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数字的奇妙：素数

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Entries A to Z.
' s8 E& s: [, ~$ i2 _abc conjecture.
 y# k5 c+ j/ P$ @; i" b6 ^abundant number. : B- N" B5 T7 R9 l5 g( h A, Y
AKS algorithm for primality testing.
) c- z. B0 Q0 d8 f" m% Kaliquot sequences (sociable chains). # z7 l4 [# W, c$ y- l% J X
almost-primes. 9 _, f" x$ \) M
amicable numbers. $ D6 M( W/ [; h6 U( q; x4 L
amicable curiosities. 8 z9 [$ Z# w3 @& J/ Y% X. l
Andrica’s conjecture.
6 l% I1 o# c2 R& qarithmetic progressions, of primes. % L( O9 z1 w3 ]. M; r
Aurifeuillian factorization.
' o. Z4 |0 [* {8 x& Haverage prime.
9 }* @( `' C! [+ o) W: } mBang’s theorem. 8 Q% I* }2 t" N; l0 d1 t3 A
Bateman’s conjecture.
2 X- c& { c# Y% s) @Beal’s conjecture, and prize.
 m6 ]5 A6 X( d$ HBenford’s law. + \; J9 r s4 w2 `% L( m9 Q7 u6 J
Bernoulli numbers.
5 a, G3 G" z, V t' s; ^% i" V( h( tBernoulli number curiosities.
" a5 l6 E+ j) T; s0 lBertrand’s postulate. " I/ X! K% x, N* K& B2 B
Bonse’s inequality.
% [4 z% g4 B9 [7 K5 HBrier numbers. - _! |2 A( u$ x# P9 }# a
Brocard’s conjecture. # C3 d4 ]+ _- U! H
Brun’s constant. . P6 `" o# X4 L$ k" J" V
Buss’s function.
" O& m3 Q; m+ n% QCarmichael numbers.
( k* T& Q% F: V: l3 y4 o1 b/ DCatalan’s conjecture.
4 A, l9 x9 P. ]% \3 e$ i) `Catalan’s Mersenne conjecture.
# b5 c/ t/ |8 sChampernowne’s constant.
% u) e1 h: o4 m* ?. gchampion numbers. 1 L4 w( b2 Q" G0 Z, l8 y' Z' O! }
Chinese remainder theorem. 1 b1 z' S8 l: k5 Z
cicadas and prime periods.
. q! ?& M' @+ L4 P) |circle, prime.
* y. \' t% }4 `/ u. {& C7 j) Vcircular prime.
. n5 F3 h6 [! A3 W" u% cClay prizes, the.
5 i5 c& C% t6 z! Z- xcompositorial. 9 |% b9 Z$ E$ m! |# F
concatenation of primes.
, \3 P8 \% e6 Y7 Z( R3 P/ b$ \conjectures. ( z4 ?/ t& I! Z5 F
consecutive integer sequence.
' {7 |' N" u: f2 bconsecutive numbers. 4 ?( s9 z$ d% b; k9 ?+ c
consecutive primes, sums of. 3 O* Z) p r( \
Conway’s prime-producing machine.
/ X/ H/ S9 U8 R4 k7 ^! |* W0 \' Ocousin primes. # t9 Y* k, A- O3 y
Cullen primes.
( E9 d' I" X I$ g d5 iCunningham project. ( p: q, z1 p9 g/ c! M2 S! o
Cunningham chains. + b7 Z" Z; J/ ~9 \- X
decimals, recurring (periodic).
* T; k' y" x+ n% ~the period of 1/13. ' r0 k; a/ `, N( m' S+ V
cyclic numbers. 6 \# _( S9 P3 ^* G: _, ~
Artin’s conjecture.
- c; l8 [' ~7 C3 `( Q' v1 gthe repunit connection.
# {0 E/ L `0 G9 kmagic squares. ( `$ \+ f, F! H6 l- b; N3 Y
deficient number. . h: i* @' A+ M
deletable and truncatable primes. % g& A- e, m/ O
Demlo numbers.
 q5 N' T7 N* y3 ^& f- b5 Zdescriptive primes. # T; P7 g# n4 Y
Dickson’s conjecture. ) I8 Z6 b0 K6 p# q+ L; a
digit properties.
* Z: }& R& L, S" {Diophantus (c. AD 200; d. 284).
/ _3 f8 @# H" m v& MDirichlet’s theorem and primes in arithmetic series.
" c5 {- h8 {) F7 e8 X9 s8 U8 Lprimes in polynomials. & U r7 F& g! x D9 h% l+ I
distributed computing. , s: P+ O" S: p0 a# }
divisibility tests.
. R) A: X* { @( Adivisors (factors). % A d2 c# S6 I; K& B: D' z, b
how many divisors? how big is d(n)?
' r8 h! T. w4 e4 trecord number of divisors.
0 r( m6 I, j( T. \* p' Z5 @3 ncuriosities of d(n). . I; s2 B; w, T# X4 g! ]
divisors and congruences. ( B, A- w5 P) j- p0 ~5 Q( d& k1 ]' W
the sum of divisors function. ) v$ b1 R2 p( Y/ J
the size of σ(n). 7 S @4 l5 C8 j1 H2 I% }$ E
a recursive formula.
7 o1 [# w- j1 ^% V8 Idivisors and partitions.
0 C& R7 z" r- d- g- ]+ z, P6 Ccuriosities of σ(n).
) j: r' H( [& kprime factors. 1 @: Y1 r. K5 R1 J
divisor curiosities. 7 Z5 Y, L. u/ g; g. u1 `( O; A
economical numbers. + F. V( f; s( B b# z: ^
Electronic Frontier Foundation.
2 a- Q4 B+ r' N* V; Zelliptic curve primality proving.
2 M/ M+ {. V* b; memirp. 3 Q% u5 ]: d' Y* O
Eratosthenes of Cyrene, the sieve of.
* e( l! K, q) Y* F) RErd?s, Paul (1913–1996). 8 C# ]* \! \, A! u
his collaborators and Erd?s numbers.
9 s* y3 ?# g4 q2 _ }3 `errors. 4 ?% y, Z; j, s* F A$ d7 D& ~
Euclid (c. 330–270 BC).
8 q, J, V; ?4 B9 zunique factorization. 2 ^+ T& k1 G( P _% o1 F
&Radic;2 is irrational.
, D" }+ A. _8 f7 h, M. j! E# [& oEuclid and the infinity of primes.
1 h$ D9 D+ |" j& B- P3 L, M; f( hconsecutive composite numbers.
- Q4 L7 v! p- l5 c# X7 @primes of the form 4n +3. & d( f# O0 K- c1 z* W( b
a recursive sequence. % S1 ^! f6 M: z$ O
Euclid and the first perfect number. 1 o( J1 X& S% u! G
Euclidean algorithm. . D/ Z: K1 q( X9 I$ |/ ^/ {
Euler, Leonhard (1707–1783). 7 ^; x8 n3 ?& Y
Euler’s convenient numbers. : }7 e' s% {0 K: W8 X! i
the Basel problem. : c9 Z6 m) S1 Q* U- e
Euler’s constant.
2 F# \+ O' j2 U" }- E$ ?% L1 ^Euler and the reciprocals of the primes. " i: N0 O: I0 z) ]) [+ {: A
Euler’s totient (phi) function. $ }- ?% c$ f+ W7 Q1 r" k, \$ u& S: k
Carmichael’s totient function conjecture.
% Q2 G: E$ F; v) L" z# n/ l" }% xcuriosities of φ(n). # G6 K; r! H& n1 x6 B' G
Euler’s quadratic.
( O7 q# f2 F7 B. q x+ Dthe Lucky Numbers of Euler. 7 R, {( ~3 d! L! a, D
factorial.
: T; t. I$ ^; ufactors of factorials.
* [4 j9 w. o1 K. z# i+ efactorial primes.
; J& \% q' F% V+ z' s( O# kfactorial sums.
& T+ g, @- J9 y; T1 Jfactorials, double, triple . . . . : G2 { e$ z! Z( Y% W
factorization, methods of. + t! J# J2 _7 U+ n; q
factors of particular forms.
0 \5 ]$ F; e# ^2 jFermat’s algorithm. 6 U# C+ i+ ]; e. w+ K# s/ ~7 q
Legendre’s method.
- U7 _% ?, j* ?( H: lcongruences and factorization.
. c4 {" d4 h* ~1 Ohow difficult is it to factor large numbers? + p; r5 e) y* i9 f7 q: q
quantum computation. ! S( p* a8 m" P- H% q/ S, j
Feit-Thompson conjecture. 0 h) E2 Z2 b7 O1 W5 [! I
Fermat, Pierre de (1607–1665).
4 Z7 Y; }" Z* Z5 _Fermat’s Little Theorem.
/ `) ^ y$ T8 z, N; H# [# aFermat quotient. ! Q# B* q0 H6 [+ d
Fermat and primes of the form x2 + y2.
# p K1 K# i; _Fermat’s conjecture, Fermat numbers, and Fermat primes. ( J& q- q. L/ O4 N) _# x
Fermat factorization, from F5 to F30.
) r m% k H' g- U5 N( W- qGeneralized Fermat numbers.
) {2 W1 V! W5 w8 k' N1 B7 A" QFermat’s Last Theorem. 4 X3 x2 R- j* l( b) d, K" i
the first case of Fermat’s Last Theorem. 1 A; E3 J9 q' D, U8 i0 G
Wall-Sun-Sun primes.
5 j* C1 S6 W6 IFermat-Catalan equation and conjecture. ! C- M- e# e, O) M; f+ u$ L
Fibonacci numbers.
/ f6 v: ]% g' j- ?divisibility properties. 4 K. |5 }6 y8 t: _5 Z9 ~5 N
Fibonacci curiosities. ; W: ^1 @# b% Z5 @$ A+ p. q
édouard Lucas and the Fibonacci numbers. . b W+ b+ [4 r# q7 Z: v9 j9 q
Fibonacci composite sequences. " |2 E! p. R) `
formulae for primes.
% ?7 i# F; R3 WFortunate numbers and Fortune’s conjecture.
: w9 M$ t& M% r" E+ Y, G' x( ogaps between primes and composite runs.
% j0 Q% R1 P' g1 N. ~Gauss, Johann Carl Friedrich (1777–1855). ' N+ N: V( c2 _. \1 p0 D
Gauss and the distribution of primes. ( |$ |. s3 m" T5 ]2 S
Gaussian primes.
Gauss’s circle problem. : M6 v" x2 S8 v0 S( O( Y
Gilbreath’s conjecture. " Z+ x0 \$ @) H* Q( ~
GIMPS—Great Internet Mersenne Prime Search.
: m! H3 H" i4 s% A$ w$ i$ h, e7 OGiuga’s conjecture.
/ Y5 ^) ?3 s P0 s7 KGiuga numbers.
% s4 N; }( E5 J4 |; e' {3 S6 NGoldbach’s conjecture.
6 s& k/ m8 r3 u2 F. y' c$ y/ a: }good primes. 8 T# q! w0 _- K8 v
Grimm’s problem. , P/ a6 D. _# o1 J" m
Hardy, G. H. (1877–1947).
( w Z) h( e$ W2 s4 iHardy-Littlewood conjectures.
7 b! g9 v: e( w6 ~. Zheuristic reasoning.
" o* I# w/ i, ^* a% {a heuristic argument by George Pólya.
2 I: v1 Q* \( p7 c' V! GHilbert’s 23 problems.
+ c1 w0 Z! F+ ^* L* p: vhome prime. ! J" v) K3 L6 b$ e
hypothesis H. % E4 B" m, R# U% L; K# a# s& y d1 ~
illegal prime.
5 B8 H8 Z$ M& D1 B* g$ r) Minconsummate number.
: H! y7 _( }3 v; Uinduction.
2 H' N, L5 N3 {) U7 ejumping champion.
) p: L/ E6 x& {2 G' zk-tuples conjecture, prime. 5 |5 I1 a2 _0 ?$ T ?$ J7 k
knots, prime and composite. 3 b0 _0 h9 u4 @
Landau, Edmund (1877–1938). 0 B/ D! p$ E, p/ u. a# E: c
left-truncatable prime. ; G* b {( B p
Legendre, A. M. (1752–1833).
9 h( J- M' P7 M% z* ]Lehmer, Derrick Norman (1867–1938). $ y) |) m5 c8 O
Lehmer, Derrick Henry (1905–1991). * b4 \/ h+ l) |# g' I. j2 p3 T2 V, G% E
Linnik’s constant.
0 s( |' R) y1 x+ d' ?- CLiouville, Joseph (1809–1882).
6 a9 r5 z# C4 m! j {" j3 ?+ HLittlewood’s theorem. / A* t1 w7 P4 x0 s7 s3 i1 c. W
the prime numbers race.
# P. i) z+ H1 a" _1 pLucas, édouard (1842–1891).
9 d6 k* F8 F) Ythe Lucas sequence.
; F2 J" ^ U7 ^8 T1 }primality testing.
6 `# h0 A7 S6 e- n2 L$ E. \8 j' l4 `Lucas’s game of calculation.
5 v/ Y9 E% _3 K) q3 \% sthe Lucas-Lehmer test.
& O$ z! G$ n( r- jlucky numbers. 1 ~ `; c* ]8 i9 U7 T( f
the number of lucky numbers and primes. & W6 w8 X* }9 ^ T
“random” primes.
% g; y1 u9 T% t \$ m3 \0 umagic squares.
4 u% H" C% {: Z, C* G8 I! ^5 u5 IMatijasevic and Hilbert’s 10th problem. , C( F( P: T! m2 p
Mersenne numbers and Mersenne primes. ( @4 n% n" n; M! t* L
Mersenne numbers.
& e4 ]6 A. N# b/ Q3 q+ Vhunting for Mersenne primes.
' @; c" [. l% i Wthe coming of electronic computers. + M, `2 Y8 Q: `
Mersenne prime conjectures.
3 U& n. o" Q! ^" E0 O0 mthe New Mersenne conjecture.
) V2 e2 ], }: S0 ohow many Mersenne primes? . Y" v2 W; U" |7 G( |
Eberhart’s conjecture. 7 x! w' L" l: `4 Q' Y
factors of Mersenne numbers. 0 m7 M; U3 f+ }9 c2 O t- b
Lucas-Lehmer test for Mersenne primes.
Mertens constant. - _% {; P) S, @' B. d
Mertens theorem. & E) O O) A1 l( r9 k8 Q
Mills’ theorem. 2 D4 f6 F9 H- @& a
Wright’s theorem.
) Q$ b# U/ _) x. n2 Bmixed bag. % v j: D- V [
multiplication, fast. X1 z3 X' P9 E
Niven numbers.
0 e+ N: y: u! G( U6 V% V8 dodd numbers as p + 2a2. # R0 E, t7 S* j. B y+ _9 M
Opperman’s conjecture.
$ Q0 r$ ^6 y$ z# F, i% [palindromic primes.
& k V6 u3 W/ K# f a- Cpandigital primes.
" v1 l2 i- [+ {+ G! ^3 ]Pascal’s ** and the binomial coefficients.
4 M4 w! J+ f! o6 T; W$ \) _Pascal’s ** and Sierpinski’s gasket. ! R5 b* v; @" g% [* Z; ^
Pascal ** curiosities.
& A6 z$ r. r1 M, p! Rpatents on prime numbers. 3 }! i( @, d q8 \
Pépin’s test for Fermat numbers.
& b' W0 T, b% B" X: jperfect numbers.
 N$ q# _/ }: `/ Rodd perfect numbers.
' `5 o+ w" y' M! Z* |7 A2 Lperfect, multiply.
/ r0 S2 B0 P, e4 `6 T4 Q& f' h: opermutable primes. 0 B! U B8 M* b$ N4 e
π, primes in the decimal expansion of. ! ^% t9 u( Z; T- v" H
Pocklington’s theorem.
) |2 z0 K$ w3 E$ L) lPolignac’s conjectures. 8 G9 s# M; `6 o$ r7 r- T
Polignac or obstinate numbers.
/ C2 @+ f. [" k0 `powerful numbers. 7 X. R+ C, k5 E- T
primality testing. # D7 t% ^4 x9 }
probabilistic methods.
& e2 S( s/ t& {7 R+ y* w, Aprime number graph.
2 D; D4 l! J" s0 D6 T8 W9 P' X/ Dprime number theorem and the prime counting function.
+ t3 H$ q8 Y& `8 l0 ^! C# D$ ^history. 5 V( b6 C2 O7 S; g* h- X9 g
elementary proof.
* C% v! t" o: v% W+ U& w6 Nrecord calculations. . z( }4 K; V/ x: n% U
estimating p(n).
/ {" ]2 i& a. s, B" @7 @. T) Hcalculating p(n).
/ J! m% |4 l( c$ w1 [ f& r5 c. ya curiosity.
9 B+ H% M# f- t8 L8 dprime pretender.
' H5 R7 Y8 ^+ T% L7 m" Pprimitive prime factor.
- h* E' | J( K- O8 A7 Xprimitive roots.
, r& B G) X0 wArtin’s conjecture. - Q2 |! x9 s) ^8 ~
a curiosity.
8 k) i" w2 |; _: nprimordial.
- r/ \" E8 R* ~7 j$ _% eprimorial primes.
! C* n R, V4 hProth’s theorem.
' ]5 S$ X X( x6 ~/ L% m8 Jpseudoperfect numbers. ; k) G/ n- |/ P# k, h3 C! { o
pseudoprimes. + b( z& r6 I9 q# B: [2 U
bases and pseudoprimes. 4 t9 N0 \% {, y2 T
pseudoprimes, strong. - x5 {9 Z, E/ @5 y1 M
public key encryption. $ f7 B0 _! Q8 {0 y# A: q, R0 n; J
pyramid, prime.
" s3 Y0 r( Z7 Z+ @Pythagorean **s, prime.
+ ]0 \3 Z$ l( q1 zquadratic residues.
- m0 z2 |2 R4 _( T- K* U1 v! G( ^residual curiosities.
9 w& X; @2 N0 E: R" g: `& opolynomial congruences.
& f! l% k0 P4 ]# I% C% w; bquadratic reciprocity, law of.
1 q# a) h; I3 `+ k2 x9 @$ @3 ]: NEuler’s criterion.
; h# p2 [. y3 }! V2 [& WRamanujan, Srinivasa (1887–1920).
" V2 k' t+ A2 v# M1 J' W4 |! x% hhighly composite numbers.
% U( z) \1 j& ~0 k) l* crandomness, of primes. 7 \5 `- k4 \9 L6 X
Von Sternach and a prime random walk. . o. k: | N/ }, C4 u7 ?
record primes. $ B& }& L1 b4 a1 V7 P" O
some records. 0 Q1 v7 E- ?) [: J! V/ Q
repunits, prime.
5 E+ e& y6 [, a0 d) }2 vRhonda numbers.
) I- I2 N" r8 \7 N# u& Y" p8 pRiemann hypothesis. ( D9 J8 x' Z l+ ~* w8 R. x1 G3 E, H
the Farey sequence and the Riemann hypothesis.
4 @9 T2 x9 g- k% p6 f& l0 mthe Riemann hypothesis and σ(n), the sum of divisors function. , i Y% v2 a. n
squarefree and blue and red numbers. " ~. I+ z% D& W2 ?
the Mertens conjecture. - q8 v& y$ i v0 k; ^4 u5 a5 A
Riemann hypothesis curiosities.
" _+ ` \( [# i* `4 YRiesel number.
6 \1 ^* x y: {right-truncatable prime. / _/ R( J7 N7 s* Q
RSA algorithm. & Q- z) p F3 r6 n( Y
Martin Gardner’s challenge. ! ^" t! ]0 o6 [3 Y2 G3 y4 V" ]
RSA Factoring Challenge, the New.
, J R7 F [: c2 FRuth-Aaron numbers. # n$ c1 m* g7 v7 D+ I
Scherk’s conjecture.
0 [0 T7 P; l: `; C- Qsemi-primes.
9 u. T# w) |1 f" n# V7 @( j: q**y primes.
; s6 j+ x% g0 x- ]4 _* |$ VShank’s conjecture. . A2 F5 [- V5 ^ ^
Siamese primes.
5 F6 }! Q6 ]0 k9 {+ a! KSierpinski numbers.
: Z: |# @, f( L) f7 I5 a3 w5 I: W1 ySierpinski strings.
, {' ^: \+ l1 O) h+ U, j7 vSierpinski’s quadratic. I" k0 R& t: m' W2 J
Sierpinski’s φ(n) conjecture.
4 S& m1 E, h4 b0 S8 R5 ?% J* FSloane’s On-Line Encyclopedia of Integer Sequences. - R7 p! H# m" x8 s4 \
Smith numbers.
/ Y# e3 S# e$ j7 F: ~Smith brothers.
: \% k# L N6 _, Gsmooth numbers. $ A) p' J, i- \- |" T
Sophie Germain primes. 5 Z9 f+ m4 T* D" l T: l( s- c$ o
safe primes.
, s, M) S6 O6 ~( f8 |4 I9 O+ Asquarefree numbers.
( P9 n* b$ f7 |9 [8 }1 t0 kStern prime.
8 ~: X1 G$ ^2 L' L3 k3 U/ Qstrong law of small numbers. 5 L) c% Z& V* U t" J
triangular numbers. 4 ?" W; P& I" I5 q7 }
trivia. & w3 E$ P2 c) |( {- A& p% A
twin primes. 5 c8 r5 P9 [" H! [6 ?+ j% v
twin curiosities.
& [! H0 f) T4 P, QUlam spiral.
; p# K0 `; f! N9 \* I7 sunitary divisors. 9 l0 F1 [& A+ a$ u2 V! R
unitary perfect. 9 w$ c' a3 i( b5 {
untouchable numbers.
8 H _/ y4 n# _ d, M- i; c; yweird numbers.
! S9 p: U1 P( |! ^Wieferich primes. & \3 v: E1 X- ~7 u
Wilson’s theorem. 6 D1 h# [! j# f2 ~3 E# b
twin primes.
, m- T' A, E6 Q/ HWilson primes. # D0 s9 H8 p2 I' ^$ C& ~$ [7 o
Wolstenholme’s numbers, and theorems. + ~8 D( W4 D n" m
more factors of Wolstenholme numbers.
% o7 T! b; A2 k) u, h! {( M! l4 ~; z' MWoodall primes.
. m3 _4 u' i5 c/ d' kzeta mysteries: the quantum connection.