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数字的奇妙：素数

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Entries A to Z.
 o, V3 r* a+ {, k0 o2 J/ Vabc conjecture. 0 N4 ?' k* z5 s- o
abundant number. N$ N% Y* r1 ~: P$ r1 O
AKS algorithm for primality testing.
. {9 W6 D* e5 r0 J; Z3 Faliquot sequences (sociable chains). 4 C2 `- q# @) i- B9 h8 T, @
almost-primes.
4 H% t- _ k5 [' s. ^0 Damicable numbers. 2 r q k/ F9 ?! T' x; F) \6 }
amicable curiosities. ' ?! Y* z* B/ L8 c( ]9 w
Andrica’s conjecture.
1 A/ C% j* P( m4 `6 v" U0 Karithmetic progressions, of primes. $ D5 M% {% X A6 @
Aurifeuillian factorization.
+ R5 z$ r4 L- X! @6 Caverage prime. / _4 U2 M& U/ M# @$ W- x$ v
Bang’s theorem.
5 H) O9 @ f$ e! N9 T& ?Bateman’s conjecture.
/ w. o, a! d9 c% x" \9 @Beal’s conjecture, and prize.
 y# |( @( o4 G0 K% r! A' MBenford’s law.
" |" x; }7 v1 c4 p) \9 zBernoulli numbers. / C7 A; K6 o. m& Z8 ]& ~
Bernoulli number curiosities. 4 b! q9 a4 C# \4 `- x: X- |1 V H
Bertrand’s postulate. m. y9 f8 a5 P( K
Bonse’s inequality.
, W' E# L/ N- I3 |' i0 V: M* @Brier numbers.
' G* _- }$ O* U2 T; c! u; O- fBrocard’s conjecture.
* L4 i; q. {8 R0 [! _ f) XBrun’s constant.
7 N: v6 W& e, U" oBuss’s function. ) J7 ?$ t5 Z& L1 m v
Carmichael numbers. , J' }- s2 ?/ t/ d% K+ \ D
Catalan’s conjecture.
) S7 \% T6 i+ B+ ^6 r6 LCatalan’s Mersenne conjecture. 6 k) O. K0 i$ ~. N6 W7 e' l
Champernowne’s constant. & R/ z- ]3 v' y9 v5 u
champion numbers.
. I3 h; C7 b% BChinese remainder theorem.
* t( f; Q6 e: c& H1 n( Z$ B! Rcicadas and prime periods. 4 t/ k8 o7 ?0 g4 w
circle, prime. + n) Y4 I. b1 I6 X" o$ ?9 l& O' W8 U
circular prime.
& J) l0 k( Z) a3 BClay prizes, the.
# ?. Z4 {8 M @& Q Tcompositorial.
 v% I) x' v% o) u1 u- r% Z$ Zconcatenation of primes.
+ E( l. s5 g2 }# J2 \7 L& u9 Uconjectures. : k$ V2 {" h0 T
consecutive integer sequence.
8 y! K! \+ ^+ }0 e, @consecutive numbers. 0 ~/ \" S: z: O
consecutive primes, sums of.
8 ^$ M [" a( t8 J m; pConway’s prime-producing machine. ) K8 X' \9 m) j7 \- X$ }
cousin primes. , H% {& ?: @% p7 N- T+ l
Cullen primes.
9 A8 C: s7 }0 tCunningham project. 7 ^: L7 J S/ H0 x& q: f) B6 T
Cunningham chains. # i( s/ W/ l% i: I4 j8 m
decimals, recurring (periodic).
( c. M* J$ C* K2 G! Ithe period of 1/13.
' `1 E% V H4 H* ecyclic numbers. , s4 Y( H( _0 Y5 v6 _
Artin’s conjecture. , s) L! |+ ?: k8 i" a' m8 x. Y1 u
the repunit connection.
7 P S6 F- c: S% D5 L; M, jmagic squares.
' N. u$ x4 N; f# |" Wdeficient number. / m6 U3 d; R9 U5 S' y
deletable and truncatable primes. ; N0 M. o7 Z* @0 P, p. Y
Demlo numbers.
5 b5 \3 c4 ]# x/ A; v, edescriptive primes. 8 A3 @0 I# o3 o, ~4 ~
Dickson’s conjecture. 0 r% F5 {# z6 h8 `7 D6 T/ A; t
digit properties. / n! E5 H- l9 Z/ x3 k- i
Diophantus (c. AD 200; d. 284). 8 `. v) i4 V3 e3 Y/ D7 P
Dirichlet’s theorem and primes in arithmetic series.
! f& Y8 v; P0 X" f" @primes in polynomials.
6 V2 B3 K# x8 v0 Kdistributed computing. 4 K; y/ n( S0 W+ @2 t
divisibility tests.
# N1 a0 X/ X8 q4 X- Z% Mdivisors (factors).
) q, J5 r+ N) r1 j' whow many divisors? how big is d(n)? ( i/ G* V6 Z$ Q, _) Z! P) l; O
record number of divisors. Y0 t5 A: \, O: p9 @; V/ S, r. [0 T
curiosities of d(n). 0 o; Q+ r0 X$ M9 L# s( J4 o7 H
divisors and congruences. / V r- z. b. {+ T
the sum of divisors function.
2 s0 k8 O0 ]* N, N4 F! \the size of σ(n). + d" }2 T$ n7 f) @7 g$ n! I
a recursive formula.
- S5 x: ]+ |1 s+ {5 b$ jdivisors and partitions.
 w6 s. S) K# ` i2 ?' ?: M- Bcuriosities of σ(n).
" q" C+ B; Q/ a: M9 D4 S% i jprime factors.
4 M) z9 Z' E+ i8 q/ ~divisor curiosities. ! s7 y% X8 G E& k1 m
economical numbers.
# ?+ U: R4 k6 |' W. U8 ^6 f t7 VElectronic Frontier Foundation. # G5 q* \: N% w, N7 i& X5 z
elliptic curve primality proving. . [6 M% p- R) @: v: M
emirp.
4 h# a. d3 w7 e) E4 oEratosthenes of Cyrene, the sieve of.
# Z$ {: J- P' _( uErd?s, Paul (1913–1996).
# N( X" G& u' o4 A3 ghis collaborators and Erd?s numbers.
( |2 @1 u6 v# ferrors.
3 c/ S4 T1 u( J% `Euclid (c. 330–270 BC). ( n8 n. S" v1 B- ^0 s
unique factorization.
9 U& ~2 s e, b- E2 \: Z9 s6 g) Q&Radic;2 is irrational. + R: {' q v6 Z1 G
Euclid and the infinity of primes.
& r6 g/ ?. ^6 [; Hconsecutive composite numbers.
1 F8 b1 d8 d! q! [primes of the form 4n +3.
 O1 O0 G) l6 c+ [a recursive sequence. ' r# [$ W! k; j9 E% z5 {
Euclid and the first perfect number. 8 _2 Z- G5 u( y# C& a# b
Euclidean algorithm. 0 Y8 k* E/ A; g3 t" L/ K: Q
Euler, Leonhard (1707–1783). + j. m6 |7 G5 A0 H% c' s
Euler’s convenient numbers.
, ]/ l# B# y: [3 U0 z0 uthe Basel problem. 0 U8 M# a7 I S4 d$ J. F$ @8 K- Y
Euler’s constant.
. o/ K. ^+ k. |7 P* DEuler and the reciprocals of the primes. : k- @" ]' b+ k! }6 e' A, c, _5 @
Euler’s totient (phi) function.
- R* _8 l6 D. {) `1 MCarmichael’s totient function conjecture.
- R( V0 @; n8 L3 z7 b7 j/ i dcuriosities of φ(n).
2 P5 Y8 [+ S% _" ]1 _Euler’s quadratic. . M5 ]6 ~* h4 C! K$ x2 h: l4 W
the Lucky Numbers of Euler. ! L7 J) |: l+ U$ `+ i; j! J! n
factorial.
+ [! p5 s; _; v" |4 \factors of factorials. ; ` ^, \2 I' j3 R; _3 O' v: o
factorial primes. 2 v: X8 H( _- e R
factorial sums. , x! j7 Z! l5 n1 I S0 J
factorials, double, triple . . . .
- A3 U0 O2 i# jfactorization, methods of.
; o. s1 ]& w( ?# T! A3 ~factors of particular forms. ( I/ F; G, D) W$ c
Fermat’s algorithm.
2 J7 u9 i) d$ kLegendre’s method. 2 w+ J' {5 c3 `( ~2 q2 K
congruences and factorization. & S/ `5 e. h9 F. v4 I6 N; b7 e! c+ \- `
how difficult is it to factor large numbers?
1 G+ D% K. H$ T- L1 vquantum computation. 5 x( c$ N4 R+ p2 b
Feit-Thompson conjecture. 9 y3 C* I; m9 m9 Z: m5 A3 _
Fermat, Pierre de (1607–1665).
$ w- B9 E' ^3 A7 B3 AFermat’s Little Theorem. - f& e7 w! O/ `1 H& `# T
Fermat quotient. - b6 @9 u9 e! W/ u" M! O
Fermat and primes of the form x2 + y2. 3 \/ A9 Q, @! R* M
Fermat’s conjecture, Fermat numbers, and Fermat primes. 1 s3 G8 I. k% y2 Q
Fermat factorization, from F5 to F30.
' ^% _* K1 X7 |( ?Generalized Fermat numbers.
3 `% E- c: p/ l& A8 t! X- r) QFermat’s Last Theorem. / E7 h" Q1 l0 ]4 N6 a7 A
the first case of Fermat’s Last Theorem.
4 x3 Q5 I- P* l5 X9 FWall-Sun-Sun primes. : Y* g, z, ]7 ^: Y0 V
Fermat-Catalan equation and conjecture.
) d5 A0 l) _. YFibonacci numbers. / i: f2 y+ v0 Z8 f6 e) y, |6 ]
divisibility properties. 6 l& y2 d5 b% h; F4 o
Fibonacci curiosities. " t2 S: p) {- }( M
édouard Lucas and the Fibonacci numbers.
; ]' s+ U ~& E& ]% J: a- ^Fibonacci composite sequences.
* i, S8 V- ?/ h: V$ Y4 w1 Vformulae for primes. 0 F- O. q5 y m9 D0 r; S& M
Fortunate numbers and Fortune’s conjecture.
2 m$ {- w4 l% egaps between primes and composite runs.
9 r5 h7 P [2 K4 S3 W7 I" fGauss, Johann Carl Friedrich (1777–1855).
* ^7 R- E5 k1 fGauss and the distribution of primes.
3 t& V! h: W" J e# a+ W( J1 lGaussian primes.
 Y# J" Q- P9 L+ a4 h. XGauss’s circle problem. " j- \$ b- P0 m+ l
Gilbreath’s conjecture. ) @# ^6 M) {' [/ Z
GIMPS—Great Internet Mersenne Prime Search. 3 w) J' K1 V, x' x3 b
Giuga’s conjecture.
+ Q! i( J* k e/ [3 s2 ]+ z/ BGiuga numbers.
* x# V! d3 e7 n- {" Q# _7 d: j7 a/ H8 vGoldbach’s conjecture. : ]6 c8 f$ L6 R: E7 w* @
good primes.
/ U) _ L% { |3 A8 }- oGrimm’s problem. 5 k" s! i r( l; w9 u! B; F
Hardy, G. H. (1877–1947).
3 P5 V# [# x k8 [Hardy-Littlewood conjectures.
9 x3 }! T* g3 ?0 I" c8 Oheuristic reasoning.
3 K. d# o9 C2 d, ^* @a heuristic argument by George Pólya. * c5 J' s d( o; P
Hilbert’s 23 problems.
) K4 w2 @9 `( R" e1 @& \& s" l7 \0 Xhome prime. & a3 ]6 h; l9 Z9 [, |, ?# R
hypothesis H.
 t: A S2 U( f. Y3 W# }+ T9 Dillegal prime.
7 t# g) |& c; E5 tinconsummate number.
 }6 R2 |+ R8 U# `" W- Xinduction. 1 k$ n% Q( ~. |/ {/ l/ l' l
jumping champion.
) B; y. O% c' T6 \& M3 k6 _4 Nk-tuples conjecture, prime. $ Z& V; f" i% i. |. ~
knots, prime and composite. " z* ~, b2 C/ v
Landau, Edmund (1877–1938). 5 O% Z6 K c8 v6 [5 I
left-truncatable prime. 6 T4 Y7 T: j- X9 N1 H y/ u
Legendre, A. M. (1752–1833). 3 d8 F+ T$ d4 |! L F
Lehmer, Derrick Norman (1867–1938).
5 i+ A5 {1 H( K5 T" A5 gLehmer, Derrick Henry (1905–1991).
. Y' M2 @ ]. U9 cLinnik’s constant.
 H2 C9 d1 y5 @* E6 e X- hLiouville, Joseph (1809–1882). 1 a9 N9 `" I4 H! v% F. `
Littlewood’s theorem.
1 H7 _3 @, m$ c) gthe prime numbers race.
, m2 d, i' t3 b5 kLucas, édouard (1842–1891). % o$ r0 F. t! f) |8 I) l& t5 |& f
the Lucas sequence. # |9 l+ s' f# V. [; x
primality testing.
, V3 O! _/ y; [) K5 z) k: N' PLucas’s game of calculation.
" k# Z7 f* {, |# ?. [% h( ], z4 ^, [the Lucas-Lehmer test. * m& S* z6 e1 X- v! h2 M
lucky numbers.
6 R/ C) i5 o+ y; F q( b: z/ r, fthe number of lucky numbers and primes.
: i! V7 T% m. n' U“random” primes.
( Q* Y% l. ~$ h/ m3 b( Vmagic squares.
. A2 x6 a2 h( X0 G% |Matijasevic and Hilbert’s 10th problem. ! y5 q5 O! B0 G( B( H& v b
Mersenne numbers and Mersenne primes.
! G( e3 S5 V q1 P @Mersenne numbers. ) ^1 ` B- B. v, x
hunting for Mersenne primes.
6 y: ]* _ M" ]& E5 k8 Bthe coming of electronic computers.
" c$ t+ n* X- S2 w; i: p* ]5 EMersenne prime conjectures. # V9 n. }3 d( `
the New Mersenne conjecture. : Z# j2 T) F0 E0 [2 V( y
how many Mersenne primes? # E' O1 D+ J' ?
Eberhart’s conjecture. , X0 W' g7 v; p& v( R3 b
factors of Mersenne numbers.
, l1 E' g3 t- q& r8 ]Lucas-Lehmer test for Mersenne primes.
. i: D0 Z& [% E5 [- `7 cMertens constant.
( t* B- q" t% Q+ q5 IMertens theorem. # X9 z& \4 w+ a) z9 t
Mills’ theorem. / t4 k) F5 ]& U
Wright’s theorem.
" u0 M5 j$ K: f& \- _, x. i3 vmixed bag. 0 g! Z+ C9 e- q. S$ m9 L: Q
multiplication, fast. 0 U: E R2 y( h& p5 r# U
Niven numbers.
. K" w$ c' E! R4 N6 S- Godd numbers as p + 2a2. 1 I% x! i9 L& l" B
Opperman’s conjecture. ! b; O, D, h5 I) O" `% C
palindromic primes. . C9 c. {' L/ I! f8 V4 I
pandigital primes.
: i; A0 }3 Y8 M6 NPascal’s ** and the binomial coefficients. ! X2 o; V' I$ e1 u" J. n% L' O
Pascal’s ** and Sierpinski’s gasket.
- `. c$ J& ~9 H3 N" ^* ]Pascal ** curiosities.
2 Q1 Z; J3 F O8 Y4 E Z$ vpatents on prime numbers.
3 J4 b/ U T QPépin’s test for Fermat numbers.
" }) w2 [" S2 M. C" q0 f. Qperfect numbers.
$ e7 q, D- t( b0 Qodd perfect numbers. 4 b" x4 T6 E3 R, g3 j
perfect, multiply.
' W _/ v v- Kpermutable primes. 1 e2 s7 u8 A; Y Y Q
π, primes in the decimal expansion of. 0 T( G2 g% c8 m/ ?6 u6 D- ~5 O
Pocklington’s theorem.
, ~* U3 x+ D9 G1 G1 i# f8 q3 u" pPolignac’s conjectures. . v% C! l1 Q0 H# } r0 B( k3 U
Polignac or obstinate numbers. 8 `" K0 b5 v) A2 [( V
powerful numbers.
+ Y ]( Z. ]: M/ @* zprimality testing. " }1 o! K" ?9 L$ W" a
probabilistic methods.
6 a% R1 P; T% n* H Q( L1 jprime number graph. 0 M& J4 C5 L' Q2 @9 S0 o) T
prime number theorem and the prime counting function. . r! |# r* q8 k3 B4 m
history.
' p9 ^( W/ j( a8 d' Ielementary proof.
6 Q% R- [3 z6 X" Rrecord calculations.
. |, n4 F8 I5 j5 L8 `9 O2 }$ Aestimating p(n).
- P% K, q( k0 Ccalculating p(n).
0 U6 H+ z, s) \' n9 `a curiosity. # J' ^# Z) \& m, J2 f6 b6 `
prime pretender.
7 C5 i0 f" y* A% j3 h" @primitive prime factor.
) q7 F, G: O0 P& y \primitive roots.
) D4 j9 }9 W. d9 J" J+ m4 R! {- aArtin’s conjecture.
3 Y( n. r& J. C) y6 @a curiosity.
2 r9 D* O. N$ W/ O* lprimordial. 0 K2 T5 w8 u6 l( B
primorial primes. - _ ] l# i B/ F
Proth’s theorem. - o' ~3 f5 B- [9 t+ V
pseudoperfect numbers.
 _9 V0 C- J5 J% J! Lpseudoprimes.
' k, ~5 g$ S4 S+ w! T1 }9 o: Sbases and pseudoprimes.
+ j& J. h: a- R9 h& y/ {pseudoprimes, strong.
' j# _: f+ J2 U% Rpublic key encryption.
1 L- C* V: J2 ~7 F0 Q. `pyramid, prime.
8 }& U5 n1 S% n. @Pythagorean **s, prime.
' J$ h0 z3 ^7 ]quadratic residues. ; A/ r( m. O# i
residual curiosities.
' o! U u$ Z9 X+ l! S5 lpolynomial congruences.
1 n& Y5 W$ ]% b" Vquadratic reciprocity, law of.
: F" ^8 H, C1 LEuler’s criterion.
& j: {, P; g, u F9 f( r: e# wRamanujan, Srinivasa (1887–1920). , q- v; e) N4 y5 S
highly composite numbers. 3 L1 b1 u# V+ d$ X! X
randomness, of primes. - e4 D0 i' \+ q& ]. U6 k
Von Sternach and a prime random walk. / C; G, _& L2 T" N! _$ h* A, i+ X
record primes. 3 r8 E v `7 h' c
some records. & @* d; U4 ~! b. q5 W9 Z' [
repunits, prime. ) P. U4 W( l. E6 z
Rhonda numbers.
0 N! b4 ~% u& FRiemann hypothesis.
$ X4 A* _7 i. n7 x1 e/ b7 L( Othe Farey sequence and the Riemann hypothesis.
/ u+ B) O; m- I1 Gthe Riemann hypothesis and σ(n), the sum of divisors function. 7 `- j& V9 t$ s
squarefree and blue and red numbers.
2 Y9 ]6 {; M$ V. ?7 }$ wthe Mertens conjecture. 9 ]9 X! s5 B& p9 i* y2 g+ J1 z
Riemann hypothesis curiosities. ) u. M" [* }8 L# |% v- l6 s) a
Riesel number. . m$ H3 }- o9 \
right-truncatable prime. / h0 b7 a; M0 G
RSA algorithm. # N$ N4 @, M- [0 N$ F: U/ A
Martin Gardner’s challenge. " T$ h. l. R) ]9 G( Y1 d
RSA Factoring Challenge, the New.
0 k6 Y0 p5 [1 F6 B6 ~Ruth-Aaron numbers.
" S/ O: b/ ^- \; C7 r+ M4 `- iScherk’s conjecture.
8 N3 q9 m/ J0 H" ]3 a) ssemi-primes. 2 S; Q$ z3 X+ G" a1 @
**y primes.
 G% X* L( U$ k# N& m: y9 PShank’s conjecture. 0 K C! `/ S5 ?2 q5 {
Siamese primes.
) V& B- C6 z, v. p5 ISierpinski numbers.
$ e* d/ o/ V/ rSierpinski strings. 7 _; j/ E4 u. G3 X4 A- M8 u7 }
Sierpinski’s quadratic.
, k, C5 C _7 ], [8 FSierpinski’s φ(n) conjecture. 3 s1 F! I# \# y
Sloane’s On-Line Encyclopedia of Integer Sequences.
* V. |, B) t) j, G: SSmith numbers. 4 Q) D1 {+ l" S: t3 N% a
Smith brothers. 0 r* W! l; l1 ]& A/ c I9 m
smooth numbers. 8 }# e0 c# w1 }" u( X
Sophie Germain primes.
! z) @+ Y; a {safe primes.
5 V! p( T/ ~8 i% q+ c# b6 Esquarefree numbers.
; K" ?# q) A3 [4 R+ v+ _Stern prime.
) O# h6 T/ C l/ z3 d7 B* Q% |strong law of small numbers.
. Y. u% L% ?) k# c6 v' rtriangular numbers. / D- c' T+ G; E
trivia.
! H/ h7 i. w3 C! rtwin primes. : |; S: |- _0 p* I+ V. q& G
twin curiosities. + ?* D; d) E) U/ o* \- c+ C
Ulam spiral. : g d ?1 {# j F5 a! N1 g
unitary divisors. & ]) V+ d9 g- m% ~& M7 G, Y
unitary perfect.
5 ^6 s# ]/ s6 F) j* L: Funtouchable numbers.
6 r& N3 S$ v. w% wweird numbers. 9 ^8 i& \: A6 Y+ L, E/ {
Wieferich primes. 9 N- F2 D8 B3 I" X
Wilson’s theorem.
% j: W) C0 L& Z f5 Wtwin primes.
% g, v$ U! @, X. C! q* @* X V3 d5 NWilson primes. ' q) A& Y2 {1 R
Wolstenholme’s numbers, and theorems.
. ]+ c1 g& Z7 u/ q" `1 t- [more factors of Wolstenholme numbers.
 m6 d7 z2 L* O: E9 lWoodall primes. : `! Z2 e9 u+ |
zeta mysteries: the quantum connection.