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数字的奇妙：素数

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Entries A to Z.
9 {9 ?* e3 d1 J ]! \. wabc conjecture. # T' H' X" T1 e
abundant number.
" v7 D( i& h/ r2 A& K5 NAKS algorithm for primality testing.
% R! Q6 G! e5 L/ O/ ~7 Maliquot sequences (sociable chains).
% t1 H4 u0 P/ M5 Y N2 Balmost-primes. # T- _/ Z# C( w" k& i% g$ x
amicable numbers.
0 P, i8 m2 l+ L6 Lamicable curiosities.
/ i" W3 j' G& l6 j; d" G" wAndrica’s conjecture. 5 |* E1 V* g3 I! x, B* |, h
arithmetic progressions, of primes.
% @. @7 i i* X- C% f tAurifeuillian factorization.
, ?/ J1 i1 J9 e& @: }average prime. . C# A3 @, i R/ I1 P
Bang’s theorem.
# i: ~) a5 w, m/ @Bateman’s conjecture. n$ j2 G$ P: d+ T' v. [; q/ K8 R1 {
Beal’s conjecture, and prize. , A) x1 s0 B2 s0 b3 d6 m
Benford’s law.
2 S' Y+ K1 w# d# ]- L9 pBernoulli numbers. - G# H1 `$ `/ c* p
Bernoulli number curiosities.
3 m! M- W4 K9 j7 }Bertrand’s postulate.
0 l" @) }" a3 BBonse’s inequality. ( B* I0 E- Y# D% f
Brier numbers. / U, s8 Q3 u, g7 J( |
Brocard’s conjecture. ( q( M" K6 `6 _8 u
Brun’s constant.
7 ^! _. d1 j* b8 t2 w3 U# D XBuss’s function. $ l9 P1 u) ~2 _' S0 o
Carmichael numbers. % U F7 M* H ^ q2 K
Catalan’s conjecture.
. k' g$ x' G. {0 y: u8 f$ KCatalan’s Mersenne conjecture. 7 F1 s4 H/ b# y5 i+ q
Champernowne’s constant.
2 _; d! D$ |: S/ E' B/ ichampion numbers. 3 V2 R1 h5 ^. ]9 r, a6 U* f
Chinese remainder theorem. ' |% L( E: v2 b4 q, N4 R
cicadas and prime periods. 1 D, G9 |+ g* ?# g6 G& Z
circle, prime.
; m& d$ @% T4 Icircular prime.
/ ~1 Q& L# ?7 B3 T( J, ^Clay prizes, the.
9 P2 F( a( d6 I8 Ncompositorial. $ w6 L8 j: g" R+ R" J9 E: s$ o
concatenation of primes.
* `( j6 j7 O; z dconjectures.
0 I6 Q7 x' Y1 W+ y( ~' o) Wconsecutive integer sequence.
 N4 t5 b- M& \7 x( J4 oconsecutive numbers. + ~1 f: F! p. q @
consecutive primes, sums of.
! o* a; x' y3 d; r6 {2 ^7 `- YConway’s prime-producing machine.
; ?* _- r4 |3 R6 [- dcousin primes.
; J v0 ?5 q( u( _) C xCullen primes. / y# n" b6 e% h1 s
Cunningham project. + }; r% W& ?) G% f/ x2 h4 }
Cunningham chains. 6 F6 I& `, A* ~7 d
decimals, recurring (periodic).
, c3 Y9 y6 E4 p& pthe period of 1/13.
, T0 l( i A6 f% n+ P% c% Q }" Acyclic numbers.
& ]' ^. M# ?& }8 E9 b, uArtin’s conjecture.
" O+ D- w3 ~( I' Q0 zthe repunit connection. ) _1 H7 q: j4 R5 i( P+ b
magic squares. ! P4 ~" y6 g! B# ]' Q# u0 g
deficient number. 3 A* a" K1 G* x* q# H) A
deletable and truncatable primes. ; }- ]' Y5 x; T0 M4 L2 @
Demlo numbers. - ?! h) B+ z3 l2 V
descriptive primes.
$ o) a3 h. G+ l/ O t: z! ~$ TDickson’s conjecture. # n! W! p# d( o
digit properties.
4 V) E: U" I7 k; Z8 nDiophantus (c. AD 200; d. 284).
3 t" ^& c# W+ p m+ mDirichlet’s theorem and primes in arithmetic series. % c# K# g5 l2 [$ b
primes in polynomials.
5 S5 X& m8 J7 Z/ l X, Ddistributed computing.
3 k0 e' Z4 g2 @5 K, G- R) s; Adivisibility tests.
8 q, |' O' T( b# Z: wdivisors (factors).
' h/ E% J' R6 u( w$ g# x% K+ Lhow many divisors? how big is d(n)?
7 g2 V8 S& C, Trecord number of divisors.
, O" a, K* {2 q% ]curiosities of d(n). ; u I# V4 V* Y- I2 _1 Y j3 I
divisors and congruences. 4 K T5 p( ~3 i9 u' ]7 m# ~
the sum of divisors function.
+ z: d8 b* X7 X1 L( G( P! H1 Z: Ithe size of σ(n). . R; g# R d) b0 k
a recursive formula. 6 q. n( l. F. K% ~8 W
divisors and partitions.
0 E: |' F0 J9 d. U3 V) jcuriosities of σ(n). * D8 H" P% J& Z
prime factors.
) M T: D& q4 ~divisor curiosities.
( U z3 P! Q4 b+ jeconomical numbers. & K% W1 R1 f* {* h
Electronic Frontier Foundation. . M2 u" V. i* O& p! {7 b& \% }
elliptic curve primality proving.
' S. L" v: c/ N8 l4 h$ s Eemirp. 5 }: S9 U8 Q5 G! q" ]% f
Eratosthenes of Cyrene, the sieve of.
, D% ~( B0 h$ C ~, PErd?s, Paul (1913–1996). $ s1 \* B, K$ K! i6 A# Y0 l* S( z7 O
his collaborators and Erd?s numbers. + v [% O% ]# n* V
errors.
% W6 ~) y& I1 J7 W- c5 {Euclid (c. 330–270 BC).
0 ~) |# U q/ I' E% x$ hunique factorization.
/ Y! f( q# C# \2 H) E' ]&Radic;2 is irrational.
$ l- {5 m, K2 Y/ j: b" j* ]2 ? fEuclid and the infinity of primes.
9 A1 U5 v$ P# G, ]) w3 t Iconsecutive composite numbers. U' ^! o. [" O& D6 {
primes of the form 4n +3.
1 g& i5 O2 F3 L; ^a recursive sequence.
% ~$ ~& A7 a* eEuclid and the first perfect number.
, x- q3 D# ]; f* S- xEuclidean algorithm. , {. |& t6 d! |; j) O
Euler, Leonhard (1707–1783).
% k* D$ P3 r3 q; r6 B& I- [( | JEuler’s convenient numbers. : b M* W3 @0 |/ P1 T) d6 }
the Basel problem.
! W. R3 n, |0 ^. E! Q# W: o# QEuler’s constant.
: ~. G% \' O* QEuler and the reciprocals of the primes. ( w* ^# t+ P" {2 e1 F
Euler’s totient (phi) function.
% i/ y% |# n. Q# R5 @Carmichael’s totient function conjecture. ' U+ _5 z& w% z
curiosities of φ(n).
& p3 q r1 o7 {( X$ p& F$ Z8 VEuler’s quadratic. & ^. Q1 c& G% B% W* U0 E* R
the Lucky Numbers of Euler. . R, t( o: K/ ~; Y( Z v
factorial. 3 f% ^# Y% ^% J7 ]. v# q7 ^
factors of factorials.
$ G t) G7 O$ Y2 vfactorial primes. 5 Y3 N# f! ?! x- u
factorial sums.
& n" n* A/ m j; ofactorials, double, triple . . . .
' X w4 H6 m2 V# E3 L m8 c1 _factorization, methods of.
2 e6 h7 A- ]2 T" z _/ r( Gfactors of particular forms.
' T X+ r: n( G% D" d+ bFermat’s algorithm. ' D( X0 o$ x/ g5 E5 m! T
Legendre’s method. . a! D, D: `; c% W
congruences and factorization.
6 x2 N" s/ z9 q; r/ a, Uhow difficult is it to factor large numbers?
9 z# A! @( P) {, ^quantum computation. : \2 k0 I ] v2 x% d6 }
Feit-Thompson conjecture.
/ t, q% @+ A5 q5 L" eFermat, Pierre de (1607–1665).
4 K7 m7 p7 R. ~4 mFermat’s Little Theorem.
* w% C- v% c9 ]7 ^; W0 j2 P. eFermat quotient.
8 C2 T8 J N3 Z2 `9 X0 jFermat and primes of the form x2 + y2.
2 w5 G( U1 ]2 v1 J2 J2 S" }Fermat’s conjecture, Fermat numbers, and Fermat primes.
8 l( Y. X, e, n, X; Z! O' [Fermat factorization, from F5 to F30.
$ E. X. s7 u# Y/ T7 S+ wGeneralized Fermat numbers.
Fermat’s Last Theorem. 5 a4 p2 K# I# i4 D" [
the first case of Fermat’s Last Theorem.
6 U. d: s, y3 Q2 o3 Y) X9 ]$ c( G3 K" sWall-Sun-Sun primes.
 z; H& N1 i) p4 F OFermat-Catalan equation and conjecture. & |- r* u! v+ r2 x
Fibonacci numbers. 0 c4 y+ P$ e8 H4 I1 I/ w
divisibility properties. ' n# T1 `2 _2 {7 z$ X
Fibonacci curiosities. $ n8 ]7 N( p1 ?. F% V
édouard Lucas and the Fibonacci numbers. ! T6 I+ N& f8 W2 s+ O6 A
Fibonacci composite sequences.
7 @6 X4 H. m: W/ m z* i8 S3 mformulae for primes. ) | @& c O4 l+ ?& b4 B
Fortunate numbers and Fortune’s conjecture.
" e( f- L) L$ f3 v9 D5 q! T. ygaps between primes and composite runs.
3 Z6 [ s; S+ r P/ p7 s- cGauss, Johann Carl Friedrich (1777–1855). / y# h! R+ S/ W( l$ V
Gauss and the distribution of primes. , B* g7 E2 R6 M9 V
Gaussian primes. 3 T x& R: m& |2 {9 }+ L( ^. e
Gauss’s circle problem.
" Q5 }, u3 V6 hGilbreath’s conjecture.
 Q! r4 b. ]- e- y- QGIMPS—Great Internet Mersenne Prime Search.
! c4 r$ e/ `) e- RGiuga’s conjecture.
0 W8 s! k2 Q3 d! |* EGiuga numbers.
7 S* K0 H/ w% B2 EGoldbach’s conjecture. - y$ l4 t+ X4 S7 k; P8 o# p
good primes. ) G- A' P" t0 n& g
Grimm’s problem. ( I n+ j0 C. V( S2 e2 D
Hardy, G. H. (1877–1947). 2 e9 [' ^' b; c% w0 x
Hardy-Littlewood conjectures. 6 A; w3 f' ^/ Q5 E5 g
heuristic reasoning.
9 Y, a6 [ ~) q5 U) o0 U2 Ta heuristic argument by George Pólya. * S% k# y: H7 u% J; k. g/ ?/ N
Hilbert’s 23 problems.
" l4 W; D9 @& a: D. c$ R1 Whome prime.
: G6 r7 l0 O% k/ @# mhypothesis H.
. e8 n; B1 y. c8 Pillegal prime. - g( H: D" {0 [. V8 d- U0 x
inconsummate number. 4 U3 r7 i. H0 _
induction. + }. q! ]9 f- y- z0 Y, W0 @ ?
jumping champion. 1 K: y6 d; p$ \+ X. o# S
k-tuples conjecture, prime.
9 ?1 W! _5 W' Y' R- U$ U9 m. jknots, prime and composite.
 A3 y2 b/ z8 O: d4 JLandau, Edmund (1877–1938). 5 { d8 ^4 V! o! d( M. d5 a9 l$ A! B
left-truncatable prime.
1 O/ L' K4 A8 O% z2 }/ W% yLegendre, A. M. (1752–1833).
) F8 l% @8 p; Y2 \0 @9 j4 A+ cLehmer, Derrick Norman (1867–1938).
7 q9 h* _$ W% w& G) `# VLehmer, Derrick Henry (1905–1991). ; P! F( ]! s3 r6 t `( i
Linnik’s constant.
2 Q7 U, a$ C" R) u# G4 A+ _Liouville, Joseph (1809–1882). - M/ M8 m! ]/ U0 }+ ?. m$ O4 {2 m
Littlewood’s theorem. # ]5 q5 F5 s& M y
the prime numbers race.
( S x! D( e$ ]8 ^8 }Lucas, édouard (1842–1891). w2 z6 ^1 I+ R) n$ x& r
the Lucas sequence.
. L2 s+ J* w G& }" _1 |primality testing. & ]/ x O4 j4 y" g8 z2 p
Lucas’s game of calculation.
; Y- E2 t) T( H, @the Lucas-Lehmer test. 7 e' b- N2 @8 O
lucky numbers.
% X$ j" T; B( o4 a8 o nthe number of lucky numbers and primes.
) w- Q& ]9 |+ w c“random” primes. 1 j k7 J8 P! n2 v
magic squares.
4 Q# A# U8 k0 j" J* E; fMatijasevic and Hilbert’s 10th problem.
9 l3 _ _9 \' L2 c KMersenne numbers and Mersenne primes. 5 E1 u. A6 j# A- C% f
Mersenne numbers. : j3 e9 _/ ]6 S4 ^* [0 S$ f( A
hunting for Mersenne primes. # a' R6 F7 { {4 ~9 `
the coming of electronic computers. {' ]# q. c' Z& _( `, |
Mersenne prime conjectures. ( B: y- ~% r8 k* n0 j2 h3 H
the New Mersenne conjecture.
3 z* ]9 f8 ^) @how many Mersenne primes? ; k7 v/ X0 w: [0 R$ q. V4 z+ V
Eberhart’s conjecture.
& ?6 q( |: \- w) xfactors of Mersenne numbers.
8 J+ l8 g9 f! P0 z+ W- K! cLucas-Lehmer test for Mersenne primes. ! s! G* i) e! T1 `+ m8 G
Mertens constant.
: z- ?, Y* i3 V8 N$ wMertens theorem.
8 B2 f' z* Z9 T$ [9 [7 jMills’ theorem. - K3 o" q( F: m. a3 R
Wright’s theorem.
! z+ P7 N, Z$ Y k; Jmixed bag.
; b8 W( p* }3 `, Amultiplication, fast. * M9 `% Y9 {. Z" Y! d
Niven numbers.
3 T! V/ U. |0 Y0 ~odd numbers as p + 2a2.
+ I/ ]9 }7 Z0 P4 |9 e/ |! s6 }( uOpperman’s conjecture. ; D; Q- F) A0 N+ R3 ~/ w
palindromic primes.
! q4 d: s. {4 l; opandigital primes. & l" D, ?# n' O2 T( t
Pascal’s ** and the binomial coefficients.
5 G9 U3 L; n( T- P7 e6 f$ QPascal’s ** and Sierpinski’s gasket. $ J( M4 Y# z R8 h
Pascal ** curiosities. 0 }$ n. E' u, l5 y3 p
patents on prime numbers. : i ?+ \( b$ R0 A( W4 M$ s
Pépin’s test for Fermat numbers.
. F7 _/ ~' I- a8 b+ w3 kperfect numbers.
3 G7 G$ t" d7 R6 o! J; T7 Uodd perfect numbers.
. A2 T( c& P! A/ H- Rperfect, multiply. d; w2 H q5 u- r/ Z0 C
permutable primes.
1 c- c% ?* i, X. C$ d1 L2 Rπ, primes in the decimal expansion of.
! @6 y o6 m/ i' ]- U2 j* RPocklington’s theorem. ! T( e2 U, O- N @$ E; r. d
Polignac’s conjectures.
" @ v8 |' V, W+ _Polignac or obstinate numbers. ) N$ p3 G$ |6 Y0 H7 Z: [
powerful numbers. 6 v; l a9 z) f$ f( A' K
primality testing. + a) G$ t1 W$ s7 v2 s7 v& {; _/ u
probabilistic methods.
; n4 S$ S- X1 g2 o2 L0 Aprime number graph.
9 w6 q4 v; r* [ Q" `prime number theorem and the prime counting function. 4 L# q" ?2 F4 ?: K
history. 5 D0 a4 \8 a# {) m
elementary proof.
2 l& f Z' o( ? mrecord calculations. " N. N$ S+ _% s
estimating p(n).
0 F' F( j4 t2 o2 L4 Y% n/ k4 _8 }calculating p(n).
" L/ P! B# |. U: @a curiosity.
 o* j7 s- A- G1 b) T( H6 Eprime pretender.
1 f' F2 C2 T( y: [0 B( Nprimitive prime factor.
0 P! L, J0 i8 F; ]2 V4 Fprimitive roots.
! {8 Y0 s) m$ S% KArtin’s conjecture. ' I/ e1 a" i9 g3 H. ^! t, c* h8 O
a curiosity. . B. S) N+ K9 Q- e, F* t$ I: K
primordial.
6 c: u* T1 q" [6 s9 Rprimorial primes.
2 k- X* y1 @5 b& \- j( kProth’s theorem.
; J' F7 b! |& @2 r" S. }) Gpseudoperfect numbers.
 o0 _$ F2 c% n& D* v' qpseudoprimes. 9 \ L" {% ?- i4 G
bases and pseudoprimes. j3 r) x2 U0 z. O" j8 J( q
pseudoprimes, strong.
$ {6 j1 W# w! e9 i3 |public key encryption. ( Y$ {2 T2 f- n' p; Z
pyramid, prime.
, m6 {, v6 j8 U6 h$ n8 S' W& TPythagorean **s, prime.
4 t z/ v' j( f* Z8 a: J" L" o4 vquadratic residues. ( f: n+ k" M# m
residual curiosities.
' | k; O* N# N0 Wpolynomial congruences.
2 {, E# E8 ~) z/ \quadratic reciprocity, law of.
' U) L/ q2 h w0 @/ bEuler’s criterion.
3 k5 t- u$ I- L. l) |Ramanujan, Srinivasa (1887–1920). ; |2 p3 ^. \% _. Y! ~9 v" A
highly composite numbers.
% [% D/ a. \$ J7 T: prandomness, of primes. 2 c1 t' x" K" O
Von Sternach and a prime random walk.
+ k0 R( v/ B6 f* @record primes. 1 x h. @0 t* r; Z1 J/ f+ a
some records.
% _% E& w J5 W. _6 Prepunits, prime.
3 R* H: G6 _) P+ @6 jRhonda numbers. ; v) E, _# j% j/ ~8 S* ^! ?
Riemann hypothesis.
( X+ `( d0 q7 e& l& h2 y6 Q# s& Ythe Farey sequence and the Riemann hypothesis.
$ R. t: k& k6 K. V! `% b8 vthe Riemann hypothesis and σ(n), the sum of divisors function.
+ T# u4 f! t1 Csquarefree and blue and red numbers. H6 L2 }6 z! U& @" X- W3 ]- N
the Mertens conjecture.
 o% J; i4 [7 m" ARiemann hypothesis curiosities. 7 z" F# l+ x0 Z
Riesel number.
* u, B3 C8 ?/ _6 ~7 k uright-truncatable prime.
+ M' u5 u8 n" b4 E7 T; DRSA algorithm.
' R+ a% A6 F' WMartin Gardner’s challenge. 0 Y3 q% \. O' O
RSA Factoring Challenge, the New. ) w3 [ O/ Q& a
Ruth-Aaron numbers. # b; k/ `6 [0 `
Scherk’s conjecture.
0 G# n* I! b! N0 O0 ksemi-primes.
4 x) b7 C0 U! I9 l**y primes. 1 L) @% _2 m/ ]0 ]" l7 c
Shank’s conjecture.
9 I9 z8 {* s. ~1 r) ESiamese primes. ' V7 K9 A6 a& k' r+ k \/ I
Sierpinski numbers.
; f: o& N' ~; x1 kSierpinski strings. , ?& A' G4 t3 w* _4 @! h: v% E' R
Sierpinski’s quadratic.
! {# E r/ ~$ D! F* A8 R- OSierpinski’s φ(n) conjecture. 0 ]+ W5 o+ X+ `7 |) H! S% \
Sloane’s On-Line Encyclopedia of Integer Sequences. + N* w: B" S8 ~8 O6 q7 q/ d: v
Smith numbers. 9 i" }* S7 B& t N7 v
Smith brothers. " T4 `- s% m3 `2 u; @ U' v
smooth numbers.
/ g0 f7 }# p- _7 H5 S& f0 ?Sophie Germain primes. ) r4 \5 ^, N* H0 D. s6 S- W" l
safe primes.
4 [; T6 t( K, Jsquarefree numbers.
$ b3 V. R; H. x. H- j, QStern prime.
9 P1 R+ _) Z# o0 Z# @strong law of small numbers. 7 t7 p: h' ?$ ?! w, X
triangular numbers. 3 C' l- z2 L) t, Z+ [5 s- i$ {8 V2 l
trivia. 7 ]0 u, }" b+ X: p: V; K0 m+ s# O
twin primes. 2 c) q) P. | P6 R2 K p
twin curiosities.
2 ^9 f! ?9 | U2 W# \Ulam spiral.
' s w$ k; d- f' C! F% aunitary divisors. # x6 Z% I# {) X9 a' b7 k( _5 }
unitary perfect. ) x0 r+ O" X$ n) Y/ K
untouchable numbers. & z8 [5 r. h& I5 k
weird numbers.
3 q" M5 e. M4 G9 g* W0 J! b% IWieferich primes. 9 L7 h% S: k9 x, `
Wilson’s theorem. 1 ?4 W% Z3 w' B$ e9 b0 Q1 f
twin primes. - B) s$ F) R' l8 Y% N
Wilson primes.
, Y, i y0 Y ~! {* ~1 {5 t% @Wolstenholme’s numbers, and theorems.
 u4 z5 M! ~2 b# S2 v9 p' B; ymore factors of Wolstenholme numbers.
1 R0 m6 o7 \/ a2 O! F6 n \Woodall primes.
$ E" z% n$ x, Z4 p' R2 u0 Q1 G2 xzeta mysteries: the quantum connection.