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数字的奇妙：素数

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Entries A to Z.
8 t/ a; G* l! U- ?- y2 W9 I' pabc conjecture. ' ~0 _0 L* u" @8 l8 ^
abundant number.
- x4 r/ ^) V7 t ~, e8 i% Y5 |AKS algorithm for primality testing. ( l5 L% r, x6 N7 W" C8 Y- t+ Y) i
aliquot sequences (sociable chains). 2 o# e6 ~1 h% g+ W
almost-primes. , w9 l4 O* E) R* Q
amicable numbers.
7 h ~0 Q# z5 A" e5 T% Wamicable curiosities.
( r3 p' r" U5 q9 _; k9 {Andrica’s conjecture. . D$ F9 h3 I A8 w2 F% g! q3 `
arithmetic progressions, of primes.
 v4 {2 J' _" }: ^* oAurifeuillian factorization.
# h# V( ]# R0 S/ k5 w: D6 Faverage prime.
6 |* g" E: T" Q: K' B' |8 JBang’s theorem. ; H' p* ]$ w9 z% C" _/ y$ ?/ q' {
Bateman’s conjecture.
! e! e/ ?$ `1 J' VBeal’s conjecture, and prize.
# w d! N0 z: t f p J, IBenford’s law. 3 h" O# R# i, L* m1 G y
Bernoulli numbers. , ^. L. G9 c) c a2 {
Bernoulli number curiosities.
3 Z# G6 m) s' \' o/ fBertrand’s postulate. u E- U( ` c+ A5 X
Bonse’s inequality.
8 [' i7 i8 `( Y! f/ d/ u; ~, r4 GBrier numbers.
& r( O6 J* A, L4 a# K1 U0 aBrocard’s conjecture.
) ^) c& v* D4 VBrun’s constant.
7 `4 k/ x; T( G% l. \Buss’s function.
& j$ E) n. u/ r6 oCarmichael numbers.
+ p8 A4 d1 r* jCatalan’s conjecture. ) p& W# h3 U+ S/ C1 l, ~
Catalan’s Mersenne conjecture. 2 o) G1 t8 k8 v9 ~! H- O
Champernowne’s constant.
6 B4 {5 H/ c3 K. ~# ?; nchampion numbers.
) @# p3 m" k! eChinese remainder theorem. % G8 K. f/ T$ r y0 t
cicadas and prime periods. 2 T. I5 b$ N+ X* V
circle, prime.
9 ^0 X5 B0 q/ | Q- Ccircular prime.
1 a/ g s" L; E i0 kClay prizes, the.
/ O% C9 t+ |2 d) Mcompositorial. ' ?, \; K3 Q0 b' i
concatenation of primes.
- c* V2 z. F* j9 B0 L4 |conjectures.
% a ~+ f, v% B6 rconsecutive integer sequence.
8 k$ }5 q, Z( L1 | V. ]3 `consecutive numbers. * J% r9 R9 S; h1 Z- Q) n- V
consecutive primes, sums of. i' u4 Z: r& q9 r" p
Conway’s prime-producing machine. / s( ?" f/ E# T6 [
cousin primes. / z F W2 a* s" Z( K% }2 k
Cullen primes.
# A$ V( u) X- h) J; dCunningham project. ( B! b2 o, I. |/ ]6 N
Cunningham chains.
: T8 ]1 ^, }5 h; d( Ydecimals, recurring (periodic).
3 u3 o2 @( W0 W, y: F) Y I" Zthe period of 1/13. 1 |( R G9 P5 m8 Z1 ]% T) e
cyclic numbers. 1 x1 N8 M& s7 `* d7 ?6 q
Artin’s conjecture. s! J' M- R9 [: I. G1 L
the repunit connection. / x) L0 G/ \3 ?
magic squares.
# Z0 F6 H: k7 m$ d' P7 Cdeficient number.
. E$ P" @! v8 W$ F, K' U# tdeletable and truncatable primes. 6 `6 I, s5 g! R1 _& X) i' Z$ i8 w( g3 K
Demlo numbers. 9 c% [; R6 @0 f) i
descriptive primes.
% g) T! J L' t( VDickson’s conjecture.
 H5 O3 i8 t6 [' G+ D( w7 Bdigit properties.
6 W* y8 w& H h- O+ c: kDiophantus (c. AD 200; d. 284).
9 y J: {5 s1 Y4 C$ J+ F- jDirichlet’s theorem and primes in arithmetic series. / E" c e) t6 r% G- t2 R
primes in polynomials. 3 |/ Y- m& H( a9 r$ P3 _ ^
distributed computing.
0 W) H; Y0 Z* ~' w- L W- X4 Sdivisibility tests. ; ^9 p; q) u- U
divisors (factors).
! P1 K- ?. s/ f: c3 U8 {9 _4 ahow many divisors? how big is d(n)? ; r; E6 E7 n V8 n
record number of divisors. . ]5 a/ W1 M, K
curiosities of d(n). & |: v) E3 K& y# V! Z
divisors and congruences.
6 n, d8 F' K4 W% T3 y& zthe sum of divisors function.
, G6 m1 U- v, p4 `' ^3 T/ \; tthe size of σ(n). ' o- c7 K2 `% T# S
a recursive formula.
+ ?, }& s2 }# j9 i9 f% sdivisors and partitions. 1 x% }& J f( [/ ]0 `5 A7 d
curiosities of σ(n).
) V- @* N0 A) s5 t fprime factors. 5 s0 q( u6 }2 b+ S- ^
divisor curiosities.
, c& p6 @& Z5 veconomical numbers. 2 Z! @2 S) q0 P! M- R
Electronic Frontier Foundation. 4 f5 G# S4 o. c) R( e
elliptic curve primality proving.
emirp. ! y1 d- p* c1 r. W
Eratosthenes of Cyrene, the sieve of.
0 ?. B0 c) M) L8 Y ]# dErd?s, Paul (1913–1996).
8 ~9 l+ R% f1 this collaborators and Erd?s numbers.
; @. ^+ P* O' b" X. w9 d4 Xerrors.
9 j0 ]" F& }; I* }5 `6 ^7 ~Euclid (c. 330–270 BC).
1 ^' ^: C8 J4 Z9 X" p( Hunique factorization. 4 u$ d- R. z" y! M' D2 P
&Radic;2 is irrational.
9 O" |- L. S* p! K8 g) e2 b) hEuclid and the infinity of primes.
0 V3 g3 E0 y5 O! t, Nconsecutive composite numbers.
: n; ^- v% W& n& N: t+ } Y& Nprimes of the form 4n +3. L" K9 p/ w9 D# q# T* f
a recursive sequence.
7 K( ~, k: _/ J6 N" ZEuclid and the first perfect number.
/ t0 C- c# L" s. `) x% I4 MEuclidean algorithm.
. A1 e% E- T7 I! j0 i1 c* JEuler, Leonhard (1707–1783). ) u: c9 ~* }$ l( Q! S8 ?
Euler’s convenient numbers.
9 R5 F; M: E0 q- ythe Basel problem.
- ]% G7 @! ^# iEuler’s constant. 7 _3 u8 L) J6 ]& ?( h( ~
Euler and the reciprocals of the primes. 0 \0 q. G- J1 H4 q% F* E5 v
Euler’s totient (phi) function.
3 e/ R8 t6 m0 ^$ xCarmichael’s totient function conjecture. 9 ?! _* b+ U" i: G& n) x
curiosities of φ(n). ( u8 e0 g4 u% S
Euler’s quadratic. 2 {: o% J) m" p+ q t V4 o
the Lucky Numbers of Euler. 9 B! l( m3 ^ {3 B
factorial. 3 F5 y4 E' D& ?8 U9 G* G3 i
factors of factorials.
0 i) o& O7 P% zfactorial primes.
. O1 X8 u9 d3 N1 C% A$ _factorial sums. ( K4 c' L7 c4 G g. k
factorials, double, triple . . . . ' |! Z& M$ o+ T4 ]8 R. V" u+ b9 V* o
factorization, methods of.
( B. E* F* C6 F3 Q1 D" z ~factors of particular forms.
: p5 d2 }1 _; F! C1 qFermat’s algorithm.
1 K9 H( ]% F8 [* X4 S7 E% wLegendre’s method.
9 d$ v9 C6 M5 N2 Wcongruences and factorization. : a g: O7 ]' H8 r# o
how difficult is it to factor large numbers?
0 j3 o1 v8 n% r' I+ w* C# lquantum computation.
7 \- V+ L( \" M* f# `Feit-Thompson conjecture.
5 Y; k& |5 k: Z5 \Fermat, Pierre de (1607–1665). , @7 T4 g) W. L' K. H1 `
Fermat’s Little Theorem. 3 c8 \# ~+ ^" [4 x
Fermat quotient. . K$ L9 r' S8 g, O0 y6 I
Fermat and primes of the form x2 + y2.
: R4 m! H* Y( Q' W. |Fermat’s conjecture, Fermat numbers, and Fermat primes.
3 ~+ ^- E1 @0 S. ]Fermat factorization, from F5 to F30.
# Y: R. {& `" AGeneralized Fermat numbers.
, p7 {6 X2 C. b, }/ q2 sFermat’s Last Theorem. 3 I, _% e5 P, E4 d! s# H
the first case of Fermat’s Last Theorem.
7 h9 E7 Q$ l; m- F2 x+ pWall-Sun-Sun primes. + h7 X% }0 N+ b9 l. g; y- ^
Fermat-Catalan equation and conjecture.
, ?& V+ z1 A+ b7 KFibonacci numbers.
0 `2 A7 L% n' Q7 A* U4 R6 }divisibility properties. 2 t% x$ W+ i* M- y) O( e. f
Fibonacci curiosities.
( D8 X9 l! S" `6 N4 [édouard Lucas and the Fibonacci numbers.
: Y/ P! R9 r9 _/ n+ C$ k- x6 \Fibonacci composite sequences. - P3 @' q1 \5 W) Y1 Z. N
formulae for primes.
 I5 v8 ]! y( {7 [) }( f" zFortunate numbers and Fortune’s conjecture. & K# P+ u: m! P
gaps between primes and composite runs. 4 u$ a3 `6 V: Q3 |2 R- i
Gauss, Johann Carl Friedrich (1777–1855).
* e- _3 h& }5 {, f7 LGauss and the distribution of primes.
( M3 N3 u9 e& {8 cGaussian primes.
7 i4 r0 Y7 @9 ]Gauss’s circle problem.
- x" o3 J7 j* c, f5 F* SGilbreath’s conjecture. 7 c1 q6 |1 ~4 A/ q
GIMPS—Great Internet Mersenne Prime Search.
( H/ J( r# ?, v% T qGiuga’s conjecture.
9 L+ c5 v! N% J4 s5 ]Giuga numbers. # P* ^) T+ v$ x: W2 P
Goldbach’s conjecture.
7 L, L3 J/ a' o: Qgood primes. 9 x3 g3 e ?: w) C5 ~6 |: G
Grimm’s problem.
0 X/ T5 r* v7 JHardy, G. H. (1877–1947).
# g* g# }% x) M; u0 Q# q& S7 X' Q7 UHardy-Littlewood conjectures.
+ `- p1 f0 O7 m% F& vheuristic reasoning. / y3 h* l& s, m* I: ^1 _
a heuristic argument by George Pólya.
& }' }& C n$ E* u; B% e- uHilbert’s 23 problems.
# a: A. `7 }* U& A" s% \5 e1 _home prime.
: i( y- ]8 C% m+ Bhypothesis H. 4 t& U. |2 O' W! ?7 R7 t0 u5 Q
illegal prime.
* c& K; s: E; L+ S3 I+ o$ ?$ yinconsummate number.
3 e/ N S. y. o* `. F- ?4 o9 Oinduction. , _$ W" T. m& Y% W1 Z
jumping champion.
8 \. N5 W4 \1 I' c8 yk-tuples conjecture, prime.
" _/ E7 Q7 W4 W" g- k3 @' {5 Eknots, prime and composite. : k' O3 H1 @3 U: L) M; Z; t
Landau, Edmund (1877–1938).
' x3 W4 D1 ~* v9 E; eleft-truncatable prime.
6 V+ Z; O% e7 K4 X5 q4 ULegendre, A. M. (1752–1833). ! N* o1 W1 R' `& F/ ? R4 d4 y
Lehmer, Derrick Norman (1867–1938).
$ K/ }( B4 ?( r' Z" p! e! R) bLehmer, Derrick Henry (1905–1991). 1 o3 a/ R, [1 {! z
Linnik’s constant.
/ |7 i w$ o, u1 T6 WLiouville, Joseph (1809–1882). " b2 b5 E) e0 _
Littlewood’s theorem. - b, C- }/ r% D
the prime numbers race. 4 D( L& p" F! v! `2 T
Lucas, édouard (1842–1891).
; e5 z3 E# c3 m d7 cthe Lucas sequence. 6 P) [, K- } M3 w
primality testing.
/ R! o V D: [5 l+ p8 K' fLucas’s game of calculation.
5 h( b9 w6 g' x7 S: Bthe Lucas-Lehmer test.
 m! P* L& {; ?9 B: f5 @8 }: vlucky numbers. / s! ~: e' d# h' h3 h5 L
the number of lucky numbers and primes.
6 c- I- N! N& i“random” primes. 0 h* V; P* E, o! e- W7 Q
magic squares. 5 H8 F4 B9 B1 }- M
Matijasevic and Hilbert’s 10th problem.
: w) V( ]+ r% H' t+ h: h3 S0 IMersenne numbers and Mersenne primes.
( c% x- W7 P0 B+ xMersenne numbers.
 K8 t3 Z( u+ e$ G6 ]hunting for Mersenne primes. 0 l7 W( }: ?0 Y/ P* a9 n
the coming of electronic computers.
, @' Z4 f7 N0 {, d) h# eMersenne prime conjectures. 8 X6 E( @) |) E }# _, J- _
the New Mersenne conjecture.
+ g( \8 B8 O0 N4 n1 |how many Mersenne primes?
: c$ o4 \, e, ~& F3 kEberhart’s conjecture. 3 P" `' t# m( B8 @" j* l: p: G
factors of Mersenne numbers.
5 _- L; H+ d8 c! a9 c; iLucas-Lehmer test for Mersenne primes.
, n9 T3 f t* H# e9 R4 G$ TMertens constant.
. M$ v7 x9 Z) l: l# Z' WMertens theorem.
" u2 ?+ {9 d: c4 i. m* CMills’ theorem.
4 J. f# a) ?0 N9 h. N% rWright’s theorem. 1 T9 X' a: \6 H: P0 o
mixed bag. : o; s, s0 P t1 b, ~8 N% R3 Z
multiplication, fast.
. w4 I; [2 O8 H. z9 k+ |+ mNiven numbers. & ~: X; H* I( \0 L* W; U+ M
odd numbers as p + 2a2. 8 c2 M. M2 z1 r' A7 `3 `
Opperman’s conjecture.
' D& G& f, w1 |& s+ i) Vpalindromic primes.
5 C' M( y/ @/ L, v4 g$ Lpandigital primes.
* t/ Q5 k/ Z6 f0 e# \Pascal’s ** and the binomial coefficients. 7 I3 E/ v7 ]' R/ w( h& l/ c
Pascal’s ** and Sierpinski’s gasket.
* T) k; Z, L6 y; k0 G5 N5 ZPascal ** curiosities. ( p+ m5 ]5 B+ ]4 @/ c6 s- |
patents on prime numbers. 8 M1 q* u/ d) ^+ D c- Q. q* t
Pépin’s test for Fermat numbers.
7 R* s" X' q! k! F" Uperfect numbers. 3 [: u# O& b2 w. K {
odd perfect numbers.
0 [$ _2 D! f- h1 Kperfect, multiply.
3 V2 h& y) s# }" A/ C: D! hpermutable primes. ( b. g8 ]; E( I% q4 F
π, primes in the decimal expansion of.
% f Y( m: W- ]! U5 ^ I4 hPocklington’s theorem. 2 M$ [& [2 E- @% a( V
Polignac’s conjectures. " Q( Z f; ^, S. h
Polignac or obstinate numbers. & f* Z3 q3 @1 g5 ~
powerful numbers.
 e, _: h% f0 jprimality testing.
probabilistic methods.
1 h7 r' W/ G% G/ @3 G V) @prime number graph. 2 S, S& s( C- `* |
prime number theorem and the prime counting function. 6 r" s6 O4 @" n/ d
history. 8 e/ r+ S2 F! X6 E
elementary proof. " y! F) P6 h9 I- L: O* ^
record calculations.
- ^: A8 e/ S( g% D, R+ f3 gestimating p(n). 4 ^" }- ]1 @- G# h/ f- j" o
calculating p(n).
+ \" B$ w9 Z/ X$ }a curiosity.
+ D8 d8 n: N3 Q8 d& \. {prime pretender.
6 }: F( y+ X8 Dprimitive prime factor.
! g0 M. I$ U4 A8 s/ W- z' sprimitive roots. " \! N- }4 d1 C+ _0 T/ J# b3 {! ~2 P- m
Artin’s conjecture.
9 B; o, d( t- ?) h9 r. wa curiosity. . {2 C% \) R# V$ N5 S
primordial.
. m, K+ a0 M% jprimorial primes. / W4 c9 }0 p6 \, q6 U4 A
Proth’s theorem. ( V. E2 O. d9 F. M8 b
pseudoperfect numbers. 1 b2 `0 W8 g5 i8 C1 o
pseudoprimes.
& B. L% l: T- K1 U7 _6 Fbases and pseudoprimes. $ D0 w* @' D. @( t0 Z2 K& h
pseudoprimes, strong.
8 e1 r7 o) ]5 x4 L4 x( U) Kpublic key encryption.
+ B0 _- S2 ~/ H, i2 [pyramid, prime.
) A3 r% P+ N1 t8 J/ @Pythagorean **s, prime.
- E% c& Y2 w5 m$ l/ dquadratic residues. ' [+ d% z. O* p( Q8 m
residual curiosities.
) O8 B3 u( `- Q# O; Y9 ~polynomial congruences. ; v: A. Q9 W% }5 Z6 T/ G- q! ^' F
quadratic reciprocity, law of. + u+ a& U3 Q+ g1 L# e9 R _0 }
Euler’s criterion.
6 N f, ^& s" o1 ]/ wRamanujan, Srinivasa (1887–1920).
8 I" C2 _# c p0 {/ t& O( Yhighly composite numbers. 9 j; Z- ]2 I1 r+ Y' Z
randomness, of primes.
$ C8 _, Q5 H" [8 x; x* p5 }Von Sternach and a prime random walk. ) ?/ l. j) X5 L, K" q, F! V( s) s9 V
record primes.
3 ~6 a2 Q) `0 i# E6 |some records.
: T- W7 v6 `- _repunits, prime. 8 F; N7 U! f' ]! H7 F
Rhonda numbers.
: T" P |. P0 ]2 r* PRiemann hypothesis.
: ]! X2 M9 s$ b. W; i, I9 ^ l! Ethe Farey sequence and the Riemann hypothesis.
) }$ ~/ F, ^0 d J$ z5 mthe Riemann hypothesis and σ(n), the sum of divisors function. 7 t2 B% {1 B, y# f- S `3 E
squarefree and blue and red numbers.
4 [0 A7 W5 ?' e' r% sthe Mertens conjecture.
" E+ D0 n! F& f" h" ERiemann hypothesis curiosities. " P$ S0 D6 f" f; [3 G
Riesel number.
& b e' Z; D* Y( N A7 jright-truncatable prime.
" C0 @2 |9 F: x0 yRSA algorithm. / H! ]# z( @+ X1 P# Z
Martin Gardner’s challenge.
( A- @, k) M( Z+ XRSA Factoring Challenge, the New. 6 i0 J5 O8 Z3 D3 e! |+ U( m# c B
Ruth-Aaron numbers.
3 V8 O# s4 \0 o9 a# y0 VScherk’s conjecture.
. L* {+ l: J/ m- wsemi-primes. ! m/ O) e% T2 E& P! [
**y primes. & {, q* s2 }$ _+ Q- m0 g
Shank’s conjecture. ( k; q t! J& q
Siamese primes. 7 l" L$ y, w) {
Sierpinski numbers. G% T, j& m% @9 Z H+ m: [
Sierpinski strings. 4 X w) Q# A- L$ T& f
Sierpinski’s quadratic.
. g. z6 m: p I k( MSierpinski’s φ(n) conjecture.
2 |3 N" R* Q/ Q1 K* p" M3 K1 g* rSloane’s On-Line Encyclopedia of Integer Sequences. . G8 z5 L/ G/ \4 w1 C: P0 Z6 l6 \
Smith numbers. . \8 C' ?7 b$ ^8 I( u1 p: v
Smith brothers.
5 @0 A" z. v1 ~' T" z, l: O) I8 J* ksmooth numbers. + G$ _# R k2 @- _; I5 v
Sophie Germain primes. ( ]" j7 O; W1 k
safe primes. ! P& X$ a- N+ U7 d" a2 g5 i( n
squarefree numbers. % N$ k6 @2 a& d8 r3 [! b% u$ s
Stern prime.
' H" c/ u2 O9 f! J2 {strong law of small numbers.
: s* o) N8 a7 N& y5 T. _triangular numbers.
. Z U& ^$ p; h) Etrivia.
2 O7 f1 m* g2 g/ Itwin primes. / M r8 _& S! E* ^1 k
twin curiosities.
3 G0 |% r: V4 v2 a5 ?. ZUlam spiral.
2 I/ f7 w3 m3 C0 q4 }unitary divisors. 4 d% g. ]7 O) R/ O3 J; i
unitary perfect.
& Z% m: t1 l7 X$ u4 D: {' x3 Duntouchable numbers.
! R6 V( i6 [0 y+ u0 b2 Dweird numbers. . b8 f/ l5 D: I+ ?. I( C8 j
Wieferich primes. 4 ]7 q1 m9 T$ f, h2 m2 e
Wilson’s theorem.
" @. R2 a# ^- q+ S0 |6 y: u7 ~ \twin primes. ; A9 B5 E+ g2 P* C
Wilson primes.
$ v2 I4 W/ ~: T' L& D7 N# ?1 a8 RWolstenholme’s numbers, and theorems. 0 w8 ]5 O; H. w* D
more factors of Wolstenholme numbers. " s/ ~! x! ~/ J# U- H* I* J
Woodall primes. ' K" n+ D7 t) o$ h4 d
zeta mysteries: the quantum connection.