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数字的奇妙：素数

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Entries A to Z.
: R! S# p7 b5 s2 \: y* n: Nabc conjecture.
/ Z7 D0 U/ _6 u5 H9 Zabundant number. ; w) Z3 y" D2 x: v5 j. t4 v, U' b% ^
AKS algorithm for primality testing. 1 L3 [4 ~- [! p( V. B1 p# y) J4 m
aliquot sequences (sociable chains).
2 x3 j0 O+ p% w, Ralmost-primes.
' Y$ k4 t# r: K- z9 ?0 Qamicable numbers. 7 ?% B* l4 z! ~. [$ ^: C
amicable curiosities.
* u) _ J; r% ~8 i+ X' _Andrica’s conjecture.
% `# `7 q; @1 _5 n- farithmetic progressions, of primes. & w; R/ r5 a: E1 _- T v
Aurifeuillian factorization.
8 R3 f! x3 X: }! yaverage prime.
+ {) r( f' \" [5 D/ iBang’s theorem.
5 s$ _! {3 Q- `$ Q, vBateman’s conjecture. , k$ w4 N8 \! u; c$ h
Beal’s conjecture, and prize. * L; T0 U0 I1 ^4 X h. P3 ~: c
Benford’s law. 3 W) F% `, s1 G% Q+ ]! t
Bernoulli numbers. / { `/ ]9 O/ e8 ?3 M% `
Bernoulli number curiosities.
( e, ~$ \: d$ f1 wBertrand’s postulate.
+ o- W: v& d, V* E4 T8 cBonse’s inequality.
/ Q& V0 ?: ^# W) B3 _Brier numbers. 1 x9 d% s6 U/ x0 u! [) k2 P5 V
Brocard’s conjecture.
9 L* l6 N# \7 w2 a( QBrun’s constant. ! h9 R. A- v) a! l6 ?4 |; ~
Buss’s function. $ M0 e& q" w; W: r: S6 k9 { V) R
Carmichael numbers. ' K% [, x5 W, Z1 S3 o4 g) [% d
Catalan’s conjecture.
* e5 Y" ?$ ^. k' oCatalan’s Mersenne conjecture.
- V1 E ]1 B& ]9 @; ]9 t" ~2 F, vChampernowne’s constant.
: N; w8 ]) m Ochampion numbers. ; b1 i( j: i7 j" V% d+ q
Chinese remainder theorem.
7 ^: ` t' `$ L- f/ t% X& |1 pcicadas and prime periods.
' F2 R) P- h5 Xcircle, prime. + b! M/ ~( I! h1 u
circular prime. & q6 a7 U* ~" j) U/ h
Clay prizes, the. 7 O5 H# I6 u% r
compositorial.
' R9 G) n1 }, m5 `concatenation of primes. / l+ O9 G( z' W* L4 y
conjectures.
 z% U$ e0 L3 yconsecutive integer sequence.
$ i! o! U% Q% g& fconsecutive numbers. ; B" S! `8 `/ j$ s3 l6 C" u. o
consecutive primes, sums of.
9 k9 a( h8 b2 d( j! w4 w/ [Conway’s prime-producing machine. 4 i9 N5 }3 M3 R
cousin primes.
4 Q }& {% v, T4 C' c7 gCullen primes. 3 o. ~, X* H; b' t$ E$ u% O9 b( u& J
Cunningham project. 4 {1 e ~7 n& D2 L/ X4 j3 D
Cunningham chains. 2 u8 r; j# `4 T8 e# g8 z, N* \+ I
decimals, recurring (periodic).
. P2 _. Q2 V8 r( `9 E" l0 Lthe period of 1/13. ) t. B/ m5 |& u* F3 h; u# L) }
cyclic numbers. * ^, \4 P" F- K" g) \
Artin’s conjecture. 2 Y. N8 @* `$ O" F; f
the repunit connection.
+ a7 ?" a; A: _2 l& fmagic squares. 3 ^! S' T! O! Y/ k, u
deficient number. 4 q8 G% i: ?; z x. P4 T- i' I' v5 Q2 D
deletable and truncatable primes. ! W: X6 Y; s9 @& C: l% M) p
Demlo numbers.
% d1 `7 o* l$ Qdescriptive primes.
" a2 h" M7 v! c" _: kDickson’s conjecture.
2 r( [/ V6 G: L/ ]) U' u# ]digit properties. 9 h% d+ p7 {2 O w/ ^
Diophantus (c. AD 200; d. 284).
8 I5 a# l' U: g* v: c" n) q DDirichlet’s theorem and primes in arithmetic series. 0 A# D, ^& i G, {. l% e6 n# n
primes in polynomials. # p/ C1 a0 g. D7 X
distributed computing.
7 u$ |6 a' v- }2 P* [) {. u* R* cdivisibility tests. $ k* D( q- c. Z. \5 W3 q( \, A
divisors (factors).
1 E' \+ ~1 A6 y! H/ w& ehow many divisors? how big is d(n)?
1 n A/ g, h: p) ?record number of divisors. " @$ Z' Q# o8 p$ P/ B# ]
curiosities of d(n). / M. ^9 o, R8 z9 g5 z/ F
divisors and congruences.
* G, {' G: ~; i; B! J, t+ Q/ d* Xthe sum of divisors function. ( Y& e& b7 b; z8 j
the size of σ(n).
+ T9 }7 b5 P! c9 t! U9 @a recursive formula. ! h! E! i3 }; Y& y
divisors and partitions. 6 ^8 ^- I- C- H3 p& H( S5 W4 {; c6 U
curiosities of σ(n).
% k: I6 o; h* @) S& bprime factors. " L- Y/ r7 z. E6 p8 ?
divisor curiosities. 0 `7 d2 W) [' ]$ Z* S, i
economical numbers.
7 p! Z8 J9 t+ C" h$ W/ {Electronic Frontier Foundation. " g% E% C3 P: ^7 V5 z
elliptic curve primality proving. 0 `" R- I' R# k
emirp. 9 d' w2 Y5 A5 s! ?! U
Eratosthenes of Cyrene, the sieve of.
( U ?0 A# `2 c6 @3 k) j0 LErd?s, Paul (1913–1996).
& S2 b- l5 F) C! d+ ^his collaborators and Erd?s numbers. 2 u& d9 l$ c; q$ o
errors. ) k: C' I# h2 O9 a6 e( F4 c4 C. _
Euclid (c. 330–270 BC).
: d) _3 Y5 ?6 aunique factorization. 3 o6 @4 F5 ?; h
&Radic;2 is irrational.
+ _7 i- u1 v+ F0 w& FEuclid and the infinity of primes. / J1 T8 @% {& F$ P
consecutive composite numbers. 3 P0 {8 c$ H4 f% K
primes of the form 4n +3.
+ y' z5 {' L: j6 Fa recursive sequence. 1 U6 ^; Z& B# @; O% B! l
Euclid and the first perfect number.
0 [& B) ]. X9 @9 I- _Euclidean algorithm. 5 z: \/ A# T1 |( Q5 B+ l q; J. f5 z
Euler, Leonhard (1707–1783). ( h' t T/ q5 O' b- u
Euler’s convenient numbers. 5 E& y" Y- }" ?" q) _8 R
the Basel problem.
3 y$ I3 S# r! ]) Q5 _Euler’s constant.
( Y: s" f. J% JEuler and the reciprocals of the primes. 2 S' q5 x2 U0 G: n5 r6 l% m
Euler’s totient (phi) function.
0 x5 W$ c( i6 W' t/ f- _Carmichael’s totient function conjecture.
: d( i$ s- d/ M" _# {; I+ fcuriosities of φ(n). 8 K0 B5 [1 v" I; e' W$ w4 @
Euler’s quadratic. 2 z2 y0 E7 f! q
the Lucky Numbers of Euler. : \" B! Y) r; W" h) [: e
factorial.
# N4 z4 P, K: jfactors of factorials. : Q5 D9 w3 G f& y
factorial primes.
7 z" \' l6 o9 z1 nfactorial sums.
! S8 x5 [! v- q( [ A0 S" c4 Lfactorials, double, triple . . . . / X; D1 Q$ m6 ?" `+ i
factorization, methods of. + s9 v$ f& w ~8 C
factors of particular forms. : Z3 O D8 D) L t+ ?
Fermat’s algorithm. " F7 v* e4 @0 ?) [ n
Legendre’s method.
; ^9 Y1 I& w, ~: @) } P: Qcongruences and factorization.
; x$ Y7 E+ x, q- d+ c/ X8 @how difficult is it to factor large numbers?
% G: }1 R& \2 ~* K; V8 D; `4 A, {3 Tquantum computation.
! P% d% }7 f; E' \Feit-Thompson conjecture. 6 u/ z( ~9 x* O' k3 s
Fermat, Pierre de (1607–1665).
. i' ~$ T* S5 g+ s2 V0 TFermat’s Little Theorem. 7 x6 b. j; c7 ~* [9 P- o Y( ?
Fermat quotient. ; {6 r1 h% }5 E0 n: x
Fermat and primes of the form x2 + y2.
) I; @9 N; K5 e; P. n' U, u# tFermat’s conjecture, Fermat numbers, and Fermat primes. " g9 h! a0 g9 [. e
Fermat factorization, from F5 to F30. ! c* U7 S& l2 ~
Generalized Fermat numbers.
' k" o. `, d! a2 kFermat’s Last Theorem. 2 _9 S) A$ j; H: ~( O5 k! `
the first case of Fermat’s Last Theorem.
. w* N3 J, x; l& X c) J4 AWall-Sun-Sun primes. 3 M. {2 g# P1 \ \) u
Fermat-Catalan equation and conjecture.
 ?, S m% r5 T( y7 O& eFibonacci numbers. 4 _. X6 Y- _1 |: G# ^. V* v* } n
divisibility properties. . Y6 E3 l }# T% a, e) Z( a$ j6 }0 m2 h
Fibonacci curiosities.
* f* G6 G( n( {2 d6 V- eédouard Lucas and the Fibonacci numbers. 1 V& K& g2 I0 P/ L% ]
Fibonacci composite sequences. ' |0 F/ R* J' v# U8 S" P
formulae for primes. ! m% X o# |9 z' @
Fortunate numbers and Fortune’s conjecture.
$ C- X& M' b$ n; ggaps between primes and composite runs. ~6 M( p7 K2 U* Y T/ i
Gauss, Johann Carl Friedrich (1777–1855). + t0 l' Q0 \$ G; v, j9 o! ?
Gauss and the distribution of primes.
3 M3 a) E" N, P3 f7 l' z+ RGaussian primes.
: i4 v+ x8 Z4 \- _+ ?Gauss’s circle problem. * h8 A9 @9 \0 ?1 J
Gilbreath’s conjecture. 9 V# ?& U3 U$ D1 g1 p# R, E0 I
GIMPS—Great Internet Mersenne Prime Search. ' c1 N- z) ?" F1 |+ I+ X
Giuga’s conjecture. $ ~, Y& X* ]' Z- r- o1 @
Giuga numbers.
- {7 T0 M$ d8 \; r5 L4 N' [Goldbach’s conjecture. & `' w; Z7 ?% F% h7 ]% L* C
good primes.
 M9 }. L" T9 Z, DGrimm’s problem. 1 A7 G0 C5 A4 w* r# G4 d
Hardy, G. H. (1877–1947).
' s! k, ]1 Z8 G% ^4 PHardy-Littlewood conjectures. 6 i7 a+ z# O5 x" R! ~; C
heuristic reasoning.
% d+ s6 Z3 N; C% o1 U. ba heuristic argument by George Pólya. 7 N% f! \3 c5 Z+ }
Hilbert’s 23 problems.
( N7 }' E1 l5 n7 D% v, j- U' }home prime. * B8 u1 ^$ l, E8 Y
hypothesis H.
# h6 ^% u1 K& \2 C5 Pillegal prime.
) h( K! c( `% V/ w. s- r' winconsummate number.
7 l8 h+ ?! I: `( Q, o4 yinduction. * n+ v/ O0 h* [/ `, H
jumping champion. : U) ?! T+ Q/ ?# e' ?+ z
k-tuples conjecture, prime. ; k1 x/ ?9 ^1 i) x% f/ s# _
knots, prime and composite. ' v2 z' a9 s n' \2 I$ L3 P) ~
Landau, Edmund (1877–1938).
: V, @+ ` f# d' _left-truncatable prime. 0 h, ?7 b3 f* A1 m+ x; ^9 t( v+ M' S% v
Legendre, A. M. (1752–1833). 2 O: C: A& s8 \/ a/ G& H2 y
Lehmer, Derrick Norman (1867–1938). , R( |: i! Z9 p4 R
Lehmer, Derrick Henry (1905–1991).
! R# F/ A* r( e6 |* U! k" nLinnik’s constant.
6 F( n3 K, a+ C+ b) iLiouville, Joseph (1809–1882). . q c9 `- m1 w9 l& d5 }" M/ c
Littlewood’s theorem.
9 Y2 p0 w2 `$ ]% { B$ wthe prime numbers race.
: o" V4 }! P2 B) sLucas, édouard (1842–1891).
3 E) k. h6 R2 [# h( w6 uthe Lucas sequence.
2 |9 e+ i! K9 h" bprimality testing.
) \/ l/ \8 S( v, c4 A, u4 H+ ~; aLucas’s game of calculation. 4 t- @1 B6 S. e0 S" [
the Lucas-Lehmer test. ! x8 `; M* C* k3 I% A
lucky numbers. - t3 d4 }3 ?$ z A
the number of lucky numbers and primes.
( U5 |1 l+ a; I+ F“random” primes.
0 m6 z) a3 D! a5 P3 }magic squares. * S$ Q" ?9 O! b1 i
Matijasevic and Hilbert’s 10th problem.
1 s4 ]/ z6 L! F4 kMersenne numbers and Mersenne primes. - t4 E% V' f% G7 _) {0 W" Z1 ]' G
Mersenne numbers.
' h2 ? C8 `& }' h: U- q0 ]hunting for Mersenne primes. $ Q- d% i1 J% z; q
the coming of electronic computers.
- ^+ h" q1 F5 a; oMersenne prime conjectures.
# b! z5 s$ ]0 \/ W/ g- T2 k6 `6 \the New Mersenne conjecture. ' k; D4 R8 `6 g# z6 Z) D
how many Mersenne primes?
: F. v2 B0 O. W5 h# T4 H7 }0 cEberhart’s conjecture.
5 z M& H* E/ t+ p7 }. ?factors of Mersenne numbers.
& J. q! ~- p- H6 t! @( eLucas-Lehmer test for Mersenne primes. ! K" W+ X" Y9 B/ @# t
Mertens constant.
8 a3 c O! b1 E# Q& cMertens theorem.
) X( f% l+ O: N: E2 ~Mills’ theorem.
7 t2 W) H! v% SWright’s theorem. 7 b5 E; V5 C/ C) R0 M
mixed bag. 7 z# y2 X) G/ N
multiplication, fast.
$ Q7 J7 c7 W/ Y0 wNiven numbers.
' `" T! V! M# @. I. z7 ], Oodd numbers as p + 2a2. 2 s3 F7 A% Q8 K2 x8 `2 Y4 g
Opperman’s conjecture.
, E' Z1 t, o* K, v# Z! X+ ]& Epalindromic primes.
$ W/ f, S6 N0 f9 R, Apandigital primes.
 H0 m$ A: Z8 SPascal’s ** and the binomial coefficients. 4 g7 L( l" _! Z$ a
Pascal’s ** and Sierpinski’s gasket.
: p5 m. n6 H& S' KPascal ** curiosities. ) a% i& V% ? b
patents on prime numbers. & e5 G: H6 `3 W" K
Pépin’s test for Fermat numbers.
1 J- k) `& N/ A7 m; @( \perfect numbers.
5 J9 O; B4 I. y R+ Todd perfect numbers.
2 @3 H0 l4 c2 W1 ^5 Zperfect, multiply.
2 c$ h. K' @: q `permutable primes. k; P( P% N! a5 u% x1 V9 j
π, primes in the decimal expansion of.
, k- i" l* q+ J4 ^3 X" X# w. ~Pocklington’s theorem. 7 W) c$ I b( ]
Polignac’s conjectures. + _! u' Q* R2 K# n- e
Polignac or obstinate numbers. ; @+ A% Z) g0 P7 Z$ |
powerful numbers.
& n* r ^: j4 \primality testing.
* j* m$ E9 |, [: R3 L, X% B% j1 Eprobabilistic methods.
 \ ^( `7 G4 u; {prime number graph.
5 I4 x- L2 X' Kprime number theorem and the prime counting function. 3 \, d5 E c' [1 F. r( u% v% _( o
history.
+ a/ e) E6 }1 l/ ~7 W# O7 Celementary proof.
8 B% I' ^8 X1 J1 frecord calculations.
! _& K. y, A% }; I2 Z Aestimating p(n).
6 W- H4 H T9 ~* [# ucalculating p(n).
) a5 Y* Y9 K: y* B& w, ~5 `/ \a curiosity.
$ ?/ f; Y7 F; Y0 n7 w" \/ u% dprime pretender. * k4 Q0 {: S* ~& v1 C7 m2 n
primitive prime factor. , }& n9 c ?3 s; e7 n* \6 B3 g, E
primitive roots. ) W) f* w$ Q6 p7 V# P7 c4 X0 o
Artin’s conjecture.
9 k+ @$ p0 b" A& p3 ~, X% |0 ja curiosity.
& p9 D# e8 k+ |7 A _primordial. 4 Y* V* h( M& c8 {$ v
primorial primes.
% K3 w6 c; L" U8 S# X, Q9 AProth’s theorem. 5 A+ t4 p B% {: ]0 t
pseudoperfect numbers.
8 g$ j7 |2 W# t. c. zpseudoprimes. 0 o& {. p- W0 r- h# }& R& a
bases and pseudoprimes. : J: K& J( ^, `& I
pseudoprimes, strong.
" N" [: S: p' y# D( k5 a& gpublic key encryption.
6 L0 M9 j# ~3 D( F( ]pyramid, prime.
! U* L5 M& F- i4 G% @+ tPythagorean **s, prime.
7 G# H q, ^, G7 G; Nquadratic residues. 7 z2 |6 Y. L! O m% ?
residual curiosities.
. O8 S9 X; B4 l5 Lpolynomial congruences. - q$ B' G2 ]4 M9 \4 u" I
quadratic reciprocity, law of. 6 w7 ~4 Z5 H W: J
Euler’s criterion. , @/ p* U5 I* s, U. E! e
Ramanujan, Srinivasa (1887–1920). ! s' x4 f* t1 S
highly composite numbers. 4 d, }. ~2 C& G1 @+ O
randomness, of primes.
/ l. i* d4 C E5 E& J* S$ WVon Sternach and a prime random walk. 2 M1 ]8 s- J) R
record primes.
) T. o# s( |/ e+ s( K5 ?some records. : W5 e% |7 w+ X, r. W
repunits, prime. + U" L0 }) L$ c
Rhonda numbers. 8 m: ], s" f9 u$ `" l3 h
Riemann hypothesis.
" _' Y Q) }+ a% T( Y9 Sthe Farey sequence and the Riemann hypothesis. 2 S. n3 d" |' W" x" a
the Riemann hypothesis and σ(n), the sum of divisors function. 5 x8 b, o8 U5 g
squarefree and blue and red numbers. $ Y& T( I2 l7 c% X _. \5 S2 M
the Mertens conjecture. ' \3 {5 @& P3 n. T& b
Riemann hypothesis curiosities. 8 `+ b2 k6 t/ U5 A" i5 `5 \
Riesel number. % e y* ^2 I# Y
right-truncatable prime.
) N' N4 k* c1 X8 j) R* JRSA algorithm. , _7 k* V0 f7 G% z
Martin Gardner’s challenge. 3 Y2 J6 l9 C9 Z# `+ S
RSA Factoring Challenge, the New. . R( c: F$ b8 a$ a/ A/ Q
Ruth-Aaron numbers.
* N: b& [5 R8 f& y9 iScherk’s conjecture. & d4 ~. F4 O n. a ^. V
semi-primes. 5 L" u1 p( R; g, O' W5 B
**y primes.
0 S0 h: R: y4 |1 cShank’s conjecture. ( x+ e6 L" U8 m% s
Siamese primes.
* e+ |+ b x+ ~# H! D5 J. y8 BSierpinski numbers. 3 z) h. i$ q0 F. y) n2 O4 B
Sierpinski strings.
! C0 p t$ ?* lSierpinski’s quadratic. 6 o* e/ R0 P3 i6 H3 m& ]
Sierpinski’s φ(n) conjecture.
# U; I& S6 k5 [8 c. }1 A) z( ?Sloane’s On-Line Encyclopedia of Integer Sequences.
4 x1 x& q" o4 I- P( Z& ySmith numbers. $ V& K9 ~, T" T' w
Smith brothers. 4 V+ ^' I( {8 s' `% m% g
smooth numbers.
/ o" j. y, m3 ]8 `! p* n6 ZSophie Germain primes.
' J' F9 N, c" o7 ]* jsafe primes.
( I- [7 w- U- ysquarefree numbers. ! R6 P- E1 ~! b
Stern prime.
- B# j) g! U Y* E. n' ystrong law of small numbers. % _$ U4 C: X0 C* _# h2 @
triangular numbers. ' x0 r' a/ q( j& m: T5 u5 O! G' ^
trivia. 6 D) c, w, Q2 U
twin primes.
- r8 K: S, P" L+ V# F) Mtwin curiosities. 7 D( k* A; W) e5 M4 t. D% o
Ulam spiral. 4 f( W+ a" D3 L
unitary divisors.
* N5 l: m* A7 U9 m j! N& Junitary perfect.
; i; b0 `0 I$ U. D9 `+ M4 Yuntouchable numbers. 4 T/ \. |8 H2 p2 \6 z
weird numbers.
) O3 {% x1 l5 rWieferich primes.
$ g+ m5 N) l7 r: i/ y IWilson’s theorem. 0 ]5 k4 @& i* Y, Q& Y N
twin primes.
, J4 }1 Q9 m: n% FWilson primes.
4 ~5 u: C6 X5 mWolstenholme’s numbers, and theorems. 7 Z( \0 X' K& E6 P, {1 w' K
more factors of Wolstenholme numbers.
; J% \+ q9 V& KWoodall primes.
) c1 c( A( b2 i" w$ R& B szeta mysteries: the quantum connection.