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数字的奇妙：素数

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Entries A to Z. 1 {8 ~0 D- R# |5 B8 s
abc conjecture. * y) K! Z! l8 d2 s3 C
abundant number. : e7 R( H2 g4 y4 h5 R5 a% h* R7 g
AKS algorithm for primality testing.
0 H9 y$ [+ d$ D* t7 |" i4 Aaliquot sequences (sociable chains). 9 ?4 \6 M/ y1 j! {. g+ o2 g
almost-primes. ! T9 ]4 d: g8 [3 [3 ]
amicable numbers.
; y" w" V1 g; S5 kamicable curiosities.
5 A9 d$ Q/ r* ^4 b+ V3 tAndrica’s conjecture.
8 X% E9 ~2 [' R( n7 |: E3 u$ tarithmetic progressions, of primes.
# z/ ?* V2 t5 SAurifeuillian factorization. $ i" ^2 J/ [4 e Q P( f
average prime.
# u7 B+ l( k' p& i$ L; V% @' uBang’s theorem.
& x( @; i& S& Q7 v, yBateman’s conjecture. 8 o0 r2 e) \1 R/ G6 n" r
Beal’s conjecture, and prize.
6 `* {9 P; U5 a' wBenford’s law. - L. `4 y8 H& w) Y, F8 Z
Bernoulli numbers. 7 g, E& }7 A k8 p5 F# v) T- b |
Bernoulli number curiosities. J$ o+ h+ E& Y2 o# |
Bertrand’s postulate.
. Q& |) ?8 O( |. W9 OBonse’s inequality.
0 d/ g* f0 a% C5 iBrier numbers.
4 V! j" B5 M/ r, [ i, Z" I% hBrocard’s conjecture.
# c: M/ Z8 X4 v; d1 \- }7 \Brun’s constant. 8 f( T/ d! ^0 I. K- k5 ^9 }2 E; {
Buss’s function.
. ~ G7 f3 Y& l8 S+ `5 e5 b+ uCarmichael numbers.
; k9 n# o: a+ M: MCatalan’s conjecture. 7 P) Z: n g8 `* ^
Catalan’s Mersenne conjecture. $ G% o, T) j8 J) q* P
Champernowne’s constant. ( z' M) x) a, l) f5 t
champion numbers. ' n, h& M/ O" \ g
Chinese remainder theorem.
9 j5 D1 i. Q# A6 }cicadas and prime periods.
) g+ V, Y0 O3 E6 ]; N ~circle, prime. 3 k2 ]7 G+ {2 _) U8 _+ N, i: `; e
circular prime.
# Y1 G, t) V$ o! u4 C/ \6 _+ k/ FClay prizes, the.
* l/ w; W" K% A& x# X" jcompositorial.
5 J3 t$ A+ U O) ?6 M9 b" wconcatenation of primes. / B8 G* N" f3 Z1 p e; w1 d8 N' }
conjectures.
+ ^$ ^0 i0 I0 E- T+ @% K. `3 t: kconsecutive integer sequence.
6 K2 X5 `! u J) H+ [* q! H: kconsecutive numbers. . S8 ]/ _5 ^+ W* G) ?* C1 Q
consecutive primes, sums of.
! [8 I9 B( D6 u0 X9 b$ d3 DConway’s prime-producing machine.
5 a6 @6 U' r& @2 J+ x4 zcousin primes. . _3 z' k& D; n! `0 n3 f
Cullen primes. , I. k* O# l! K* A7 M' R" N4 q
Cunningham project.
 [1 s) m. T Q: V: k9 D" i. SCunningham chains.
3 v0 v3 A" V- w9 l% Z7 w! ]( D; ldecimals, recurring (periodic).
& t7 S6 F& c( k% x& lthe period of 1/13.
( S) W9 z- X) a$ ccyclic numbers.
9 D- d5 t$ s) e9 L9 C: mArtin’s conjecture.
9 |& X! L% B: p3 e$ o/ |; Fthe repunit connection.
; R! y `7 f# E8 L3 kmagic squares. # Y: z1 T% z) I. U
deficient number. / M1 T/ [: G+ {% b
deletable and truncatable primes. ( ?7 ^1 w! n4 g% Q) j" {
Demlo numbers. . e& | O. i* u, _! M" @
descriptive primes.
% L' k. z; E" g! V6 p2 s. S% BDickson’s conjecture.
. k! W2 ]/ Z, ~# O f- j4 w$ udigit properties.
, J" |+ o* I( H$ L- [, ~! [Diophantus (c. AD 200; d. 284). , P/ z* k: `6 j1 f6 D% y! V
Dirichlet’s theorem and primes in arithmetic series. 3 u/ {) X# D) t, W2 G- r7 k% E
primes in polynomials. ' V8 q' R- m8 D4 r. z
distributed computing. 6 D& g G% Q* @( |" Z8 f% p
divisibility tests. ! q4 B, W; B5 b( _9 I( q8 N
divisors (factors). - r' k* g& O; _5 c2 c
how many divisors? how big is d(n)? \7 R( }; h& k; O
record number of divisors. 5 [/ W4 v% I; \. _% t B
curiosities of d(n). " z4 w5 a! Q! d6 W
divisors and congruences. 8 a& b9 ^) h- w& m" k
the sum of divisors function.
/ L7 ?7 ], H) nthe size of σ(n).
$ I. V3 ?0 }# e5 |4 sa recursive formula. ' Y' c" Z% {. [: K4 {
divisors and partitions. * c/ X5 L9 _1 _! f
curiosities of σ(n). ' X! Z7 i+ i0 j+ O. C1 v. R+ `: ~
prime factors.
. _( I. i, P1 qdivisor curiosities. 5 b7 H! l" ~# z; N( \" T* H$ m
economical numbers. 5 A" l4 Q" d2 u$ U, K
Electronic Frontier Foundation.
% ]- q. C( X5 E8 \) ^ n4 C1 xelliptic curve primality proving.
4 \$ d4 `; T: r4 G5 V% Zemirp.
4 t* [0 }* V% [9 x1 a1 c I9 qEratosthenes of Cyrene, the sieve of. + g9 W; x# e+ r, U# ~9 s- H
Erd?s, Paul (1913–1996). 1 o7 R7 V5 r% p
his collaborators and Erd?s numbers.
& f" V: F3 [" q% serrors. _. n/ J1 Y4 `" E6 ]
Euclid (c. 330–270 BC).
% d+ B/ d u, T5 H* Zunique factorization.
0 q% z3 C2 M/ Q( Y7 {/ o&Radic;2 is irrational.
: [2 M9 T* Y6 ~* _Euclid and the infinity of primes.
8 F1 K8 X) C( F9 U6 ^7 C9 N7 @# Tconsecutive composite numbers. : p& Y) B. }( `/ k+ W
primes of the form 4n +3. 9 d- l1 G/ |2 O3 U
a recursive sequence.
8 Q5 S9 M) ]7 P) B4 c. @) g' QEuclid and the first perfect number. % K" ]% H5 ?* K5 V3 k$ l
Euclidean algorithm. ; N- }, J* J4 m
Euler, Leonhard (1707–1783).
( D0 o" r$ Z; Z* h2 Q- kEuler’s convenient numbers. ! k1 `( X4 }+ i
the Basel problem.
" z) F$ C7 K+ I4 p0 hEuler’s constant. ) R; L; L# h9 V$ A0 e
Euler and the reciprocals of the primes. ) m- |# x9 ^4 K I/ b9 G8 _% v! K
Euler’s totient (phi) function.
" v+ s+ B2 c+ {# y- y8 zCarmichael’s totient function conjecture. & Z( \6 |; q) q2 m e
curiosities of φ(n).
" w5 a9 E% q' o1 Y8 |Euler’s quadratic.
& s7 z v% V. g& y9 ^the Lucky Numbers of Euler.
9 [' p8 n; [$ w: v) L5 {factorial.
 K; z5 N# D9 D" T1 Xfactors of factorials.
4 s- \% X- A/ p$ a2 ^. k4 vfactorial primes.
2 R1 R, @: s! k2 j) {factorial sums.
 G& a! d6 N& b( }( H, [factorials, double, triple . . . .
# y# @- h3 O5 u9 R, ]factorization, methods of.
; V' p* E1 c1 A( t5 i7 \- X1 i% cfactors of particular forms. 0 e2 y& c+ T4 C8 B/ \, O
Fermat’s algorithm.
( i. i. O+ C5 WLegendre’s method.
' h; [8 n: d/ ?2 f0 w! ncongruences and factorization.
& o9 k: h8 O' B {5 l, C6 {7 zhow difficult is it to factor large numbers?
" n7 R. E" K+ ~2 {quantum computation. ]+ @% A: ~6 \2 M! m/ r$ s) T3 t
Feit-Thompson conjecture. , j4 w2 K6 _3 [5 X" X9 y+ x
Fermat, Pierre de (1607–1665).
" n4 Y A# I8 X: zFermat’s Little Theorem.
/ }4 A+ {8 [0 ^Fermat quotient. ; F* [ |/ ^/ v- n+ h1 _+ \
Fermat and primes of the form x2 + y2.
: C) N3 d8 }$ vFermat’s conjecture, Fermat numbers, and Fermat primes. 3 k6 y4 a1 W& y; d/ {3 l6 s) c
Fermat factorization, from F5 to F30.
% q. P. k& M& G! r* hGeneralized Fermat numbers.
: h8 D1 b @, J- _5 xFermat’s Last Theorem.
: i6 {' U x. z/ f$ T0 Lthe first case of Fermat’s Last Theorem. * [7 A# `5 ]" [" U6 T0 R( U J$ ~
Wall-Sun-Sun primes.
* V. B% s6 Y) ~Fermat-Catalan equation and conjecture. 3 F" }# a" f [4 L
Fibonacci numbers. & s6 c) [* X' {: p9 [
divisibility properties. " l T& W0 u. {2 X
Fibonacci curiosities.
' f5 ^9 m: q3 b! F, O8 rédouard Lucas and the Fibonacci numbers.
9 w$ e) d$ j: aFibonacci composite sequences.
' r9 Y' ?! l- [6 aformulae for primes.
* V4 ]" o9 K3 [, m" jFortunate numbers and Fortune’s conjecture.
8 _: D1 n3 _3 B/ |+ [$ K9 _gaps between primes and composite runs. 6 T, B) g; S" q1 L% g0 v
Gauss, Johann Carl Friedrich (1777–1855). - n, M! P/ Z Y+ h2 ]
Gauss and the distribution of primes. ) B( D' }5 J, T: b
Gaussian primes.
4 R h! p+ U' l8 W4 a9 VGauss’s circle problem. 9 r7 n% ~. F0 p! O5 R
Gilbreath’s conjecture.
1 h, v/ H1 |+ F- K! x3 YGIMPS—Great Internet Mersenne Prime Search. 1 ]! Y* H- f' Y# L2 i
Giuga’s conjecture.
! \. m6 p( N3 j$ g4 R1 qGiuga numbers. a$ N( W6 R8 r( V( P; {
Goldbach’s conjecture. & X1 `5 Z/ n) w* ~ S4 ^
good primes. $ W# l4 B( p4 S" Q. b
Grimm’s problem. 8 [! o. Q, D9 u( ?7 f) Z
Hardy, G. H. (1877–1947). 6 ^3 D2 T) J7 H2 v4 j0 ^
Hardy-Littlewood conjectures. 3 `! I6 ~. R7 V
heuristic reasoning. 2 d$ ?4 i" B. D9 m$ j
a heuristic argument by George Pólya.
Hilbert’s 23 problems. 6 t% L9 K0 E, z& Z4 Q
home prime. % T- v& s: e8 _$ ]/ Y7 h
hypothesis H.
2 N) D+ X1 ]# ?( D8 ~, Q6 Uillegal prime. 7 @; F2 k: k5 p9 t, o9 w5 B
inconsummate number. * u6 n& e- v6 W/ F' K
induction.
" W5 T+ r0 P7 J' v0 W7 ?jumping champion.
2 j# ^% [) Z9 E5 x" Dk-tuples conjecture, prime.
; i7 q& X) m* s B* y) q% Cknots, prime and composite.
7 [+ r# k- n4 p C% _' _Landau, Edmund (1877–1938).
% O" V" L% K, y. r2 sleft-truncatable prime.
) X5 U& p; l# r- R3 P* ILegendre, A. M. (1752–1833).
9 Z: K+ A7 ~& J% z# u$ ]! tLehmer, Derrick Norman (1867–1938).
, Y4 u8 B9 R. m7 HLehmer, Derrick Henry (1905–1991). + P) _$ y) r2 L9 \0 K- p
Linnik’s constant.
, ]- }$ u! _1 A" @* r; X8 CLiouville, Joseph (1809–1882).
- F# ^0 d' a1 k1 {Littlewood’s theorem.
0 i- G" f/ s' Y9 F4 Uthe prime numbers race.
1 O& x; r0 A3 O. xLucas, édouard (1842–1891).
& i" P: K7 C$ X8 zthe Lucas sequence.
0 R, w: L4 e2 Gprimality testing.
 n7 k, Q: J- V' Q, ~" HLucas’s game of calculation.
, R/ S& o# s6 _: bthe Lucas-Lehmer test. 5 F4 C- O" N( Y* U, K- l& M
lucky numbers.
6 ?# `9 w& x6 N0 e; u+ {the number of lucky numbers and primes. 2 I9 `& S. n* ~6 C( q8 u" i
“random” primes.
4 h/ {2 j2 H' |5 @. xmagic squares.
/ A& c# m% I. S3 p1 I- eMatijasevic and Hilbert’s 10th problem.
1 a+ T. X; J7 w: S o4 V. V$ zMersenne numbers and Mersenne primes.
. n' `1 p3 q& n9 j/ {) `7 V6 I- nMersenne numbers.
! s/ r6 j8 h) O, i* Yhunting for Mersenne primes. + N6 [- {' z N8 U S. k- G( \5 E
the coming of electronic computers. ' O% {. R @( J9 k2 Z6 Z
Mersenne prime conjectures.
! q. j/ I+ Z" K& _the New Mersenne conjecture. 5 m! V7 w7 @6 G! m% L
how many Mersenne primes? . h! E% e: _" s9 S+ J0 c( X
Eberhart’s conjecture. I; e+ T. E* s: T7 A
factors of Mersenne numbers. : U d( h. x; y* v f
Lucas-Lehmer test for Mersenne primes. 8 W+ I! p* ^- j! E) V
Mertens constant.
. k; K8 Q7 J2 O: H) @7 p: \$ n2 XMertens theorem. 1 W# j( \: ^' A6 o( Z1 `1 L F+ N) U
Mills’ theorem. c1 A7 w& i" m# E( l. o& Z
Wright’s theorem. - V ~$ A8 ?1 ]9 a0 \+ L
mixed bag. & ~" _6 w L, Q
multiplication, fast. 2 a2 E% @* U1 K& R( Y( ~
Niven numbers. - k( a+ p, c% v9 F: O F
odd numbers as p + 2a2. + R+ R" `8 a. ?
Opperman’s conjecture.
7 s5 Y: ]! L+ A7 P6 \palindromic primes. G* c; E l, P" F/ W4 q& P+ N
pandigital primes.
5 z1 @' f$ F$ I) S S E0 K9 CPascal’s ** and the binomial coefficients.
" ~$ b$ A+ A' s- j5 O4 VPascal’s ** and Sierpinski’s gasket.
8 K7 x ~ \% K0 t L) hPascal ** curiosities.
: K" d7 I$ z6 ^" \% A; K" k' Spatents on prime numbers.
0 T6 `/ x, l7 z4 {1 Y( U- }Pépin’s test for Fermat numbers.
! E2 V: C @1 m# v# m; |perfect numbers. 7 F1 h3 {5 ?; _+ ~5 Z
odd perfect numbers.
, p+ B t+ ]" M y, |! Eperfect, multiply. " L0 @2 t4 T- X; x% s' B2 k* |
permutable primes. , o8 _+ m2 O. g9 q
π, primes in the decimal expansion of. 8 f, H+ _# X! c, m, [5 D
Pocklington’s theorem.
) u; F$ x% X6 NPolignac’s conjectures.
8 o) a2 U. x: j$ N( ePolignac or obstinate numbers. . l# y, K9 t0 N/ Z& ^( o8 z
powerful numbers. ' O7 N% \4 S8 B
primality testing. - p3 k+ _+ Z. Q, N$ H/ ~2 B9 T
probabilistic methods.
3 c, p: }8 W; e6 Z: y/ q1 Bprime number graph. 2 t: t/ \' h# M( y% \; m' J3 c
prime number theorem and the prime counting function. * G4 b+ w" r8 r4 J. M; `
history.
6 ~. N: E$ K0 O) n) relementary proof.
' P3 }" f6 y# w- Zrecord calculations. 1 O2 `: `+ L- D
estimating p(n). $ G% A8 k3 x+ b6 V4 p) y
calculating p(n).
- h+ {: v9 J+ X5 t4 d0 ^' la curiosity.
* V! A1 Y2 R' J4 g" Q Vprime pretender. - i1 @; B: k/ S. g
primitive prime factor. 3 W* C7 N! m9 T' o1 n5 T
primitive roots. 6 W% i Q' b7 p& F4 m0 ^4 E
Artin’s conjecture.
9 f y8 O. J3 A$ D( ?+ E/ s: Ba curiosity. 1 p3 g9 u, \7 a2 o" o6 n: |
primordial.
7 W9 j+ ?8 r% A- l' ` k6 b2 tprimorial primes. 5 u" N0 b0 f/ a- H0 x! l2 S
Proth’s theorem. + N1 T2 S& s6 l% _: J
pseudoperfect numbers. 3 p1 q, ^- K9 u$ }& A5 l) v
pseudoprimes. ; Z) B% j, e/ g r1 Y, I
bases and pseudoprimes. & @, ^/ q" R( f
pseudoprimes, strong. 8 |; {9 H0 Y1 s! g: f# u: q9 E
public key encryption. 9 o* [" m6 D) x0 Y" d, b
pyramid, prime.
: w0 H" i* u% ^0 ~Pythagorean **s, prime. ) H) \. g% _ L1 D+ c) P
quadratic residues.
7 s' k5 Q9 `, `/ M8 m4 {1 w6 a# Qresidual curiosities.
- r; ^! n7 l1 h; M% v _8 Z8 cpolynomial congruences. ( A9 l5 m% s% s& i# \2 K3 Y6 |
quadratic reciprocity, law of.
5 C) K; `9 ^- X# g9 D) X/ EEuler’s criterion. * p3 o% Y2 C$ x) {
Ramanujan, Srinivasa (1887–1920).
( T; S, T* T6 B: u P. H6 yhighly composite numbers.
' G4 v5 W0 O& l' m1 Y4 L" `! ? Mrandomness, of primes.
; {. x+ n7 z6 e3 A% q- I$ X5 Z; n! ]Von Sternach and a prime random walk. 4 D T8 _$ T4 ]& \" k, Q0 r6 b
record primes.
; ^/ b; `# r' ]1 e( v' [# ^some records. 0 d4 ^: }0 D# d1 M. h$ X
repunits, prime.
7 W4 o6 T7 V% s- T& Q% z3 LRhonda numbers. " X* i* V' I- t
Riemann hypothesis.
. K0 d& {: J# s3 ]5 k, ythe Farey sequence and the Riemann hypothesis.
6 Z5 O5 F4 c/ {& l7 ?& Rthe Riemann hypothesis and σ(n), the sum of divisors function. + K" D( T: N# {8 k9 i! B1 b( u
squarefree and blue and red numbers.
/ K8 e9 l$ D6 y a+ |5 wthe Mertens conjecture. - t2 C! @8 \" M1 p9 W
Riemann hypothesis curiosities.
/ ?- |" N% M3 Q9 Z, Y! c% c2 m6 zRiesel number. 5 Y8 c% Y# u: w+ `
right-truncatable prime. 2 U' [. P- {; W; d# E
RSA algorithm.
' @, M0 Y, U5 \4 n+ {Martin Gardner’s challenge.
; X9 {) |4 b9 Y7 q$ MRSA Factoring Challenge, the New. & W& B. R% N: N, ^# |! _7 b, Y' }
Ruth-Aaron numbers. 0 C0 l8 I2 W' t" ?4 g0 t' {
Scherk’s conjecture. 1 z, X" z! Z T+ k$ B+ p" A
semi-primes.
) c/ M; w' l+ I7 r" y$ N**y primes.
. t2 P! s( N- W6 h: U6 c* q$ ?Shank’s conjecture.
( G7 d" m) C1 d' e1 Q. C* f" pSiamese primes.
- ~" i$ V; H' T0 q( m; FSierpinski numbers. . d: ?" b* t7 \- J9 Q4 m3 F
Sierpinski strings. ) Q! ]/ p% k& C; t3 w
Sierpinski’s quadratic. 4 |4 N1 g4 n" h3 A
Sierpinski’s φ(n) conjecture. - b, P1 v# g6 r( m. }( r
Sloane’s On-Line Encyclopedia of Integer Sequences. 3 [$ E& @& I0 F! E8 t" m- S" d
Smith numbers. % q( f7 w( ~( [- g
Smith brothers. - L8 ~ c# G$ _$ l, R
smooth numbers.
( a9 n% S& m8 E4 ?9 g: g |Sophie Germain primes.
" X2 z7 ~" V: msafe primes. & r/ h7 S G( B3 Z; J5 ~
squarefree numbers. ( w) T8 j5 o o% K% D8 L
Stern prime. : `1 P& ~2 P1 a1 z, c
strong law of small numbers. y# B# A& G0 N. ]
triangular numbers. 3 n9 ]. r# [; r" K, ^7 j
trivia.
* h }9 X. ]. `7 d. H+ Ftwin primes. ) [8 s5 V, T. }5 r9 O+ N
twin curiosities.
, g! e1 |% b E i& j7 u @' @; PUlam spiral.
/ M7 _" R; V% Y5 P* N# Aunitary divisors. $ i1 W/ |7 m* ?+ k
unitary perfect.
, ]4 I+ F& P* Z9 d9 L* muntouchable numbers. " `2 I3 z3 A$ a+ c* f& v' W- T
weird numbers.
8 K5 K" [, J& BWieferich primes. % B6 s' @2 D. g! A2 C J' [. K
Wilson’s theorem. u- c2 N9 w. R
twin primes.
! t% t( y' J/ q* Q6 eWilson primes. 7 ^# U% v$ b! G% Q8 k; W# i
Wolstenholme’s numbers, and theorems. ! y* ]8 e# {8 \
more factors of Wolstenholme numbers.
$ I( C" b0 W/ I% w) Y6 H4 cWoodall primes.
6 p" ^1 Z) y1 t' yzeta mysteries: the quantum connection.