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数字的奇妙：素数

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Entries A to Z. ! N; O# _& m; |; e
abc conjecture.
6 b8 D+ d1 |& E$ S& w l8 F7 n) |! pabundant number.
& b8 d4 c. [* A: j6 [4 V2 ]; q: H7 LAKS algorithm for primality testing.
( t- L7 C1 d- U; k' }+ S1 ealiquot sequences (sociable chains). ?9 r7 N. z! @+ i2 Z( n) y
almost-primes.
- d! I8 B! t' j6 Y7 G5 |0 A( bamicable numbers. 6 O) D$ h) h- Y+ R5 N$ C+ [$ s
amicable curiosities. 9 A7 R+ w- ^: I2 s* q# N
Andrica’s conjecture. " Z9 H1 _ D& w0 l# R5 n
arithmetic progressions, of primes.
* H# | N7 C/ J2 }1 o+ z- @Aurifeuillian factorization. ; r1 c! F, E: x O. B
average prime. . f" g: ]0 s; z6 p/ }) `) {7 q
Bang’s theorem. 9 l* ]) R d! h3 r
Bateman’s conjecture.
# l" @( \5 X8 j' IBeal’s conjecture, and prize.
$ Z. [4 d* B* l+ v6 ^Benford’s law.
 ?2 C" R4 h, ]3 e4 S5 ]Bernoulli numbers.
1 S! S4 B, O$ J# J# gBernoulli number curiosities.
, d8 M& y: ~1 B6 Z6 ?, bBertrand’s postulate.
+ q1 `7 T! d4 {) C, f* R$ x7 q3 @Bonse’s inequality. % d- d* x) c/ U( w5 f R
Brier numbers. : U _- L& [5 e
Brocard’s conjecture.
4 n g3 P4 j3 S$ Q9 V* ~6 qBrun’s constant. : W: f; W1 X& N. B5 T
Buss’s function. ' r R" t8 B0 D5 d
Carmichael numbers.
& u" n& L! E% u8 K P* r6 _" E2 cCatalan’s conjecture.
- Y0 P: f$ p% a/ ~Catalan’s Mersenne conjecture. % [* p' \- r4 h+ J
Champernowne’s constant.
% y, \& z# [1 c5 z+ Ochampion numbers.
- G2 b+ y0 S0 @) DChinese remainder theorem.
4 w4 `- |9 Q. B4 h) Kcicadas and prime periods. % i. R5 A3 n5 U6 K) H, {
circle, prime. , Q/ N6 f: q! v: ~9 c, k4 j
circular prime. " J) `. I: X+ G
Clay prizes, the.
6 V7 d$ f" C, w) W' \compositorial.
; ^$ f7 w4 S: V: `! ]. ^concatenation of primes.
$ E3 w# w. A" r) U) qconjectures.
, [3 U: N8 s; p1 Z5 C% nconsecutive integer sequence. 3 w! B# M" P }
consecutive numbers. 0 f3 T- A6 N/ R0 s
consecutive primes, sums of. % ]; ]- P3 a9 C( h9 k3 k
Conway’s prime-producing machine.
5 z& I; r5 j$ y% e1 ]cousin primes.
9 }' ]" b6 m. M( q0 M) xCullen primes.
; ?3 W, \1 L$ OCunningham project. # Q1 k& c4 w5 p" r& R
Cunningham chains. 4 {9 o1 o; d5 t1 T6 q8 J. V
decimals, recurring (periodic).
' a2 i# W5 Z0 h8 e6 }6 D6 ^# `0 vthe period of 1/13.
* ]8 G, b! D$ P: e4 }& [cyclic numbers. 4 b8 P; M& `0 I j, S6 l
Artin’s conjecture.
% o- y9 |2 @( c _/ Vthe repunit connection.
4 @& K+ P/ e8 Hmagic squares.
; B: X- e5 ~% y- vdeficient number.
1 B/ U6 x3 t( r+ h" a3 k3 b: Ydeletable and truncatable primes. w6 A4 a2 e! y2 {) @, \; c# C
Demlo numbers. 0 f( D) G6 h( U5 k
descriptive primes.
; n2 X$ Z( N& \$ |& S0 ?2 _Dickson’s conjecture.
% u) H H5 y% Edigit properties.
: c6 `9 `# l, g3 x- VDiophantus (c. AD 200; d. 284).
& ^3 B8 V2 [& UDirichlet’s theorem and primes in arithmetic series. 5 \! W: P6 K, f: E% a8 {
primes in polynomials. * h* R! T3 y- C
distributed computing. % h. q5 S! ~( ~6 r& i D, y8 _, K
divisibility tests. 7 h7 v M8 U6 @5 Z
divisors (factors).
- D' Y: M: {0 y+ _% ?% X8 S7 yhow many divisors? how big is d(n)?
6 v5 @6 H, F+ k1 E; m5 brecord number of divisors.
/ I9 F% f9 e1 K/ q8 P" Mcuriosities of d(n).
) g- B' b4 Q" S3 \0 @divisors and congruences.
* x7 P+ X$ \& Athe sum of divisors function.
# t6 r6 H2 i& ^7 b+ U* J# {, uthe size of σ(n).
! {5 q8 S( t- ~9 r5 ja recursive formula. . z& y9 \7 j1 ?3 B
divisors and partitions. ' u1 D8 ^6 r% R# c9 t4 I
curiosities of σ(n).
- D0 @0 O, {' v9 {0 v3 O. rprime factors.
/ @1 a: t) S4 _0 Y3 r- N. y/ ~divisor curiosities.
5 g' M9 H' G1 m" geconomical numbers. 4 Z _7 X# ^- u
Electronic Frontier Foundation. 7 U) @) A/ W9 i: H: @0 {
elliptic curve primality proving.
# ?" Y; G+ ^, Y: oemirp.
) r& l9 T( Q9 P8 I1 Z( x, AEratosthenes of Cyrene, the sieve of.
1 f" L. y2 w; [Erd?s, Paul (1913–1996).
) K8 ~% f1 _8 M j2 D& mhis collaborators and Erd?s numbers. N6 E' \, `( Z: v. F* D
errors.
% t. z% W8 `! ^7 ^6 R* O' F3 g7 nEuclid (c. 330–270 BC). 6 b* W7 w/ q7 O& U# t4 o
unique factorization. ' C- Q4 r0 C1 g, e0 x
&Radic;2 is irrational.
; w! \, @: a' }) l* ~$ J& Z6 PEuclid and the infinity of primes. 6 Q. ^/ q3 ~% ]9 S
consecutive composite numbers.
" J2 L& n. v7 j7 i) U0 Wprimes of the form 4n +3.
5 [* G0 C5 r0 a6 ea recursive sequence.
5 G& ?) H, e2 x- k9 O5 @- Y0 a' _Euclid and the first perfect number. ) y: N6 q4 @% Z2 \& }6 c1 w! b7 O' D
Euclidean algorithm. / [) b) [) @& c! Q$ x) T
Euler, Leonhard (1707–1783). # i% \1 {" v/ A7 n u2 Z5 ~
Euler’s convenient numbers.
8 P N! |; G _" u; L+ x N1 \the Basel problem.
0 K" j9 T7 W0 d. e3 fEuler’s constant. ! {5 J. J# @3 r/ `/ e W
Euler and the reciprocals of the primes. 7 ^, u* R# ?! S9 G0 v2 e
Euler’s totient (phi) function. . W( t% x# g2 A7 G4 a
Carmichael’s totient function conjecture.
9 A' b7 W6 s2 {" b. S: ecuriosities of φ(n).
6 u( O2 H1 x$ @" zEuler’s quadratic.
 q5 K% K2 z% E3 Rthe Lucky Numbers of Euler. e6 J! j; }, E ?7 K3 g5 X1 C
factorial. 4 {# j5 k! O1 |. u# S
factors of factorials. v6 P3 A8 p: P9 {, s1 Y' i) B9 Z
factorial primes.
2 J ^+ o' s- p; B% G3 P) Ffactorial sums. 1 Y7 b5 D5 ~+ r' y
factorials, double, triple . . . .
* x1 ]4 R! l+ @9 x1 a6 ?factorization, methods of. / W' B* A ]# _7 v+ U: ]
factors of particular forms.
3 V. K2 Q1 T9 F! J# w. BFermat’s algorithm. 8 {9 y. M2 ^+ \0 {# c# x- b% w
Legendre’s method.
% v, j0 o" s y8 f; r; acongruences and factorization.
# m1 U2 o& U3 F# Q3 w# C3 [1 Xhow difficult is it to factor large numbers?
! ^/ B' b' z/ \$ f: bquantum computation.
0 I. ~3 M9 G8 ` w" oFeit-Thompson conjecture. 3 o4 x0 q) M* L7 y8 k* I( B
Fermat, Pierre de (1607–1665).
; C- O8 D8 V( `; F4 GFermat’s Little Theorem.
Fermat quotient.
8 R' p8 P6 a4 x5 d8 J* @Fermat and primes of the form x2 + y2. . R% ^5 ^1 z% l1 q# a$ ]
Fermat’s conjecture, Fermat numbers, and Fermat primes. 7 Z" o0 d0 \0 w8 {+ T# H
Fermat factorization, from F5 to F30.
& n# N; H3 w* ]5 K- R- P* q8 }Generalized Fermat numbers. . o& D0 s c; C/ s
Fermat’s Last Theorem.
/ m: {7 k" F& t; cthe first case of Fermat’s Last Theorem.
6 y) L2 {$ G6 O) EWall-Sun-Sun primes. w7 q. K" g+ G) O- [
Fermat-Catalan equation and conjecture.
! d% r7 U6 I) {' ^7 h6 K* EFibonacci numbers. 2 D" }3 K/ k( W
divisibility properties. ' `+ d% i0 d2 L* }+ ]0 B6 p3 x
Fibonacci curiosities. ' ^4 R( y* B$ a L# i) e8 e
édouard Lucas and the Fibonacci numbers.
) f. s& x( t$ G: |+ HFibonacci composite sequences.
9 U$ i N5 ]" J, n gformulae for primes.
' b/ P) T5 b1 S+ kFortunate numbers and Fortune’s conjecture.
! v+ K" d( b8 g$ u# m4 f) @gaps between primes and composite runs.
% }2 t# J- K" ]5 k& a5 D6 tGauss, Johann Carl Friedrich (1777–1855). , [' L$ ^% S; D; P
Gauss and the distribution of primes.
- |5 v; P" Z9 f$ ?( @0 G/ F- W5 h3 kGaussian primes.
( d* j: h/ h- SGauss’s circle problem. 8 o0 e' S) g- i! E
Gilbreath’s conjecture.
: {6 [, O5 J5 r. XGIMPS—Great Internet Mersenne Prime Search. / Q; N' J' o; N4 q2 S. b
Giuga’s conjecture.
1 O/ a8 ?3 ~* F; ?Giuga numbers.
2 h- u: v( q S$ n( I& EGoldbach’s conjecture.
7 Z) z0 }- m" }) rgood primes. 0 ]; S! }7 ^5 H+ n( I0 P. {
Grimm’s problem.
/ p* U H% }1 a4 {, QHardy, G. H. (1877–1947).
$ X$ m0 C, d4 H$ _Hardy-Littlewood conjectures. / I6 ~6 ]2 Z/ P
heuristic reasoning.
( c; x0 j" J& K5 {" w0 N6 ~a heuristic argument by George Pólya.
1 H. c0 [. D! h* k: W4 c8 o: b/ uHilbert’s 23 problems. ) z3 V X' u! P {$ _ E1 h
home prime.
- v- U9 P1 y Khypothesis H.
' x7 x( `& n& [6 w9 o Q1 x. Eillegal prime. + P; |. H7 ]! g, E! D1 d- L
inconsummate number. 3 e2 V. O( W, V0 s4 [4 v2 O
induction. . Q, g) A) N, r: l
jumping champion.
" J L/ ]4 w5 \" d" z8 Dk-tuples conjecture, prime.
$ c) e. O9 \6 ~( u; [# @3 pknots, prime and composite.
! K9 ? k; s- R- R/ NLandau, Edmund (1877–1938). % _( M: m5 _ o
left-truncatable prime.
' M3 l+ w( P/ Q$ k, w7 [) k) GLegendre, A. M. (1752–1833).
/ z6 _) U i. _' g& ALehmer, Derrick Norman (1867–1938).
1 ~; w" W0 U) q8 e; f$ [! _Lehmer, Derrick Henry (1905–1991). & q# Q+ R3 n0 V ?
Linnik’s constant. & M. N2 b' c$ L* V/ Q" {6 y( w! N
Liouville, Joseph (1809–1882).
/ s+ M& o4 b- [* x- _Littlewood’s theorem.
( E$ K: S0 U7 v: b- @) |0 _3 ethe prime numbers race.
& x0 w v9 B0 X$ S j# ^0 LLucas, édouard (1842–1891).
" ]/ o5 f! u9 \0 Q6 [( Uthe Lucas sequence. ; y1 U+ B* r# j3 `
primality testing. 1 | B- \: r; G6 K, V0 [
Lucas’s game of calculation.
( Q+ s3 v% I X( N$ k) Q' l( hthe Lucas-Lehmer test. 2 S( k0 L2 B- d% k- ^
lucky numbers.
! t+ {9 y& ]) I. E0 A. Q1 A- C, sthe number of lucky numbers and primes. . I; h% G9 j# `& M1 h
“random” primes.
; T* P( `& ?/ [magic squares.
. _( w/ C2 M9 Z; x4 f# WMatijasevic and Hilbert’s 10th problem. # l N) S R6 b3 K D9 R. J# @
Mersenne numbers and Mersenne primes.
8 x8 r. n- M, w1 yMersenne numbers.
+ K X4 L# c, J( p; s6 i, vhunting for Mersenne primes.
9 E+ d4 m0 n8 w1 B* b1 rthe coming of electronic computers.
/ P5 u ?2 \6 T: @/ F7 |Mersenne prime conjectures. 8 F6 G! I& R# Q1 o- c& S* }
the New Mersenne conjecture.
" _/ V8 E3 u5 {2 rhow many Mersenne primes? ( ]% X2 V2 Z: w: g0 W" z
Eberhart’s conjecture.
0 b$ V# f4 e: x; K/ b. o I. mfactors of Mersenne numbers.
8 \+ W4 a6 H( R k# rLucas-Lehmer test for Mersenne primes.
# p! X+ Y' ]7 l5 P( PMertens constant. $ ?6 J$ s4 w1 n5 @+ J
Mertens theorem. 3 m. N% T5 H% X( b
Mills’ theorem. 1 R) c, e+ Q5 T x
Wright’s theorem. 2 f- x( m0 s! `* n8 j4 A
mixed bag. ( I% e% \- r' r1 y
multiplication, fast. 5 q1 z0 z4 T5 l; i$ H' A, U% a z3 U
Niven numbers. ' V. ~% x! l. a; ]
odd numbers as p + 2a2. ' q- K+ z" \0 x# ~
Opperman’s conjecture.
( a4 R( s2 ?9 v: e( hpalindromic primes. 9 B" O! A9 d& X- i. e9 T; N
pandigital primes.
& z# E! M! [, A( R JPascal’s ** and the binomial coefficients. 9 j/ u* E- {5 n: m
Pascal’s ** and Sierpinski’s gasket. 1 a" ^7 k0 f7 R6 t: n
Pascal ** curiosities.
2 x5 D+ Q+ q7 Spatents on prime numbers.
" u! C8 H7 K y& V2 _Pépin’s test for Fermat numbers.
; R$ f& A! ^4 Z) n- d2 [, lperfect numbers. + ^2 D& u" l% g/ J6 c$ L2 T
odd perfect numbers.
/ x: S. V4 O" g8 Qperfect, multiply. 0 o ~, L4 Y0 m2 P {1 E' U+ S
permutable primes.
/ d( R2 i$ C( Q% [4 Eπ, primes in the decimal expansion of. % J; V; N T0 \9 h7 {" V0 Q8 L
Pocklington’s theorem.
Polignac’s conjectures. + O+ D. d" I/ ]
Polignac or obstinate numbers. 8 z/ V. ?! ~6 l1 Q {( H
powerful numbers.
. T ~ o \* Jprimality testing.
1 ^6 [: W M5 v# _# ^( F$ Vprobabilistic methods.
: S' g7 w' D; b O% wprime number graph. 1 \) Q2 Y; ?% U
prime number theorem and the prime counting function.
- ]9 B! W8 D: L* e$ z: B! ], _) W- }history. - O9 n1 T+ T5 j4 }- E
elementary proof. * {$ c% o4 m8 X; B4 E
record calculations.
0 z0 i' `% O1 J! E- uestimating p(n). 4 J- [: W% D, d! ~ [3 L
calculating p(n).
0 i8 B7 K; W4 f/ Ba curiosity.
: T5 ?. a" k5 @! O: k- ~" Aprime pretender. : X$ s T7 e% r1 L( t
primitive prime factor. 9 X5 x; Z8 P; ]! n5 S4 O
primitive roots. ( j' M( G/ g! M7 p1 _6 Z# P
Artin’s conjecture. ( H0 h7 C4 R/ M1 J% N6 n
a curiosity.
7 R, \: I, b) D: b) Nprimordial. 5 O X9 G& P" ] i1 H
primorial primes. 9 A3 M. d8 U, {- y' q" J I
Proth’s theorem. 8 [: D' [/ r; l, o- X
pseudoperfect numbers.
7 S, e. `3 |! h9 |) Qpseudoprimes. 8 F% R6 T0 S: D! D: |# a
bases and pseudoprimes. 4 k& P5 w5 @8 o: F/ i# k' m9 S
pseudoprimes, strong.
( C; Z/ y+ I A7 h% ~public key encryption.
) u; o; @; }% Z; gpyramid, prime. / |+ q- T& q& q# H
Pythagorean **s, prime.
! ]2 e; {' I- o. T) w% c- \7 c. iquadratic residues. & g' W% @0 X" s7 N
residual curiosities.
. R- e$ f* e- a+ O* Fpolynomial congruences.
6 H& y, H& \! J/ A: i4 z/ M- rquadratic reciprocity, law of. 1 E; K0 {: q$ s2 s, [7 q
Euler’s criterion.
3 b* `" T3 }1 pRamanujan, Srinivasa (1887–1920). + ~' V0 O) G: G
highly composite numbers.
0 g2 j N2 z& brandomness, of primes.
2 C6 g0 T, @& V3 `Von Sternach and a prime random walk. . s" W# ]$ L+ G$ I, D$ }
record primes.
2 Z8 P/ g s/ P/ xsome records.
7 ^5 T! q6 H. Drepunits, prime. - s! b: O! w9 A% }
Rhonda numbers.
7 ~/ ]: a1 P2 D! v9 BRiemann hypothesis.
, m, q: y4 E& U4 [4 q" c* cthe Farey sequence and the Riemann hypothesis. 2 T! f9 D: h1 T- R* H' F
the Riemann hypothesis and σ(n), the sum of divisors function. 8 \# K, g d2 Z2 U
squarefree and blue and red numbers. & ^& c4 [1 a5 n
the Mertens conjecture.
, ^9 {/ j: j5 q, T8 }Riemann hypothesis curiosities.
8 ?; _# i+ F8 }% u' d5 @- RRiesel number. 5 G) Q" f. h) N2 ~* q' a
right-truncatable prime. + V; V6 S( a5 c) [" K" a7 [5 F
RSA algorithm. ' k# m! l6 y) W
Martin Gardner’s challenge. ( O5 g; `$ A& V& ~$ w
RSA Factoring Challenge, the New. ( F6 b5 O) T8 z
Ruth-Aaron numbers. Y# L' Q7 L8 `: l: o
Scherk’s conjecture. 7 n7 X! o% |) q g3 C& x% x" r7 C
semi-primes.
* l/ U2 e, a" M3 o**y primes.
; N2 i$ m/ o5 {& z/ J, B0 Q# eShank’s conjecture. 8 X" Q7 ~- b7 O# W
Siamese primes. / [5 W' l; i* H. f( i
Sierpinski numbers. / ?. m: P3 W1 V+ |0 k' e' v- v
Sierpinski strings. ; V+ P1 L, L2 \
Sierpinski’s quadratic.
% U0 ~3 e/ o- l& C9 fSierpinski’s φ(n) conjecture.
Sloane’s On-Line Encyclopedia of Integer Sequences.
& ~6 R8 x4 E. H% b5 \; L) QSmith numbers. ; g9 ?( F* p1 [. [$ v
Smith brothers. 0 u4 s' ]5 Y N: r# |
smooth numbers.
+ B e! F$ @& ~9 K7 fSophie Germain primes.
! ^/ z! Y: H4 A* Zsafe primes.
! Z! F4 n+ j1 q$ O1 s; w: h" Asquarefree numbers. 4 n4 t- T7 ]% f) [
Stern prime.
. f2 e% A" `/ J0 ]8 ostrong law of small numbers. + X1 Z( Y% R: @' _! G
triangular numbers. ; m6 S6 V K/ j! v
trivia. 2 w- j; W0 [; W# M
twin primes.
: W$ ^7 I% D" h! t' ytwin curiosities. 7 t1 q# t/ q- A2 K. x& y
Ulam spiral. 1 n/ h" I, Y! x3 K5 ?
unitary divisors. " @, ]; n9 B9 M
unitary perfect.
( y6 z9 o% ?' b2 ]untouchable numbers. 9 F% \% `. K6 d- [
weird numbers.
9 V3 d1 l0 Y A2 P: x2 r2 R2 VWieferich primes. ! M/ _& @6 N$ V" r
Wilson’s theorem.
& W4 c, r% O0 _$ f) s8 h& e# g4 V$ qtwin primes. 1 X R% [. t1 E9 \- ^9 F. H3 P
Wilson primes.
6 _! }: y/ S/ D4 q: \+ J+ a3 D/ KWolstenholme’s numbers, and theorems.
& S" W9 |2 B1 {/ V- j% @' ]more factors of Wolstenholme numbers. 8 Q. ~' L+ _5 d: z
Woodall primes. / X( n# F1 e: ]
zeta mysteries: the quantum connection.