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数字的奇妙：素数

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Entries A to Z.
. K7 N8 Z2 M) C$ p- k6 ~; ^abc conjecture. ) S2 m+ b1 G; X' ?; a% T
abundant number.
/ T- C3 P) Q4 H- `+ BAKS algorithm for primality testing. # a% e, o3 C- V
aliquot sequences (sociable chains).
) K U% Z @# ]8 ?almost-primes.
* o* \+ A9 s( \5 C8 {2 Aamicable numbers. 8 ?- \" X, n- u
amicable curiosities. ) R3 U# ]! R) Z! ]' B
Andrica’s conjecture.
% A* f7 U5 F6 U. warithmetic progressions, of primes.
# K1 P7 @: s+ G1 CAurifeuillian factorization.
& v3 x) ^$ L2 n' m3 I$ |average prime.
5 C# p4 G2 I' J1 K4 `" gBang’s theorem.
0 g8 d6 U) D1 a, z) u1 y4 F4 t3 YBateman’s conjecture. $ B+ I0 ?0 b" y1 N( o# p
Beal’s conjecture, and prize.
! `- w& f5 W4 b- ]: KBenford’s law.
5 ?0 O- Q. ~; ?" v3 n- i8 TBernoulli numbers. ! R1 K v: h2 j: H% m% E
Bernoulli number curiosities. 6 j$ m* H# D: j8 `$ f
Bertrand’s postulate. 9 ^6 S$ }# b8 R
Bonse’s inequality. 8 m. D2 i% H2 N1 [
Brier numbers.
) y* b) |0 k- E) f0 g. zBrocard’s conjecture.
1 H- Q7 m! i# a) P% V( o+ T& RBrun’s constant. 6 q0 x8 o, B# }+ h4 X
Buss’s function.
) H5 z n7 w' ~3 Z7 sCarmichael numbers. $ C. U% S+ w% ^- |3 g: U0 B
Catalan’s conjecture. " S) n7 |7 K* o2 Y" T9 W
Catalan’s Mersenne conjecture.
; |/ i* a. B: K! o) X d5 kChampernowne’s constant.
! R' b) x: i2 z/ @champion numbers. ( m6 F$ V/ N% K
Chinese remainder theorem.
9 a5 M" y+ a1 ~/ acicadas and prime periods.
" B$ i$ m$ x2 P4 J0 M( F0 i2 lcircle, prime. , @. ]5 S6 q+ b0 ]) t8 J! D7 k4 F2 n
circular prime. . ?) S6 ?8 k# k& y: f- Z) Y6 V1 K
Clay prizes, the. 0 u5 l, b" m: B: r, x
compositorial. # ?# N. N0 Q2 N1 {! _% q
concatenation of primes. ( J7 J! E: o3 g1 Y) C
conjectures. 5 H- N' L0 ^* g+ ~5 O8 _9 a8 H
consecutive integer sequence. Z6 p6 x3 s, {( a |# B
consecutive numbers.
& s/ l# K% P: x8 ?' ~consecutive primes, sums of. 5 \. t j/ S s0 w; f# s P1 O( i
Conway’s prime-producing machine.
' `. m7 o9 S2 I; acousin primes. 8 S3 m$ f* }/ y& B9 C/ H
Cullen primes.
) ?/ O5 \8 J" {3 g H& BCunningham project. : i4 _5 ~0 F- b: G4 U
Cunningham chains. ) U" P1 z9 y Q2 i- d5 y- v6 A
decimals, recurring (periodic). 0 Y1 O+ Q6 E3 n7 L% |. n" C
the period of 1/13.
0 ^8 H# T& j2 Z* E, O+ ~cyclic numbers.
/ X9 a* r# ]' x/ q/ n# j. UArtin’s conjecture. + v' ]4 U1 t z7 c' P1 ?
the repunit connection.
; v* T; T% j! V- Dmagic squares. + j8 z: i6 M3 R" z! U
deficient number. 3 F. T4 Q1 i: N! y O7 n. h* e
deletable and truncatable primes. ; w% T) }0 {# h# K4 i8 E2 @
Demlo numbers.
0 M7 ]0 W# ^3 Idescriptive primes.
& o7 T# [+ z- O/ |Dickson’s conjecture. - y8 G8 A" I4 M. ]$ K. K- O
digit properties. * h. N) ~ B" y7 ]
Diophantus (c. AD 200; d. 284).
- `7 y2 t: z3 g/ F0 IDirichlet’s theorem and primes in arithmetic series. 7 F- l/ M' B# `; X5 g* P7 q# G
primes in polynomials.
( w" s8 X; h3 \/ `0 mdistributed computing. % A, G/ V' W: M7 c! f
divisibility tests. + ?. `. u2 ~6 B$ B9 n# M
divisors (factors).
! w' C" m! n* _8 D1 {! T. E; k5 `how many divisors? how big is d(n)? - r: S7 j1 ^% n) t
record number of divisors. % S/ e& b+ Y& t) s
curiosities of d(n). ( Z) i0 S# R/ r8 Q+ E# x, d/ I4 E
divisors and congruences.
$ ~/ _' u; h- Kthe sum of divisors function. , [) [) v, a* D' w
the size of σ(n). 2 e9 p5 ?+ T% W) a; d5 U, P
a recursive formula.
; S" O( Q9 Z# v& ]! jdivisors and partitions.
* J& q7 F, H. Z: P7 L/ V- |curiosities of σ(n).
4 v" c1 K' J- m2 ~* c3 Qprime factors.
( H1 D- o8 ~. |divisor curiosities.
$ I4 K8 `% q) q8 Ceconomical numbers. $ c" `1 |. {$ [* M2 W( i- m, z
Electronic Frontier Foundation.
( F# m e' }/ A: W F4 t" @elliptic curve primality proving.
! D$ h/ \9 w" ?2 Femirp.
1 A7 F5 h4 | z8 h$ REratosthenes of Cyrene, the sieve of. 9 E( L6 \4 I' L% {: U: N
Erd?s, Paul (1913–1996). ; ^. u2 l" h. i% R. m
his collaborators and Erd?s numbers. 5 G: Q3 h" c0 y6 U& P+ D& g
errors.
4 I3 r! |% u, G/ dEuclid (c. 330–270 BC).
4 U8 Z& ^ ]3 I+ ]/ `2 t7 N( s8 punique factorization.
6 e) ?5 a4 g6 |) c&Radic;2 is irrational. ) e" q5 S* Q1 i! e, i
Euclid and the infinity of primes. & C, E+ C0 L- S
consecutive composite numbers.
, O, o8 W. B" g* n3 h, ?3 }primes of the form 4n +3. & a. V( H; O& [. H
a recursive sequence. 3 A/ F+ e* Y, v/ b
Euclid and the first perfect number.
% e; Y4 k1 B! M9 _7 J' w. u+ W8 VEuclidean algorithm. 7 X3 |, N, ?3 R
Euler, Leonhard (1707–1783).
% I& ]6 `1 t; y; _Euler’s convenient numbers.
( I3 _. c3 i3 q( M- J uthe Basel problem. ! F2 g% Q" l: _7 D! [, v3 B8 L
Euler’s constant.
; j) F- p" ~( O$ @7 hEuler and the reciprocals of the primes.
( U- ^8 ^/ U6 q) h. T* JEuler’s totient (phi) function. . Z6 X' X& ^( S2 ^9 ?
Carmichael’s totient function conjecture.
3 y& Z/ i! g. H, Q Vcuriosities of φ(n). $ B) ?6 C8 k3 F( b
Euler’s quadratic.
+ F& C2 g: k! W% Kthe Lucky Numbers of Euler. $ q. R& R9 E' ]$ d1 s0 f/ P+ ]
factorial. ' Q& Y3 [+ M. f$ l2 ]3 U: U0 V
factors of factorials.
3 _0 e* S6 p( v. l; K2 Ffactorial primes.
9 P8 O4 @: {! I. X! f, ofactorial sums.
: h9 R' _8 q0 C& l" l) ]factorials, double, triple . . . . & h7 R. k1 W; ~, p, k. w& V5 G
factorization, methods of. + g( K( c+ i! n! Q: r
factors of particular forms.
+ ?3 H/ k" F( IFermat’s algorithm.
: z3 @/ M" k' b: ^Legendre’s method. 5 D3 I% Q" L2 ^0 X" w# E
congruences and factorization. : h& l* R% x5 O, q" x" {' d
how difficult is it to factor large numbers? & ~: [/ `$ h; ?) _# Q- ?
quantum computation.
7 o$ e5 `+ ?5 a- V: GFeit-Thompson conjecture. t: s+ R. [/ V! Z" N! G, ]
Fermat, Pierre de (1607–1665).
' a: |; Q' V E; E2 n/ M. LFermat’s Little Theorem. ! C, W. [6 [0 ]" ]2 r: {5 z4 S/ r
Fermat quotient. 1 M0 H2 h- I. R- i* i2 W
Fermat and primes of the form x2 + y2.
5 F, n/ C% u$ q$ M3 Z0 U$ {7 f$ w# z! \Fermat’s conjecture, Fermat numbers, and Fermat primes. * o4 ~4 e3 U7 {% \! w; g' ]0 V* i
Fermat factorization, from F5 to F30.
$ B9 ~2 S, ?3 t+ sGeneralized Fermat numbers.
! F" o ]1 r, ^/ fFermat’s Last Theorem.
9 y6 O; _4 ~# R2 u. O5 A9 Q; `- F3 @the first case of Fermat’s Last Theorem. " N5 @* M9 }2 l. Q
Wall-Sun-Sun primes. % C" u& O" ?) T) E" L0 a3 v% x
Fermat-Catalan equation and conjecture.
6 f. @$ N6 m8 r, AFibonacci numbers.
! U# M! {5 w2 B* u9 `divisibility properties.
! |3 `* L$ }9 f4 }. kFibonacci curiosities. # B; Y5 S r8 B
édouard Lucas and the Fibonacci numbers. % _( g: Y& d3 W+ I+ x) C% o
Fibonacci composite sequences. / g2 ?( M, j- f9 J' u' c
formulae for primes. 3 T2 w5 C1 M' M* |% |+ n: b1 A# Q4 J1 d
Fortunate numbers and Fortune’s conjecture.
: E- ^' F: d S! n4 |gaps between primes and composite runs. " E) m# b' o& g- ^
Gauss, Johann Carl Friedrich (1777–1855). - M: i1 n/ i% e4 N* a
Gauss and the distribution of primes.
# b$ W5 c. Q) sGaussian primes.
0 k4 E) F% t/ j- MGauss’s circle problem. 7 _9 H" n* N! E
Gilbreath’s conjecture. ( \9 t' a( R- |0 j
GIMPS—Great Internet Mersenne Prime Search.
) l: L! r7 P6 M4 N$ s9 @8 r) y6 PGiuga’s conjecture. 2 `8 w% z( u( x* @& J/ ~ b
Giuga numbers.
% ~* q o% {( J9 EGoldbach’s conjecture. ) q# O' Z9 X/ G- Y4 Z, A3 I
good primes. $ G, c3 L+ h, F: k+ h2 G9 U! K1 ?& i$ F' y
Grimm’s problem. % w k, Z, R1 X8 m
Hardy, G. H. (1877–1947).
6 t) D. J5 h( t! V9 k: _Hardy-Littlewood conjectures. , [' {) T; `% Q7 w9 v
heuristic reasoning.
3 ?% E, x! r6 ^ Sa heuristic argument by George Pólya.
% X; H7 l- |) B6 m! o# hHilbert’s 23 problems.
+ o8 Z( j8 E6 M3 |" L9 G) D8 O8 thome prime. ) p3 u& w4 {8 W, U
hypothesis H. : F8 b1 I+ e1 l' U9 N3 [# ]
illegal prime. Q; X( p! h& s8 N
inconsummate number. 4 L- t; e# x. \) u: u& f( O
induction. . l# C( W: k( L4 Q
jumping champion. 5 _$ K N: ~0 L6 \* ]
k-tuples conjecture, prime.
1 I* a+ v7 n( v' e) I/ `& mknots, prime and composite. . m4 C2 j/ _2 ]8 G# h& l+ t
Landau, Edmund (1877–1938).
$ m3 f- P- W' l8 V7 H9 J- Kleft-truncatable prime. 8 J8 d" o, [- z F% e
Legendre, A. M. (1752–1833).
) p8 q( N- R' D2 q4 W/ M {Lehmer, Derrick Norman (1867–1938). 9 v1 c, i/ Q9 J4 q
Lehmer, Derrick Henry (1905–1991).
# s3 W. K2 K, S0 ILinnik’s constant.
( Y2 n3 t, ~- O& G* W7 ?& X; pLiouville, Joseph (1809–1882).
: j% [3 y; o; f/ q. C3 J0 ULittlewood’s theorem. % }8 W7 T9 l5 O. P
the prime numbers race.
, L5 f/ x6 p! T4 }' NLucas, édouard (1842–1891).
5 O: s! D3 I# d" |* ithe Lucas sequence.
& i( y9 e! d7 o# nprimality testing.
# K; l6 a) o! Q: }4 G/ {6 gLucas’s game of calculation. , t; K$ l. K* U( f( k5 n- P! k4 I
the Lucas-Lehmer test.
' e% C, F# c% k- a5 N3 r, Elucky numbers. : b2 h# ~9 z N! B
the number of lucky numbers and primes. ' F, ~: x9 r& P
“random” primes. + C6 c f& g; M3 K% [
magic squares. . Q! p* E# V5 Y: }- [4 Z
Matijasevic and Hilbert’s 10th problem. " g4 E/ S9 R6 j1 I7 r% Y
Mersenne numbers and Mersenne primes.
' {3 n, {& O5 A7 ?* |( x' C2 s; x1 ^Mersenne numbers. # R$ A1 D: J: B( O5 c. l$ M3 |
hunting for Mersenne primes. 5 @- e# Z( G, x) @
the coming of electronic computers. $ r. B% J$ r/ e( g
Mersenne prime conjectures.
2 ?, }8 e2 ?! e& D% _the New Mersenne conjecture. # f! e: ]2 F& b
how many Mersenne primes? % B$ T, |( h; s" d% y
Eberhart’s conjecture. - f3 l: v$ R; z! ?: _* ?7 b4 \
factors of Mersenne numbers. $ A! u, A3 c" @8 P) U3 h4 ?
Lucas-Lehmer test for Mersenne primes. 1 t0 u0 ?" B/ [
Mertens constant. 5 M% i) {0 P# y
Mertens theorem.
* i7 v2 f" j n" ?: O3 T! ]3 \& @Mills’ theorem.
; s K) y# c+ t& CWright’s theorem.
5 a; E1 `7 M/ v r7 M' umixed bag.
& K( T8 L7 t/ u; }* z( Z. Emultiplication, fast. & ?5 a+ Y5 H E9 P$ \+ |9 C
Niven numbers.
% Q/ W7 u3 ?# t) @; x# |% qodd numbers as p + 2a2.
) h/ K! f$ e i# L" POpperman’s conjecture.
6 T0 u& K2 i4 r- ^palindromic primes. ( b* d4 d, T. b9 N
pandigital primes. 9 o5 n# u+ z; n J
Pascal’s ** and the binomial coefficients. ) K# N) G, |5 S8 c! c
Pascal’s ** and Sierpinski’s gasket. 9 S+ @" `# Q# F/ N: G
Pascal ** curiosities.
4 n z9 y1 v8 i* Z! A; ~patents on prime numbers.
2 I) d- Q! I/ N5 a, h# oPépin’s test for Fermat numbers.
; t, `- i2 Y( r. wperfect numbers. / P% b$ z( x2 u' T3 Q
odd perfect numbers.
; \- }, [# S/ l) `- U$ Mperfect, multiply. 2 M! M3 Y' P9 y% K* \, H% X
permutable primes.
/ `" h. `8 s- h# `/ D9 Y+ [π, primes in the decimal expansion of. 3 w7 Q" T% ~: X9 w- R( q0 t
Pocklington’s theorem.
" o( v& B/ l0 a" Y& Q; | l8 uPolignac’s conjectures.
5 a! M t& E8 C9 FPolignac or obstinate numbers.
- D" l- ]3 v2 I3 F& d( Jpowerful numbers.
8 I9 X! e5 T% P, t( xprimality testing.
4 E, j; Z( }4 E1 S7 ~probabilistic methods.
! E8 n# f2 e2 f4 U# iprime number graph.
% ]- U# @5 Q5 b. fprime number theorem and the prime counting function.
" n% x; u; `$ \8 ]: H' whistory.
: b% ? _) r/ l/ b' @elementary proof. ; K% x( V: d1 _" D6 |$ t+ X
record calculations. % \3 c! P) J4 q6 w* H; o# \3 s7 _ s
estimating p(n). . W; N/ r5 z6 X9 p8 x; [$ ^ h5 n
calculating p(n). 5 v. N# w. H+ N3 h% ^
a curiosity. . e+ d3 v5 s6 i! O+ \) k$ m& r
prime pretender.
3 C2 v, q( O# N6 Y' `( oprimitive prime factor.
4 C( X- N' Y& J7 i/ V4 @; h% xprimitive roots.
- }' l' K/ g; \& o8 iArtin’s conjecture. 4 q2 |. d ?+ M4 b. A
a curiosity.
9 g6 _9 c6 n: Iprimordial.
2 a' }1 `9 l4 V; Zprimorial primes.
2 {2 m9 U0 h& c f! yProth’s theorem.
) e$ f c$ H, U) ~5 w( S" ypseudoperfect numbers.
6 c, q$ Y$ A0 ^7 `3 P9 W, upseudoprimes. 4 c2 Q4 ~/ _2 Y) `4 `5 m a
bases and pseudoprimes.
* N1 V# x, j; t, m, r4 ^pseudoprimes, strong.
) \3 b @* C( f8 t& u1 c( kpublic key encryption. ; x4 e+ L0 H! F7 u; ] c0 m
pyramid, prime. 8 c8 S4 m3 ]; g0 P( W
Pythagorean **s, prime.
( q" V0 m7 D4 ^quadratic residues.
" d4 G7 G9 t# B( Y' o2 dresidual curiosities.
" g, T, j H' K# |polynomial congruences. 6 O5 ^$ M. g, ]' m) c
quadratic reciprocity, law of.
. a8 T e% [8 {9 f3 ~Euler’s criterion. , K, u6 W( J: X+ k! T- i
Ramanujan, Srinivasa (1887–1920).
( R N# V5 i3 @ yhighly composite numbers. - c; K. V( G/ Z2 t# H
randomness, of primes.
" M4 O% F. j3 |$ ?% I1 hVon Sternach and a prime random walk. 8 z+ I8 b/ u, A; m- j
record primes. / y& x) W, d4 L( l( H+ H2 _ W
some records. $ r6 t- L* K% L4 w# T% m) @
repunits, prime.
* _. j4 t6 j% V3 JRhonda numbers.
+ `& T+ c% c' @# s1 ^/ t) oRiemann hypothesis.
% L0 w0 Q* m( ]) ~; o1 ythe Farey sequence and the Riemann hypothesis. 1 r0 V. o9 Q0 c
the Riemann hypothesis and σ(n), the sum of divisors function.
7 K! ~% x' O: }/ qsquarefree and blue and red numbers. ! A- J3 T4 A2 t3 \
the Mertens conjecture. * ?0 E9 A ~, ]. V. q. H" q
Riemann hypothesis curiosities.
5 b# u K+ b8 Y: a( m: m+ }1 zRiesel number. " O; ~6 a8 l* x" L
right-truncatable prime. & h; z2 }# Y3 c& Z0 W+ `: M
RSA algorithm. 3 K2 J. g1 U" t. F1 m
Martin Gardner’s challenge. % a! N8 e! M e- s$ v! x3 G/ i [! \
RSA Factoring Challenge, the New.
. ~, `4 [+ K+ F! g4 I- K8 F, I% GRuth-Aaron numbers.
" C8 @# @( x6 o! P: K6 O( I0 m/ O8 gScherk’s conjecture.
1 }5 t5 V$ w# D6 R* W7 `3 D4 j) Psemi-primes. ( h# x8 Z* M/ G/ r9 A% n9 P
**y primes. * O& N" { ?9 g1 U! \
Shank’s conjecture. % Z' m6 A" a4 P9 i0 V
Siamese primes.
4 l# k- k7 ?5 Z$ D: CSierpinski numbers. ) j1 d* |( W" `9 N6 ?; [, o
Sierpinski strings.
* g5 }. Y0 z* E/ FSierpinski’s quadratic.
8 W0 P4 B/ X u) M6 N/ Q) J) H1 YSierpinski’s φ(n) conjecture. 7 f, Z7 ?4 x0 w1 `9 j, m8 C1 }( }
Sloane’s On-Line Encyclopedia of Integer Sequences. 7 r' J6 C v4 ?& M! b$ o& H1 @
Smith numbers.
7 i- \6 Q0 h$ @: b: B# {# p5 zSmith brothers.
0 g2 F6 S& y. [1 Xsmooth numbers. 0 ?2 H0 K: ?/ d* b2 b; i
Sophie Germain primes.
 e4 @2 U- r% Y4 U {9 V, Q/ Zsafe primes. 0 r" D' h& D1 H" z. r1 k
squarefree numbers.
: x4 Y+ \9 v9 X- B, qStern prime.
) q+ Y* R) O9 F% Wstrong law of small numbers. + C, F' h+ {$ V; ~& S% [
triangular numbers. + ~! R) V) O, ~- E% c# ^3 a, ]
trivia.
* a& y7 G# J/ p4 @: {) P+ mtwin primes.
/ Q6 |* I. r+ L3 [: n' ]# c- Gtwin curiosities. ( N9 i1 f g0 T
Ulam spiral.
) e5 u; b; n1 M) ?7 _( tunitary divisors.
/ |9 n9 k0 D* `2 Q8 m2 r punitary perfect.
( V6 a. C& N% @untouchable numbers.
+ w" E0 U+ c% N: a, ?3 I0 nweird numbers.
- k" U2 E% r' M' A3 d0 n% dWieferich primes. % q" ~$ r" N1 k9 P4 _, F
Wilson’s theorem.
/ i3 }6 }) R. \/ n% L2 ttwin primes. 2 Q- J, h# Z$ S! q# M4 r
Wilson primes. * E) B+ c' Y' K( t, \2 u2 C
Wolstenholme’s numbers, and theorems. 8 }% H+ O6 \" O# C2 G
more factors of Wolstenholme numbers.
4 J) |# X4 n5 }& X0 Y4 lWoodall primes.
 f \* b. _1 K* K$ Wzeta mysteries: the quantum connection.