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数字的奇妙：素数

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Entries A to Z.
# `/ r! I) S' a* `( Labc conjecture.
$ k" l! ~. p( e& y) y; xabundant number.
5 S, Z2 w; z% e. ]# g0 y$ [6 WAKS algorithm for primality testing. * |7 b# l" r. j" ~+ ~' V* D
aliquot sequences (sociable chains).
- h5 v9 U4 D2 K$ F- j. f. Ralmost-primes. ' m- @3 Q% {% b* \# R. C4 g% M
amicable numbers. # P* I5 D& p0 ?# i
amicable curiosities.
2 e) E, ^; N# o+ VAndrica’s conjecture.
+ s. ^- R) c6 w, B- Q; X0 marithmetic progressions, of primes.
- t7 F4 I0 j* o/ OAurifeuillian factorization. 4 p J. w! z7 b8 \& M# F
average prime.
# m+ k$ L- v: z( T! CBang’s theorem. 2 D: j+ X0 p1 s# p% v* s3 j) _
Bateman’s conjecture. 2 ~9 ~( }: W1 b* O2 W% R! `
Beal’s conjecture, and prize.
7 c. E/ k5 F3 w. W1 g) _Benford’s law. # E0 o/ |$ Z3 L0 R
Bernoulli numbers. a9 E: t6 K6 q6 Y+ v+ I4 O
Bernoulli number curiosities. * U' n: F7 I! l* `+ z
Bertrand’s postulate. 9 @3 F9 @" M. y }3 Z
Bonse’s inequality.
) G$ F/ s1 W* v" m5 C$ KBrier numbers.
7 H5 r* }2 e, O5 n; r" JBrocard’s conjecture. & n$ i( b# E% n+ f
Brun’s constant. 7 y: N7 X5 M- Y3 U1 ~7 I
Buss’s function.
7 p# Q9 E* n: gCarmichael numbers.
; v, n/ p% T8 C H! r3 W- }! jCatalan’s conjecture. . J/ B) A* _6 n7 z: z4 Z
Catalan’s Mersenne conjecture.
; e: i: X* w5 T, G. AChampernowne’s constant.
0 s6 `7 j+ j: ^% N2 Echampion numbers.
9 W$ z0 `+ ]. d9 ?: M5 S! N3 u+ |Chinese remainder theorem. 2 I( C- }9 C2 P4 ]) l$ H' |
cicadas and prime periods.
# e0 O7 y) j! Z+ R* B" {circle, prime. T( y' J1 T) V4 e- E
circular prime. ! M5 ]0 G* v6 f
Clay prizes, the.
& v0 o/ o" I+ [& R/ pcompositorial. 6 w; C' o) X2 ]# _
concatenation of primes. ; w* S: n. d! r9 Z$ D: |3 b( n- k
conjectures.
& U8 ?! P( s) L& aconsecutive integer sequence. : @0 `1 M& U$ [. y( ?. a1 p8 z
consecutive numbers.
" m& S! L5 I6 g4 @consecutive primes, sums of.
5 }$ V, D; W; m8 @& `4 \Conway’s prime-producing machine. ( X3 n/ Q0 N. g
cousin primes.
. M, ?: x8 q1 B* o& H5 }& m }8 `Cullen primes.
0 A2 s( L: g8 v5 _) O( |! OCunningham project. : o0 n5 e% w" W( \9 ]: t E
Cunningham chains.
" I; j I$ I6 o2 Z4 q4 B1 b) Gdecimals, recurring (periodic).
! M0 H- i; d& A% D( ^& nthe period of 1/13.
( O5 F# C3 ?: \7 ncyclic numbers.
* o6 B9 j3 ~$ O/ b LArtin’s conjecture.
& ]0 j8 d% y2 o1 Z2 \" ]" C6 Athe repunit connection.
" C7 ]/ {: W) ], c( _magic squares.
3 |. V, p) h2 B4 vdeficient number. * {- I& i/ x5 P; n9 y2 v
deletable and truncatable primes. S% Z) O, N# p; c7 W
Demlo numbers.
! L) V! q; ], e4 T1 Y9 Hdescriptive primes.
- w H- g2 |3 Z0 f; b7 Z- G% |Dickson’s conjecture.
% t9 A3 e* G- S# f9 s- V2 c Odigit properties.
& w9 j7 K% R" G* n dDiophantus (c. AD 200; d. 284).
) v1 @/ b5 j- X% f3 r2 aDirichlet’s theorem and primes in arithmetic series. & H- _. [& L- \2 a! L6 P B
primes in polynomials.
+ a; D: s: s$ \, _1 E- V2 tdistributed computing.
% g" n% J f- _6 K6 v! m3 Rdivisibility tests.
- u# _) |0 f1 ] vdivisors (factors). 1 G* W* }# B$ D
how many divisors? how big is d(n)?
7 M. B3 Z$ g: ~; r. Hrecord number of divisors.
; ~# ?/ ?$ f' e8 M$ n' gcuriosities of d(n).
) V. d( c; K6 {1 b1 adivisors and congruences.
' ?8 P: K: Z0 s) j* Wthe sum of divisors function. @# L: M& r% k' ^
the size of σ(n).
0 L s* A, h6 c D) xa recursive formula.
 k6 `2 I8 F) s: A1 N mdivisors and partitions. 0 ?* s/ ~% P$ d
curiosities of σ(n). * V7 n5 n, Q9 h; }* Z
prime factors. $ r$ g; ~, J' w) P+ q$ W/ M2 E
divisor curiosities.
- p( U3 q0 D! B3 ]4 s0 W1 a peconomical numbers.
* a' c9 O' W$ A6 |) q# RElectronic Frontier Foundation. ; v$ P3 ]3 O* \7 x
elliptic curve primality proving. ; y: e" X. G' o* i" V4 b, c
emirp. 5 p7 a7 u# |6 p* q) j6 T, l
Eratosthenes of Cyrene, the sieve of.
' i8 r* M. Z2 x. `1 p- XErd?s, Paul (1913–1996). & S* L, T, n/ T4 y
his collaborators and Erd?s numbers.
5 F! ?3 w( Z$ g, `9 b$ Oerrors. ( r5 t( z! @: I, R
Euclid (c. 330–270 BC).
: ~* B# Z; {& @" K+ ]& D' ~7 B% Nunique factorization.
: s+ m* P/ Z" W3 B$ _& W8 f" J&Radic;2 is irrational.
 j4 f9 g; Y6 w4 j* l" sEuclid and the infinity of primes.
; p1 K2 W- F4 ]1 D, \consecutive composite numbers. 7 v: S9 p( e, Y% R* x. B
primes of the form 4n +3.
, h1 U5 x; y4 |0 J! ~! b& Ca recursive sequence. , E! R O, Y: n7 M( {: E
Euclid and the first perfect number. + _) ?1 R2 @$ F! H5 F7 K% g
Euclidean algorithm.
! v" q1 c. F. qEuler, Leonhard (1707–1783). # i/ f7 U: E' s6 e% A" ~$ D
Euler’s convenient numbers. 1 m) g& _; o. b# w8 _
the Basel problem.
! y2 k& p2 P6 H- VEuler’s constant. # n; }2 i8 J+ Q/ [7 g0 p
Euler and the reciprocals of the primes. & a) @5 `. a5 @) m0 ^( D# a+ S* c
Euler’s totient (phi) function.
- d5 H1 \$ a* u6 H0 F) M% `' [: o5 PCarmichael’s totient function conjecture.
, l% F+ z O9 fcuriosities of φ(n). ! {" ?- Q# j6 n. U$ O7 o! H5 r
Euler’s quadratic.
' q! j8 A4 P: {; ]2 i7 Wthe Lucky Numbers of Euler.
/ H4 W# j( q# m* g5 d8 |% Rfactorial.
8 v& F, g0 G. @) H+ {) efactors of factorials. 5 a& U0 }& m" X3 R4 j
factorial primes. ) G. v$ K T+ @+ v$ z0 G
factorial sums. ; F, c$ a6 B; j; ?3 B
factorials, double, triple . . . . % z3 O% a* G6 p, a
factorization, methods of.
! j( S7 n3 Y8 W ~) @' ^+ z9 Ifactors of particular forms. ! E9 c3 r: t1 W, k( K
Fermat’s algorithm. ; O! }8 }8 g! x8 L' y8 a
Legendre’s method. . { V7 W5 d+ S( i5 ?
congruences and factorization. 3 |) {; o5 I1 D3 ?1 p4 k3 n' {
how difficult is it to factor large numbers? , O1 _0 s9 L' D3 I2 U" S; R1 c6 Z
quantum computation. $ Q: O" q7 D% M- E0 [/ f! z
Feit-Thompson conjecture.
4 x& H) Z: `) u# L" PFermat, Pierre de (1607–1665).
8 V0 S& D' z" G9 d1 mFermat’s Little Theorem. E) c, F5 l7 K8 f0 [+ u }, G
Fermat quotient.
% `" \7 \! R ], NFermat and primes of the form x2 + y2. 8 h' s9 D6 {" s! d" f3 g; P) {
Fermat’s conjecture, Fermat numbers, and Fermat primes.
8 A) G+ Z8 k% T; x' yFermat factorization, from F5 to F30. 0 h0 m1 |1 o$ r& [$ U- ?
Generalized Fermat numbers.
3 Q" i. E3 r2 Z- W+ MFermat’s Last Theorem. # f1 d, s6 a: b" `
the first case of Fermat’s Last Theorem. 4 G# X, _2 S4 ]! g# j
Wall-Sun-Sun primes.
, a. s5 E! l: t9 ZFermat-Catalan equation and conjecture.
8 s; U, Y5 H: E2 Z8 JFibonacci numbers.
2 e- r& ]* L) A) kdivisibility properties.
- p3 p" h% ]8 G: H# p7 z- M6 F1 NFibonacci curiosities. " s/ n/ N) V. L7 f$ t" ?4 ?! q5 E
édouard Lucas and the Fibonacci numbers. / q! u5 F0 _7 m( S' o' V
Fibonacci composite sequences.
; n. Q- B: |9 s' x, Mformulae for primes.
9 q* w9 ~* J8 }5 J* d" ]- Z8 UFortunate numbers and Fortune’s conjecture.
/ O& g" L3 K$ b) `6 x* i& Ugaps between primes and composite runs.
) U8 z+ T' o, E& O% v8 @ UGauss, Johann Carl Friedrich (1777–1855).
$ @+ K* t2 j- C+ c8 OGauss and the distribution of primes.
' F% N7 e Q, c- |0 A+ b6 n$ ?Gaussian primes.
 h- z- X, `# k8 zGauss’s circle problem.
6 _- Y8 Q% E( E9 x6 C$ v3 J0 ?Gilbreath’s conjecture.
& K/ _ y/ ]- @: Q; dGIMPS—Great Internet Mersenne Prime Search. 6 B5 Q% s& O0 \5 D: [
Giuga’s conjecture. ; P; n2 z& K* ~: m
Giuga numbers. # U% |, r! [! x
Goldbach’s conjecture.
8 K9 |5 W% _/ b' m5 F' h' mgood primes.
3 _4 f; }7 \8 ^* qGrimm’s problem. % n0 {7 b9 a) ~* W0 \
Hardy, G. H. (1877–1947).
# B1 Q# L0 R" y4 T8 wHardy-Littlewood conjectures.
- m9 D- P0 K1 Nheuristic reasoning. 8 z) ?5 p* q2 o
a heuristic argument by George Pólya. # @# _, Y* H, P% J' ~- j
Hilbert’s 23 problems. & M" {8 e$ Y3 v2 B! H
home prime. ! s4 T$ r* ^% Y. s" B
hypothesis H. $ t# P1 {" P$ v6 i: _3 [9 a
illegal prime.
, p8 f9 a/ ]7 x1 Xinconsummate number.
5 `3 q- _2 `3 N2 M# @0 e& ^induction.
7 N0 N! j5 d" [0 A2 Y* pjumping champion.
7 {& y" D- y8 G( L2 @" }8 X; \, Nk-tuples conjecture, prime.
, l% |1 r- q" U2 U! Y3 Xknots, prime and composite.
5 U/ x' d$ Z! l' t! U, p2 uLandau, Edmund (1877–1938).
8 b$ n8 o' z9 r: }, ^: `: }+ i% nleft-truncatable prime. * T0 |& |/ ?9 Y4 a; d8 \. q
Legendre, A. M. (1752–1833). 8 Q* V' z g$ p' Q8 |5 C/ v* J0 X
Lehmer, Derrick Norman (1867–1938). + q7 i7 \" r' i' i
Lehmer, Derrick Henry (1905–1991). & o0 Z" \# M) i* {% |
Linnik’s constant.
# @3 s$ [$ C% m. WLiouville, Joseph (1809–1882).
Littlewood’s theorem.
0 D1 R1 n# M. z& q+ q7 Dthe prime numbers race.
( q2 U) B+ N1 `% |% R# \) RLucas, édouard (1842–1891). # x; U! }$ }3 I
the Lucas sequence. 7 j9 h8 R5 u6 q
primality testing. 7 |0 C0 q6 R0 y2 c, |. `. w
Lucas’s game of calculation. ! V: H, R3 H+ q" `; y* O
the Lucas-Lehmer test. ' {; X' L" d6 [2 c3 r) Z
lucky numbers. 2 b6 l' c' W2 q& K1 n; _$ V+ L
the number of lucky numbers and primes. 2 T) h. K" H# R4 D ^
“random” primes.
' S& S1 i* B& ~magic squares.
- d) ?! A& v" x1 eMatijasevic and Hilbert’s 10th problem.
5 L* }' [) O2 LMersenne numbers and Mersenne primes.
1 h) l" B. f5 G3 gMersenne numbers.
7 ?6 D" ~0 N, d7 _ Mhunting for Mersenne primes. ! t% d2 H r% z) J2 f
the coming of electronic computers. 8 v- V: r. f4 E* u! N
Mersenne prime conjectures.
7 o3 q. I( `4 H6 |4 lthe New Mersenne conjecture. : a7 E/ r. W/ c) }) ^
how many Mersenne primes? % y; d" N0 m* j2 R+ H7 w
Eberhart’s conjecture.
2 P" w" ]. k& x. E% I8 d \7 k7 }- kfactors of Mersenne numbers.
$ `9 Y% g8 k# n7 r$ o/ C, ?Lucas-Lehmer test for Mersenne primes.
. S4 ~$ m* j# J6 D' o3 P0 NMertens constant. - Q( B S' f5 H2 S% _3 L
Mertens theorem. # k e$ K7 a( `/ X" b- E. Q
Mills’ theorem. - L- I3 D. B3 x' A) j% H5 N+ N
Wright’s theorem.
' E6 i% q/ c( W0 ]; Rmixed bag. - P7 ^) S9 Z; r, n+ G: C6 t
multiplication, fast. o& @, _3 w0 v+ f1 h* C! [3 K* y2 X A y
Niven numbers.
5 e- X" d1 D& \odd numbers as p + 2a2. * S- b# K' X- S* ~6 k
Opperman’s conjecture. ; `" t! r4 Q# b. y
palindromic primes. ( I+ l& J$ \, \) U
pandigital primes. " a+ Z0 K3 t# {/ m) {$ M
Pascal’s ** and the binomial coefficients. & ^0 R5 S ]" ]2 d
Pascal’s ** and Sierpinski’s gasket. ( d& [; B, ?& n* v+ m6 G/ a+ x
Pascal ** curiosities. 0 Q2 k7 V/ G9 G2 e
patents on prime numbers.
6 K3 L( H# L5 l# q6 \4 ~Pépin’s test for Fermat numbers. * h* K9 C9 o5 B7 j- r2 B8 k, X
perfect numbers. + a# I* A3 H( p" O
odd perfect numbers. 5 \+ l3 |1 k% R* r
perfect, multiply. T' z: |- \ V: N, j, S X
permutable primes.
- O/ ~* n/ P& W$ Y' D4 v7 vπ, primes in the decimal expansion of. 1 i; @# Q( O3 i- ?
Pocklington’s theorem. C( T" A% `$ F, D
Polignac’s conjectures. 5 X/ c; _8 p6 a7 d
Polignac or obstinate numbers. $ k7 u. E t- }2 S! _, D
powerful numbers. 7 f+ A0 Y' ?2 H' O6 b
primality testing.
5 u* g+ S$ H/ d" U9 M( Y; Tprobabilistic methods. ! B: n( C5 C9 O0 g B( M
prime number graph. 3 b- y$ b; |8 ?% }* _
prime number theorem and the prime counting function.
( Y% f1 {7 Y" ~, rhistory.
! j z; Z* P v8 k3 k* j& Relementary proof.
6 w) o+ X" @/ L' V4 S9 U0 q! Q% irecord calculations. , x5 y- y g- m; ?8 U5 j5 W
estimating p(n).
, K) t' A! T o3 S. n( @calculating p(n).
' A+ ^3 ?- ], Y# t' T5 X8 Ua curiosity. ) X q1 a) r3 E1 K+ t" C
prime pretender.
: d; d8 v# D4 Z- {$ Xprimitive prime factor. j2 P7 p; x, N" ^
primitive roots. v& H5 B) v$ F/ n o. p
Artin’s conjecture. 4 k, v! q! ^ W2 d; q+ e% S
a curiosity. 7 n0 ^; W' |8 X, q' Z9 r
primordial.
4 P( Q! I9 a' C2 ] m, _primorial primes. 4 @% Y4 t& _/ ~7 O9 d
Proth’s theorem.
4 r. m* q1 o0 _1 _5 t9 cpseudoperfect numbers. _% ^" h7 e8 C8 {
pseudoprimes. 1 g" G; u; t" [$ q1 p
bases and pseudoprimes. / ?' m4 Q8 K; B! U! Q
pseudoprimes, strong. 4 S! F: B( L0 s2 S& o7 i
public key encryption. # w0 O! X& `) W; Z% V
pyramid, prime.
# ?: F! h- b# H& {- c5 ?Pythagorean **s, prime.
 L6 ^: \ P) c* _/ P; k/ A8 d' Qquadratic residues. : v" J. t; }1 `7 N: T7 M. v
residual curiosities.
' @, W4 r q# u( p; l: T% [polynomial congruences.
" Q w- Y5 N9 c. s4 vquadratic reciprocity, law of.
$ _$ c) e1 F5 R' M# |" ]* yEuler’s criterion.
6 X `! f9 e" @( [2 g" l$ x$ x# nRamanujan, Srinivasa (1887–1920). 1 p$ m( M5 @& K8 { u" r3 b0 m
highly composite numbers. $ V7 d0 G% _7 f& o0 }9 [
randomness, of primes. 4 G6 s" B+ c! Y# S- l0 O
Von Sternach and a prime random walk.
$ P$ R; P8 w- ]record primes.
. m6 S0 D* ^: F0 tsome records. & k) D0 i" R+ C2 o1 j
repunits, prime.
! V i" Q$ S; X" a1 gRhonda numbers. ( B( X9 }' r$ E4 w
Riemann hypothesis. - N& B. B B; E% ^$ U9 U6 S- {9 N
the Farey sequence and the Riemann hypothesis. # w8 X+ x& E% w/ a3 g
the Riemann hypothesis and σ(n), the sum of divisors function. ; {: h8 v0 m A1 x9 M" W. \
squarefree and blue and red numbers.
. U8 o4 c; l2 S" z8 g* c4 g) s othe Mertens conjecture.
- V* ~/ R+ q( N9 Y, ]Riemann hypothesis curiosities.
9 I) a# C. z) j' V* V& qRiesel number.
5 e% g! J* I' C' m! eright-truncatable prime. 5 E- I. f2 _3 d2 m9 e4 o0 e$ o/ w
RSA algorithm. ( E" p- }# Q: B, G- d5 J: C
Martin Gardner’s challenge. * j' W; F5 H3 b, A0 D
RSA Factoring Challenge, the New. / M4 _$ `2 V* ~) i- J; |! Z
Ruth-Aaron numbers. 9 @/ w( Q' d1 I# y* D4 B
Scherk’s conjecture.
, i% _# `1 R, f' b& M4 o5 ?semi-primes.
- `/ H; s$ M8 e**y primes. ( e H# R6 ]/ }3 [
Shank’s conjecture. ! |9 g2 x6 s; x" G8 ?
Siamese primes.
7 I. n; }+ y3 d0 @Sierpinski numbers.
+ {: p% P: \( o% ?Sierpinski strings.
' R4 K+ w8 C+ B. T. c( T( i3 O0 |Sierpinski’s quadratic.
5 J) R, u0 E6 D4 f/ _* c$ e BSierpinski’s φ(n) conjecture. ) Z# ^; O4 u, G: A+ y& e" }
Sloane’s On-Line Encyclopedia of Integer Sequences.
# k$ Q. g7 J3 ISmith numbers.
/ y6 g& f+ `: k* }Smith brothers.
( A9 b6 a/ ~' K, Z2 J/ v% M2 zsmooth numbers.
+ L1 S. x: \- L; F& C' m' {Sophie Germain primes.
" f+ z& N7 {. P! zsafe primes.
1 Z, L2 b9 T4 G" @0 X4 T! N; u7 bsquarefree numbers.
- B% ]2 D2 b* ^! DStern prime.
: ^) }- s, K3 U, f' I* sstrong law of small numbers. ' w7 ^! n4 c. `0 b! x" Y- L. K
triangular numbers. % u! S- G5 j( m7 l8 t, Y
trivia.
5 Z$ h4 ?1 Z; R- b9 J$ |0 D6 Ltwin primes.
4 H7 A$ y7 N* J3 Vtwin curiosities. ( H4 k/ y5 w% u# N: A
Ulam spiral. # }! P" }' q- ^5 ]8 \ b6 q$ b
unitary divisors. ; z4 `6 F. D/ l0 k: @
unitary perfect.
" b \2 {" v8 r- h; q' t* g. Funtouchable numbers. . H( }* ^2 X0 K ^+ M# a! E8 P0 f
weird numbers. 3 U( M6 l; R' Z4 V9 \
Wieferich primes. / f1 D' a6 i2 e: t0 g% h
Wilson’s theorem.
5 h* z/ A% P b4 e( Y0 rtwin primes. % @1 _3 B# t% j. i/ P/ x
Wilson primes. ) ~/ k0 ~( z& t7 y
Wolstenholme’s numbers, and theorems.
+ ~. s- g1 t2 R# J% c( rmore factors of Wolstenholme numbers. 3 C. o' B0 O5 p7 P9 K* r* B% e2 K
Woodall primes.
# g' T; y6 S' I/ U8 [* }0 Lzeta mysteries: the quantum connection.