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数字的奇妙：素数

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Entries A to Z. . z+ O9 t6 H8 D
abc conjecture.
* q7 p# ?* W$ `$ ~; }9 Zabundant number. % B% P0 N, f- l0 w4 m" g3 T
AKS algorithm for primality testing. . L9 M( T2 _! J; |/ v" S
aliquot sequences (sociable chains). / N* b' o) `2 ^7 [
almost-primes.
7 F2 N; h. \0 V2 K$ t6 ramicable numbers.
( t) h8 s% C% ^7 Jamicable curiosities. ' w' ]2 i" O9 H% W4 I2 m0 W8 \
Andrica’s conjecture. + Q: A/ l. _5 x
arithmetic progressions, of primes. % n3 a& C( }; y" \' P* Z) H
Aurifeuillian factorization.
1 X! U `# s+ Naverage prime.
' P" r+ b, `) A1 e6 n8 `Bang’s theorem.
/ `0 l; J- y2 iBateman’s conjecture.
# ]8 i$ h& ^* A$ n. [+ R. MBeal’s conjecture, and prize. # _9 D$ P: D) S
Benford’s law. 4 i$ v7 W9 N; H4 Q8 a7 r
Bernoulli numbers. ! s& _' [8 n; A$ [4 x# T, p' G
Bernoulli number curiosities. : Q7 J9 M5 D$ O
Bertrand’s postulate. 8 e" n9 r6 R8 e0 u: F/ r- ~
Bonse’s inequality. ) a% Z0 _/ v; a: W2 u) i% O
Brier numbers.
' ^$ @0 Z7 T2 T! qBrocard’s conjecture.
7 \7 Q/ n, {# ?! gBrun’s constant. 8 s0 _1 s- B7 H
Buss’s function. 5 F# _5 c! o9 [! s0 t( d
Carmichael numbers.
' v8 B9 A# o) e) b) i" dCatalan’s conjecture. . `+ B. U) u: s
Catalan’s Mersenne conjecture.
! B3 n& v+ W3 X) w9 lChampernowne’s constant. % B/ q3 e" ~2 ?/ O9 n/ h$ h8 s
champion numbers. + o$ T1 h+ X1 r5 @/ q
Chinese remainder theorem. / q9 u! n H* R0 L0 {( w9 d8 b7 r
cicadas and prime periods. 5 Q& f! z9 @5 l& Y$ e% z9 P
circle, prime. X2 q$ X& D, |. g
circular prime.
' `5 o" c. X% O( r1 l! M% q, E& [2 RClay prizes, the.
1 O+ Q* z3 w# O) k; zcompositorial.
 x5 Q( H+ A8 C) x2 p: [0 Bconcatenation of primes. 3 q& Q, }" {6 d2 F" i
conjectures.
/ F8 p, ]5 y* |. u) `9 Pconsecutive integer sequence.
+ i6 A$ W5 {; B y: cconsecutive numbers. 0 Z W) y' G! a! D, H
consecutive primes, sums of.
 R$ @5 x5 S M4 {5 k1 bConway’s prime-producing machine.
' e% U' Q2 r1 c- p2 C% ~9 Acousin primes. / H& S8 h" \! o6 f: ~+ Y: Z
Cullen primes.
" k9 h! h$ ]1 m) E8 XCunningham project. 5 W* |" ?2 h1 L: \8 P. M8 a3 D- {
Cunningham chains.
4 w+ s F4 I& V$ K9 Udecimals, recurring (periodic).
8 U, N6 w' r$ Y! lthe period of 1/13. ! w) ~: F) n, d0 w2 w
cyclic numbers.
9 @4 O( u' Z% w( U; aArtin’s conjecture.
9 r- E! \' N7 p4 I7 U1 r3 j R2 I. Uthe repunit connection.
: Y1 l. e) f& d$ { }7 o Bmagic squares.
4 E9 i' R/ r8 e) j& Z, ^deficient number. . M3 @% z* F/ f* }) f! B3 `
deletable and truncatable primes. & ~ J+ o h9 ^# U- Z- Z
Demlo numbers. ' J, P( S, c9 d3 M' D
descriptive primes.
$ F& r) D7 L7 d) ~4 o) vDickson’s conjecture. ) ? {7 {3 e2 ?+ e1 f- e+ M7 g
digit properties. 7 i. G! s: m" s8 w: c
Diophantus (c. AD 200; d. 284).
& ~+ \2 r! J6 P' {! {" GDirichlet’s theorem and primes in arithmetic series. 4 W7 f2 a' D* i; |/ g7 K
primes in polynomials.
$ L% I: q0 z$ z# S% T; R( e* T$ idistributed computing.
$ q+ O" m5 h9 L+ P/ A) odivisibility tests. 3 O2 `! f8 H, S& k- I4 r6 O
divisors (factors). + M) k8 I) v7 Y( S0 d
how many divisors? how big is d(n)? - j( D; ~) P3 H j% o2 L
record number of divisors.
0 {3 O6 h; r. _4 ycuriosities of d(n). 2 l* M8 c' _3 y0 P9 \$ x4 I$ E
divisors and congruences. , |" _5 ~$ o0 ^" V
the sum of divisors function.
, u4 o" i' {$ f3 Sthe size of σ(n).
& ^9 ^" P7 f9 ~ G. {, O6 ]% ^a recursive formula. * G4 Y; b; r: _9 z/ g* ]) L
divisors and partitions.
# R8 U$ l$ V8 w! Z: jcuriosities of σ(n). 8 F( m, o+ t5 ]- x% d
prime factors.
$ n* f v0 O5 c3 |8 }divisor curiosities.
- u8 d/ Q' d3 o7 i- b" U! ]/ Deconomical numbers. + L* C7 Y. C a& Q
Electronic Frontier Foundation.
/ S% w0 o/ @4 J2 relliptic curve primality proving. 3 v4 `2 Z: `; S! g) C
emirp.
0 ]8 w& ]7 G7 t A( hEratosthenes of Cyrene, the sieve of. . R& ~" @ w F+ S
Erd?s, Paul (1913–1996). 4 z2 X; O9 C& d: T3 T( W
his collaborators and Erd?s numbers. : J9 o; r; i" i1 g) W ^
errors. 4 F; ]( w9 b9 g$ s
Euclid (c. 330–270 BC). , [2 v( f9 t/ ~' [' L" L& \
unique factorization.
4 s/ A D: s O" V# b% t&Radic;2 is irrational.
, z" ?+ |+ y+ S# `/ m& TEuclid and the infinity of primes.
 ]5 g, @& ?6 c3 A; |% @consecutive composite numbers. # m7 O+ z/ T3 i' I3 o% W- |3 j
primes of the form 4n +3.
) l3 M& X, Q) L$ Ma recursive sequence.
9 l& q- ^, f. ]# V! mEuclid and the first perfect number. & R7 ~& Y; T1 a J5 Z
Euclidean algorithm. " [ g1 g4 T& T. S- ~. e% D3 I6 c9 W1 `/ C
Euler, Leonhard (1707–1783). 3 B Z, ] w( F3 Z$ c
Euler’s convenient numbers. ( [- k6 Z# e Q
the Basel problem.
 ]+ w' C/ F& }7 vEuler’s constant.
- B( g' [, L5 h& {1 x7 QEuler and the reciprocals of the primes. " ?5 ~# P4 {* B2 O
Euler’s totient (phi) function. & D' A4 H7 R) q2 [0 c. }
Carmichael’s totient function conjecture.
( V7 o f. m/ a' Q8 t7 J' T& Q, Ncuriosities of φ(n). " ]8 Y- h/ O5 M
Euler’s quadratic. 7 B6 l: J2 H( b& S/ I
the Lucky Numbers of Euler.
8 w7 w6 A' i4 c' o7 yfactorial. 0 B. z: @$ ~# u, q3 p- O2 u
factors of factorials.
9 t( n' I; R7 S" D$ ^4 T/ Q9 Nfactorial primes. & D5 e" l7 O0 i4 m0 ?0 _/ u
factorial sums. 0 `' e$ \8 g: Z1 z. z& v
factorials, double, triple . . . . 6 Y2 J2 Q3 j6 k4 y$ L/ d
factorization, methods of.
) V3 h2 O# M0 e x8 {; ^- Zfactors of particular forms.
( F% H; S+ n, R3 \9 l0 S$ P2 oFermat’s algorithm.
 E$ y# T3 t8 S" P# G2 l* hLegendre’s method.
' d' v! o, C8 b" n9 m+ i, \congruences and factorization. , M+ _! `3 K- m& i* \. |3 H7 B8 d3 F
how difficult is it to factor large numbers? , w5 E! {+ a' r( q
quantum computation.
- }6 f1 G+ j7 F2 k" g) GFeit-Thompson conjecture. ; ~. Q' o5 U5 k+ w( _
Fermat, Pierre de (1607–1665).
- F: s- _( L& h; F7 Y# P8 z9 nFermat’s Little Theorem.
$ m) _; }! ?8 r. fFermat quotient. 8 t4 @; E, n! |. ]( Y- W+ U
Fermat and primes of the form x2 + y2. % I# z; t' t: _4 ]
Fermat’s conjecture, Fermat numbers, and Fermat primes. 0 I7 K) z: j% j: w8 m8 A" r$ l
Fermat factorization, from F5 to F30. ) w5 r* M$ [) g$ J* m; s& Q% W
Generalized Fermat numbers.
, N" s" I* H! T- IFermat’s Last Theorem. , \9 P/ [. |) I
the first case of Fermat’s Last Theorem. . q/ k {7 b: `8 b+ ?5 |8 F
Wall-Sun-Sun primes. 8 c' q$ B0 \) u# l: B; {! W
Fermat-Catalan equation and conjecture.
' W9 f s, G+ o5 |Fibonacci numbers. + B% c! g' T& E' P4 I6 x3 |7 n6 U: O
divisibility properties.
0 r/ h: r+ p% \. S! vFibonacci curiosities. t a% t$ ^' I% J$ N
édouard Lucas and the Fibonacci numbers.
# ]- H* ]$ ^# }9 z0 q& s7 b8 I8 x3 `Fibonacci composite sequences.
) @6 H1 G4 r- mformulae for primes.
% c5 k3 ~) \9 ^, ~9 u& vFortunate numbers and Fortune’s conjecture. # `* Y% x# g6 q; m$ W0 E
gaps between primes and composite runs. 7 E3 C8 B a/ y, r3 K+ l
Gauss, Johann Carl Friedrich (1777–1855).
 a2 I1 g8 p4 @5 O( \/ Q$ dGauss and the distribution of primes.
3 I0 O, g0 P/ n) A$ eGaussian primes.
+ K/ w- z, F/ t0 i: yGauss’s circle problem. 1 b$ F4 @0 A! o. e
Gilbreath’s conjecture.
$ ~1 w7 Y" o& S3 G3 JGIMPS—Great Internet Mersenne Prime Search. - x4 G+ W! u4 f5 F" V& B
Giuga’s conjecture.
% l7 q8 v& d- OGiuga numbers. 2 ^- t4 A8 Q/ `1 l$ E8 ~- H9 o
Goldbach’s conjecture. B9 K: ~1 ^- c i) _9 ~ }( ]
good primes. 0 c2 ]/ V% z; w+ m: {
Grimm’s problem. , d7 |, U( E5 ?; p' n0 y' ]
Hardy, G. H. (1877–1947).
2 L' s" U2 v8 F- l! P& ~% l3 C zHardy-Littlewood conjectures. : [; q. G! _1 m o6 I: O* }
heuristic reasoning. 2 t. g9 c8 F1 B/ i, u/ v1 B
a heuristic argument by George Pólya.
) `% v3 W. h {Hilbert’s 23 problems.
% }' I. k: J' E% m( P/ Jhome prime.
% N( z) z7 ?' A N( `# |hypothesis H.
& s+ H9 x- ~+ Willegal prime.
8 E/ r0 T+ R7 {. @# F- K" E( |) @/ }inconsummate number.
7 w% A* \2 g2 O: i: o- uinduction. $ z% M! f; P0 \( H
jumping champion.
; P& h8 l4 J* B! W$ Y/ r+ B. E2 a4 ek-tuples conjecture, prime.
+ \0 K h5 H0 E- R# g+ Xknots, prime and composite. . e+ ]/ z) Y8 R9 [4 [$ K
Landau, Edmund (1877–1938). 0 f6 L8 `# c n& r. D& M+ {: Y9 K
left-truncatable prime. 1 R4 I0 |: m/ ^3 {8 s
Legendre, A. M. (1752–1833). 1 q0 S. v3 `2 H" }! k* o8 R. Y
Lehmer, Derrick Norman (1867–1938). + b4 a4 q# c% k& s# ~
Lehmer, Derrick Henry (1905–1991). . E) O+ m: q, ?. A9 D
Linnik’s constant.
Liouville, Joseph (1809–1882).
( g' H# q# b; WLittlewood’s theorem. " R& R. H; E! x, u1 N
the prime numbers race. 4 j6 P, I8 J8 p
Lucas, édouard (1842–1891).
8 h% H: S8 M: v6 mthe Lucas sequence.
# }- C8 L/ s6 S5 j+ q, E) oprimality testing. 7 ?$ H& Q) ]4 p2 s. [4 w9 w
Lucas’s game of calculation.
% P# }$ T0 W% B( e' Z8 Fthe Lucas-Lehmer test.
$ s* i& h& R% I) b. j+ Hlucky numbers.
) O" x S2 L" |& W" F# h" D4 _the number of lucky numbers and primes. % J+ k7 ^" X) w
“random” primes.
( ^, J4 l/ ~, A% }# N% b! n! qmagic squares.
9 {6 D# u# q6 S- G2 _ P$ Y3 O0 v4 uMatijasevic and Hilbert’s 10th problem. $ a) \$ z. c! H. c( Q
Mersenne numbers and Mersenne primes. , K# e3 i' @* Y; t) { G
Mersenne numbers. % p7 ]4 M9 l* M/ l5 j& X! S. P
hunting for Mersenne primes.
1 c8 @( Q% Z7 vthe coming of electronic computers. $ f0 b; D5 i q9 `0 [7 C
Mersenne prime conjectures. 5 b; J4 `: r8 @
the New Mersenne conjecture. 5 F3 I& s2 E( U7 @# N. h, \
how many Mersenne primes?
7 u5 o* K, a U: I4 ?Eberhart’s conjecture. : s' k8 C& a* ?( G5 Q. y" `+ s
factors of Mersenne numbers.
, q7 T* Y7 p6 sLucas-Lehmer test for Mersenne primes. , i5 k" j0 s8 N
Mertens constant.
! l7 b% H# @( g9 s2 `6 p5 U: UMertens theorem.
0 _$ T5 y& r! _( d$ `) h! NMills’ theorem. $ r3 $ Q' ?4 }7 U6 S; k* z
Wright’s theorem.
$ q: e$ ~7 ?% Q! V% Cmixed bag.
 ]; _7 T) Q( E1 i1 u8 e# ` Amultiplication, fast.
0 d/ _# Q( i. t, xNiven numbers. d2 q+ s" ^2 F
odd numbers as p + 2a2.
7 P' B0 t# q; D5 q3 oOpperman’s conjecture. 6 Q" b0 w6 i% e. n; B1 d
palindromic primes.
3 u6 n1 g7 W7 v& F. J1 Ppandigital primes.
& r5 ^0 }7 Y+ u0 s lPascal’s ** and the binomial coefficients. 3 I/ w. k. L5 $ V! x# A
Pascal’s ** and Sierpinski’s gasket.
2 {- Y1 M! X7 ~1 oPascal ** curiosities.
$ d) L" x! [4 M e0 ~patents on prime numbers.
6 B6 R5 T, s! K, T3 jPépin’s test for Fermat numbers. 4 c2 I( S2 b- R- ^* P- C) \( W! d
perfect numbers. ! I' S8 s7 k5 V" \/ \
odd perfect numbers. # t6 X2 H% I! p% p% p& r+ z- D1 Q
perfect, multiply. + D7 A6 ^: W, C. J4 f
permutable primes.
. b, y4 d7 A" ?9 `π, primes in the decimal expansion of. 7 f7 s; U V: G7 N. b# m. O
Pocklington’s theorem. + x: X! H0 P8 f2 [, \( Q' G( B
Polignac’s conjectures.
! P3 \1 z1 _& s; dPolignac or obstinate numbers. 5 g Z3 x c" b# ?, D9 t
powerful numbers.
+ `, w$ L5 {# r" T/ a/ D% ?+ iprimality testing. o3 q( v* O3 J2 R- L4 \+ Y
probabilistic methods. + t" L8 {" `4 ~9 d6 Y. ] o
prime number graph. 4 D0 M) P! a4 s$ \
prime number theorem and the prime counting function. * S. ?( o" s" d
history. J9 q( m% P1 ]) x! E$ P/ L& b4 @6 `
elementary proof. + x8 g" |$ g1 J' n
record calculations.
: ~, y% i3 k; I2 Bestimating p(n). 9 f! f0 l6 i, d# \' @. L# }# x
calculating p(n). ) ^; ~& [" A1 r+ @+ X7 C
a curiosity. N4 g: k, Q; V# Q5 e! \$ i# j! p1 Y
prime pretender.
8 z+ ]) V* S" l3 _% jprimitive prime factor.
8 s7 }- g6 T: h) g0 L- h" i$ _2 O& Dprimitive roots. , _6 E9 c7 R4 I7 I
Artin’s conjecture.
6 q; y' x2 k+ W6 E- x! ja curiosity.
) o0 @/ d% |: @3 d4 zprimordial.
$ e( ?0 P7 R( c- [# B: F! Z9 a2 uprimorial primes. E' [6 E, s6 M3 r/ A( n/ O
Proth’s theorem.
4 b8 ]3 V; j* b" upseudoperfect numbers.
$ B; x( `, O! [1 E) \pseudoprimes. H0 J P0 ?& ~5 q0 g
bases and pseudoprimes.
/ K0 s) G6 ]) s% E% y: opseudoprimes, strong. % H2 [/ }% k0 r$ u W9 H' V
public key encryption.
6 r6 Q2 u M" Q$ C O. u) r& Ppyramid, prime. 6 d0 P' r$ \7 q. V) B8 v2 k
Pythagorean **s, prime. . W7 m0 B; L8 f; t; E) i* y; p$ L
quadratic residues.
9 S2 T+ H- J/ v! A& R6 Vresidual curiosities. . q$ ?* I7 k [* C2 J. F
polynomial congruences. - |6 u1 W# p5 b5 Z6 s+ M
quadratic reciprocity, law of.
6 G c X1 P' Y2 HEuler’s criterion. ) i7 z, D$ M3 a) i# k
Ramanujan, Srinivasa (1887–1920).
5 u& W* a, ]) ~' ihighly composite numbers.
: @+ E' `0 c2 J5 n3 z, Y2 grandomness, of primes.
 N* I+ X+ i& F) l2 dVon Sternach and a prime random walk.
1 A! f h9 Q8 I: K: l0 Vrecord primes.
6 v# o. k: M6 B' @4 c5 D8 u5 ?some records.
+ t* O3 n, q9 [3 Krepunits, prime.
& S1 i+ ]( o8 LRhonda numbers.
( s8 \" f& F2 s; dRiemann hypothesis. 4 Z" m, \7 e, ]: j/ n/ s, X
the Farey sequence and the Riemann hypothesis.
- _+ o8 x* X5 w' \1 X; c- gthe Riemann hypothesis and σ(n), the sum of divisors function. # q* x4 x: i* M* s4 t! d- s0 T3 q1 w
squarefree and blue and red numbers. 8 H9 t3 X& d2 G
the Mertens conjecture.
+ p* A; B \0 R9 {1 j% MRiemann hypothesis curiosities.
8 R$ a! N* I$ k. `: }% |" k+ ]Riesel number. X/ X" z A1 Q5 ]
right-truncatable prime.
, s5 @2 q% f; ?. X: L; y& ~RSA algorithm. ) I! f; j- |! f% p. {; v+ h$ M
Martin Gardner’s challenge.
6 i# J1 R) e1 ~9 K9 {. K+ ERSA Factoring Challenge, the New.
5 p1 ?; G$ X5 o! L. @Ruth-Aaron numbers. # }) J" ^8 [- ?; }% I: j1 U
Scherk’s conjecture.
2 N; I1 z. N! N1 {4 [% k* o0 Vsemi-primes.
& v# ~ u2 ?7 U**y primes. $ h9 z$ b, @; s% z
Shank’s conjecture.
2 r3 l- ]9 H- sSiamese primes.
# e. v& @0 n* h% A/ V6 Y3 bSierpinski numbers.
3 b5 m# E i8 C3 q# NSierpinski strings. , m9 |: g6 `% Y0 L$ M5 k0 p' w
Sierpinski’s quadratic. 1 R% G% s, p/ e2 C1 x
Sierpinski’s φ(n) conjecture.
+ e8 a5 K4 D: \0 | d7 R. bSloane’s On-Line Encyclopedia of Integer Sequences. 4 O) l8 L! U$ l$ j, `
Smith numbers.
! [7 r; x1 i9 z' h. iSmith brothers. ) V; Y G. K2 h- e+ o4 Y5 K6 |; F
smooth numbers. * B" J. i" `( S m( @4 w: v
Sophie Germain primes.
/ v/ a1 p8 r) @/ p: x4 fsafe primes.
4 u/ r ]' O u* E$ Osquarefree numbers. 3 b2 a$ b4 x. v5 \- _1 K
Stern prime. + s& [8 j6 X8 b) A7 _: t
strong law of small numbers.
/ Q- f& H4 y2 C$ {triangular numbers.
4 B6 s% N7 K% V' |: U) N$ Atrivia.
4 X" A9 y. F5 A y1 p7 v; c) ntwin primes. ! O, U5 Z& Q! ^: x
twin curiosities. 9 U, `+ ~! O* Q0 U0 }
Ulam spiral. ' I R" [+ [' i0 a) T
unitary divisors. : D, |8 V) r& r$ c& [9 a. f
unitary perfect. 4 `. A$ E/ c3 U' Q1 P* G' N
untouchable numbers. / K, B7 s# H: B7 A8 k- |3 \
weird numbers.
$ j% ^7 \& c' jWieferich primes.
6 e: }1 p+ y/ \5 s! f: S, h3 g7 IWilson’s theorem.
8 ~$ s. |9 G1 e4 r* otwin primes. : o% f, s7 r% S E/ x2 s) q
Wilson primes.
 ^: w/ T9 m/ z" h( B$ H& u, mWolstenholme’s numbers, and theorems.
! @0 O) ]6 M! [) p% |more factors of Wolstenholme numbers.
: H( I- ]3 U, L, q8 J5 o+ EWoodall primes.
% u# h) |& H* x4 Izeta mysteries: the quantum connection.