~the Riemann hypothesis and σ(n), the sum of divisors function.
 D' m0 Y, O0 e+ Nsquarefree and blue and red numbers.
+ ~* g0 m/ S$ X) ~( [the Mertens conjecture.
# O' I& N$ C) z8 GRiemann hypothesis curiosities.
4 _& O3 w3 x6 n4 b9 JRiesel number.
! A& u% S9 a- \, Zright-truncatable prime. & C; i" ?7 |) J+ [* k" `
RSA algorithm. : l4 k9 {/ e' s( X' j3 e9 {$ ?) j
Martin Gardner’s challenge. % ?$ r6 o" G+ g( K2 o7 ~0 R
RSA Factoring Challenge, the New.
8 Y. _& l- S1 \! N+ V2 J- SRuth-Aaron numbers.
% L- _; Z3 s) J; M3 l4 JScherk’s conjecture. : z) |6 W8 Z: s8 Z. Z
semi-primes.
- A1 z; p6 V% L2 c**y primes.
- B. i& ^6 j6 J4 n# g, b5 GShank’s conjecture.
 G% X: R* V' N& k# F0 J$ u% XSiamese primes. ; S9 ^; _6 D* p5 h; H
Sierpinski numbers. 5 N% D6 X5 f. i4 S. N! K& u" ?
Sierpinski strings. # k! G2 k. K ^% H2 H; T! Q( U6 O$ m( X
Sierpinski’s quadratic. ( W; x, _5 Y2 ?! I
Sierpinski’s φ(n) conjecture.
5 l6 [( D7 Z% q; K/ h. RSloane’s On-Line Encyclopedia of Integer Sequences. 8 m. F7 z3 c" [8 N+ H0 v8 Q
Smith numbers.
7 h% B- Q4 c9 k: FSmith brothers. 5 D# _& L$ y$ x0 l
smooth numbers.
% j! u5 u2 F/ u0 |7 A( P# LSophie Germain primes. ! d7 ?0 o5 @9 `
safe primes.
$ Q1 H% G" O# B7 u- S. q! [squarefree numbers. 4 z; A5 Z* b" a& a% I
Stern prime.
6 C9 d4 k' M- I* f3 ~strong law of small numbers.
9 U6 N. `3 }5 S( N7 x/ k0 s. i1 E! htriangular numbers.
9 m( R# v, m' `/ ?2 ztrivia. 7 R) l. B; J' A) M
twin primes. . \7 [+ A# u- B! X% j
twin curiosities.
) _5 o* k. L. ~Ulam spiral.
6 x0 Y% U. A! M) i9 H8 k$ u# ]unitary divisors. ' A- D4 Q: G1 l% a6 ]
unitary perfect.
, y$ S1 T" e! d. a6 J& Euntouchable numbers.
6 ?/ p. |( q$ D7 w/ p. Bweird numbers.
/ Q* S, e! t* i2 X3 bWieferich primes. ! K- ^5 I% T3 Q( O
Wilson’s theorem. 1 Q8 p; ^8 z8 [2 r" U
twin primes.
0 G, `" y! p9 j' K' H1 \Wilson primes.
& ^" _$ R K, S( fWolstenholme’s numbers, and theorems. $ Q5 S5 b @# I# O& ~: Y
more factors of Wolstenholme numbers. ( Z; e$ m. Q; C6 w/ H' X
Woodall primes.
! K1 U3 c& a* W" c2 s; d& ?zeta mysteries: the quantum connection.