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Entries A to Z. , S, F' k6 b7 p
abc conjecture. s6 V. v% D' w2 k* z
abundant number. + I& t1 |; b+ e- g5 \. F+ z$ Q
AKS algorithm for primality testing.
( ?6 [: N1 m4 Y% g1 T- laliquot sequences (sociable chains).
& b) F' {8 L; } Qalmost-primes. ! R. I' l5 l8 g' g2 e
amicable numbers. * o2 o! ?' m+ B, C$ i2 {: W8 ?
amicable curiosities. ! ~! E: `- \( j# i! f3 v: b
Andrica’s conjecture. 0 k1 Q/ N! U1 D) K6 M( z
arithmetic progressions, of primes.
. v Z; S8 I1 I, t" IAurifeuillian factorization. $ _% v# F3 b9 `$ O# ]. P& R5 h3 T+ z
average prime.
% F/ m- T% n* S2 O, H3 e8 ~7 F, |& [Bang’s theorem. + G& X7 `; s; M; K
Bateman’s conjecture.
3 ?( y( w* N) T2 q; A& w/ W) M$ @Beal’s conjecture, and prize. * e3 c* v Y* A+ s
Benford’s law.
: r8 Q8 p% ]$ C5 {% PBernoulli numbers.
. q) c- a3 i% A3 C. [0 ]Bernoulli number curiosities. 4 T2 k# d: K: y6 G
Bertrand’s postulate. / E5 W( Q, r% A, A
Bonse’s inequality.
% P' y4 N) m0 X8 b- CBrier numbers.
; K0 c v6 S3 W1 sBrocard’s conjecture.
/ q5 x2 J1 O$ k* h* M& IBrun’s constant.
: h1 D- a% x! G9 k# j2 t2 }6 TBuss’s function. * Q$ e- k, h A. Q
Carmichael numbers. + {8 j, F T" a! d5 M( Z: E2 A) W+ Y7 a
Catalan’s conjecture.
$ C9 A( T8 |# M7 `% ACatalan’s Mersenne conjecture.
. n/ h* q8 V: o0 cChampernowne’s constant. ; O+ ^, e& o" c; O$ B8 w
champion numbers.
, q0 D6 f( K5 s: s* ZChinese remainder theorem.
9 C4 c, o' e0 C( kcicadas and prime periods. . s) j1 t/ x0 x: v3 P; {
circle, prime. % S( L) s% W; B% n
circular prime. ) j b/ W3 w' l0 B
Clay prizes, the. 5 L' J; A, I( n' N% ?0 Y
compositorial.
5 b) \. Q# q6 P1 x, rconcatenation of primes. 0 z& T2 M$ G4 b6 y. \
conjectures.
$ x$ i& J8 M% M) pconsecutive integer sequence. ' K! v R2 ?" E; b, w
consecutive numbers. ( J: |/ @0 B7 l9 ~6 L
consecutive primes, sums of.
) ?0 p) {, C% P% KConway’s prime-producing machine.
4 X8 \2 p- t! {% y" ~7 ocousin primes.
2 j3 c/ }2 A) vCullen primes.
, a. G0 g- a/ F# v6 b; XCunningham project.
8 t4 ] \% S( y bCunningham chains.
/ W0 Y+ l9 L# d! Fdecimals, recurring (periodic). ! r& T! b3 K5 L+ H, T0 ?8 b' q) B
the period of 1/13.
# r( d5 F0 f: @9 T3 h$ Mcyclic numbers. ) [+ m2 `, r7 y+ @
Artin’s conjecture.
) }1 O1 |9 Y1 |0 i/ C, a4 b5 mthe repunit connection. : X s* q! ~' s$ ~% Z8 R1 Z
magic squares. 4 R, T: ?6 ?6 P% t2 k
deficient number. 7 p8 r3 \1 i! x
deletable and truncatable primes. / s% E }3 G% y. P$ ]* ^
Demlo numbers. 2 N* t; E9 `5 Y+ X+ A0 U, ^
descriptive primes. ; U _# D3 n; L$ D1 f( C) T
Dickson’s conjecture.
: d9 Z9 b) D; C1 \/ bdigit properties.
6 w$ U! T! W, @. x4 aDiophantus (c. AD 200; d. 284). ) O1 E! \6 r1 B4 m- ]
Dirichlet’s theorem and primes in arithmetic series.
0 c$ }: [' ~0 ]1 [& ~primes in polynomials.
. X) {: f& |, [* ndistributed computing. ! j% [0 v: v' e* N6 n/ }% B! K
divisibility tests.
0 O0 O* G) ~0 d: Odivisors (factors).
& V$ }' `3 H" k0 b# N, M. E0 ahow many divisors? how big is d(n)?
. E. D) b2 H9 Z# ^) |9 j) ^record number of divisors. ' f6 M: I- {/ _1 a+ ~7 \2 z
curiosities of d(n).
. |: W" @: ?$ v- r9 w1 V& S3 Gdivisors and congruences.
# d! N8 h* f, {% G: c1 athe sum of divisors function.
* ^1 y" f' J% G/ a2 m! N7 Zthe size of σ(n). " b K! B7 K) R0 H, U
a recursive formula. 0 F4 P- _) `/ T5 g+ x( y
divisors and partitions. % e* y+ P9 e& i% B
curiosities of σ(n).
4 o; s0 I. i. n1 |prime factors. * b$ }8 ?9 O1 h ~. k3 I
divisor curiosities. ! Y$ U; N; C3 u- E9 f( r
economical numbers.
, E9 L+ Q6 I) Q9 D HElectronic Frontier Foundation.
 S5 Q/ ]$ H1 H6 b+ gelliptic curve primality proving. 1 }! A X& p+ i
emirp.
5 i8 X1 r/ M4 c2 M# gEratosthenes of Cyrene, the sieve of.
4 y# [7 W! w- \0 n/ H; SErd?s, Paul (1913–1996).
* V7 H7 Z8 r! W3 u6 |$ H$ rhis collaborators and Erd?s numbers. . }5 e; ^+ J2 C) w" E: h. W
errors.
8 M0 t* m/ z! D& [$ l1 Y1 o8 ?Euclid (c. 330–270 BC).
& a _1 v1 g7 B4 gunique factorization.
& B) L d% Y1 p5 B2 ~; j& l&Radic;2 is irrational.
8 D& u, \9 ]6 l" BEuclid and the infinity of primes.
5 l% v7 ?$ Z6 Q, Y/ U9 F( U) `0 Rconsecutive composite numbers. ( y" e+ E7 K' F5 }* B/ t, k
primes of the form 4n +3.
6 ^1 { U6 O, ya recursive sequence. ' s+ Q }- t" P# ^
Euclid and the first perfect number. " v1 d& X* b/ h; N6 s
Euclidean algorithm. - P! t/ [- R d0 P( ~& F
Euler, Leonhard (1707–1783). 4 a& f* c- J9 k+ }7 d) n4 _
Euler’s convenient numbers.
" o+ h0 L* y; H* `% ^the Basel problem.
* x3 E" l; {" o% ~" }: l, {( Z* cEuler’s constant.
 @4 y& c; P# Z$ T f& H% ~Euler and the reciprocals of the primes. # ]; p7 ?7 u9 T- I7 w N& \
Euler’s totient (phi) function.
' j4 x3 ^$ l& ^8 sCarmichael’s totient function conjecture. + d( k4 g0 ~9 P2 z
curiosities of φ(n).
/ `5 O+ ?$ v! m& k6 ^Euler’s quadratic. 1 ^( b4 b: o" F3 Q1 L% |- {. N
the Lucky Numbers of Euler.
 l6 h' w4 S7 d4 f! lfactorial.
& _( f' T" ^) @* i/ Tfactors of factorials. " }- {1 w2 i2 C% Z; d
factorial primes.
4 C2 T B" [4 X+ V0 m5 {factorial sums. 2 o3 Z4 n* t+ q5 e! C% z) Q
factorials, double, triple . . . .
$ a6 Z$ @- L) K, wfactorization, methods of.
7 }, _4 i+ u7 efactors of particular forms.
0 Q* C& t0 m& w9 n+ J# b* E! qFermat’s algorithm.
* j2 H( B& L: @. W7 U, V7 {Legendre’s method.
+ n9 B6 q# J1 o3 j6 [6 Hcongruences and factorization.
+ Z# ]" r3 D2 z, P* ghow difficult is it to factor large numbers? ' U' m+ M6 ]9 x0 P5 a, P0 G
quantum computation. 6 ?! X3 ^8 {; y" u0 x+ b+ E
Feit-Thompson conjecture.
0 [0 v, R7 P1 N: t) iFermat, Pierre de (1607–1665).
, [5 f$ r2 s& Z: cFermat’s Little Theorem.
2 E, R) o3 ]! Y. V* k" l) KFermat quotient.
( U" U; y, o: m0 wFermat and primes of the form x2 + y2. $ D/ }2 \2 a, V1 n! w, r) c
Fermat’s conjecture, Fermat numbers, and Fermat primes.
$ R7 }9 t9 h6 ]" lFermat factorization, from F5 to F30. % `5 y9 `3 n$ V0 A* ~/ _% _6 _( `
Generalized Fermat numbers. , H* y" p# T8 n
Fermat’s Last Theorem. + h: N( k3 n' ~9 M( D$ q
the first case of Fermat’s Last Theorem. 5 g7 r- X8 j+ f, N
Wall-Sun-Sun primes. ; h7 ~. U Z) O
Fermat-Catalan equation and conjecture. ( o, D& N. m( g2 E* W+ M( r: l; s1 H
Fibonacci numbers.
2 j$ z- t& q6 g9 G% s$ ]) odivisibility properties. # h( Q- [$ c3 F. @# X
Fibonacci curiosities.
: M1 C3 n5 s6 O4 Y. \8 _5 ~édouard Lucas and the Fibonacci numbers. & C1 r9 J& \; [
Fibonacci composite sequences. 8 v$ U( u6 `# W3 `
formulae for primes.
3 [6 f# ^+ y& z j% YFortunate numbers and Fortune’s conjecture. , ?3 i+ ~: P$ V& }, c! i& T% z
gaps between primes and composite runs. $ N% |5 [" a$ F* {2 ~+ C
Gauss, Johann Carl Friedrich (1777–1855). 9 r! E! o2 A, L }7 L
Gauss and the distribution of primes. 3 ]5 v7 R+ x5 |
Gaussian primes.
! g; j% P! o7 z. ]0 gGauss’s circle problem.
" K6 b; W1 Q2 I" WGilbreath’s conjecture.
6 X2 t2 a! d, ZGIMPS—Great Internet Mersenne Prime Search. ! d8 i- Z4 p Z3 x, r( x5 o; ?
Giuga’s conjecture.
 a2 S, X- e3 N- H6 i7 d3 XGiuga numbers.
/ P) w. z- `* D& HGoldbach’s conjecture. 4 [# N) D9 h9 q7 v4 m
good primes.
* T- t; j- r5 Y5 w& XGrimm’s problem.
3 u0 A' c& `5 G2 } b6 D NHardy, G. H. (1877–1947).
2 a6 s2 Y% T3 Y8 c& K! FHardy-Littlewood conjectures. 7 l6 W2 N" C8 {* K5 I" F9 g
heuristic reasoning. : i$ N1 O+ K+ r6 Q) d2 I$ k( s# c
a heuristic argument by George Pólya.
) W4 |: r/ }8 ]% @4 |5 h- QHilbert’s 23 problems. 2 M* I( k& f4 ? s
home prime. ' d7 k0 Z0 c& I5 @; ` D
hypothesis H.
# Y3 O x. K% c1 m6 @illegal prime. 0 H! Q8 {* _$ e' ^
inconsummate number. 2 L0 C1 K/ _9 G5 u l
induction. 0 M4 B1 W/ k% e j6 P9 R( P" q# I! X
jumping champion. % \& X% b9 l, o' s' M
k-tuples conjecture, prime. & X; s+ z$ c# C$ n. N
knots, prime and composite. / B$ V; b5 B6 n
Landau, Edmund (1877–1938).
# |& E" z8 V4 Bleft-truncatable prime.
; N$ B+ E7 G9 S* XLegendre, A. M. (1752–1833). + K4 N& I5 q# n& O/ t6 |9 @: l1 U
Lehmer, Derrick Norman (1867–1938).
% ?$ z$ [* u- H" @. ?3 t3 T8 D; g3 fLehmer, Derrick Henry (1905–1991).
9 M* `4 y+ W: ZLinnik’s constant.
- h' V8 g+ ~! V, f& _4 ]7 VLiouville, Joseph (1809–1882). / @- x" C+ c1 B. G
Littlewood’s theorem.
4 E: A) S/ h' v2 V$ X" Cthe prime numbers race. % Z0 D' E' l+ ~ q1 u6 x$ z
Lucas, édouard (1842–1891).
5 f0 D1 x" h i0 Gthe Lucas sequence.
! g" r F# _( D: Uprimality testing.
) |; o9 d& I3 \% n/ M1 f" TLucas’s game of calculation. - n! ~2 T7 d) Z
the Lucas-Lehmer test. 2 Y/ P) w8 u' Y
lucky numbers.
6 G1 x! v h) z1 i4 `) z7 T, z8 |the number of lucky numbers and primes. + W8 _- L& H6 O. b( @1 s
“random” primes.
/ Q! I) p$ {" j, z! E+ H+ Hmagic squares. 2 S3 A) ]9 D3 ?& Z( ]' j
Matijasevic and Hilbert’s 10th problem.
% v0 e2 q: ~& hMersenne numbers and Mersenne primes. % ?5 f9 H# U- q9 C( V( R+ ]
Mersenne numbers. - p+ V* e( A- y
hunting for Mersenne primes. ; P2 H- n2 ]3 t8 Q* _1 l B
the coming of electronic computers. . g. S& n8 x+ D5 X7 T2 @4 U! [
Mersenne prime conjectures. 5 R6 o* y1 U, T6 R0 q+ O$ q! m1 P
the New Mersenne conjecture. ) P0 q l6 h' L5 b! R, C
how many Mersenne primes?
* M' \) L- ~! s+ L9 E0 N) AEberhart’s conjecture.
# L) M* Z: Z+ f, _2 j3 Bfactors of Mersenne numbers. 0 P2 r4 k7 Y6 m2 J2 Q; M' F; M0 V
Lucas-Lehmer test for Mersenne primes. * n$ l; q: s4 O8 B$ Q6 S0 U- m
Mertens constant. 1 b' R0 n9 H: I' k4 K
Mertens theorem. 8 U" T8 t; y* s( k1 H) P% w
Mills’ theorem. 6 @' e4 h+ {/ i. o- k( _
Wright’s theorem.
) J6 q: ]9 T' rmixed bag. . E# c9 y, Y6 c& O: w
multiplication, fast.
( {: k! v ^! s5 e( sNiven numbers. w7 \9 A$ D5 u3 d7 H( Q& F
odd numbers as p + 2a2.
( [4 |) y) g1 v, c( ^1 H' c8 wOpperman’s conjecture.
# ]3 B+ \ Q, X3 a [4 Y! l4 epalindromic primes.
% N' x8 k& J p& j/ \$ A/ E, Cpandigital primes. / i0 L" h) t! H
Pascal’s ** and the binomial coefficients.
* y1 m5 |9 T- G2 K- s% x2 HPascal’s ** and Sierpinski’s gasket.
6 d$ ]+ X- ], ]/ o9 JPascal ** curiosities. # T/ |( Y6 E$ J) d- h
patents on prime numbers. $ R0 Z' ^' h" V& W, m$ |+ `
Pépin’s test for Fermat numbers.
! U& ] [) g* u3 Y+ O; v7 V/ Dperfect numbers. / ^$ Z: n+ e9 G* p
odd perfect numbers. " t) h/ M* p% o
perfect, multiply.
, h& r, ^+ x w8 ]' dpermutable primes.
; e, v. r8 x3 c% I# d4 [- _- cπ, primes in the decimal expansion of.
2 Z5 g$ }* r' ^$ J4 Q' wPocklington’s theorem.
& V0 T8 V# z# K* RPolignac’s conjectures.
# Q5 b6 Z% F9 _Polignac or obstinate numbers. , k7 B/ ~0 [" f2 n7 |/ O
powerful numbers.
9 H3 y7 ^+ e; N* H4 K bprimality testing.
+ a4 M* I: J: @, Y% P- yprobabilistic methods. $ t# }: }& A6 |2 b& k
prime number graph. & b3 N, v# H0 A8 k
prime number theorem and the prime counting function.
7 I" {) d) B4 C& Hhistory.
4 o! g9 x5 t+ l+ b. p% ~1 @4 W4 Pelementary proof.
' L( \4 f/ v4 B9 {5 n- crecord calculations. 0 L0 \" s$ q3 N/ t* w
estimating p(n).
: R# Y4 i5 Q( ?* c' R# o. a) ycalculating p(n). 8 ?9 y; x- O" _
a curiosity.
 C K$ H' d7 w7 }. v# ^3 P2 dprime pretender. + T: A7 g3 m" D8 d+ g- _8 u
primitive prime factor.
9 M1 [4 I% V, N+ V8 `8 E( G9 yprimitive roots. ( H2 Q$ T% A9 ~" c
Artin’s conjecture.
8 r: M- x% H; |# S; r- La curiosity.
* c& @: y: b; I6 B: S ?primordial. . h7 H4 V8 D& u" J. r7 s1 O5 j
primorial primes.
" n; n. {; d1 M; B- ?8 XProth’s theorem. 8 [1 y, w6 {( i3 k- g
pseudoperfect numbers.
, a; g- _8 O. n9 ^pseudoprimes.
, z4 w. i4 L0 E9 bbases and pseudoprimes. F4 K1 i }) Z" Z C* _ b
pseudoprimes, strong. 0 i6 H" r' a: ~7 U5 @
public key encryption.
8 E: ^" s" B8 W: P$ p8 ]5 zpyramid, prime.
4 R h# }. F/ b* d7 b& Z1 KPythagorean **s, prime. 8 c' d3 A3 i9 Z' _, s
quadratic residues. + q# t, @+ Y- ?
residual curiosities.
 Z4 n) s; d9 Y) |polynomial congruences. 8 H0 ~0 x8 W0 U# ?7 z. _% f* o
quadratic reciprocity, law of. 1 K; K {/ X! Q% X
Euler’s criterion.
5 K: `5 J! t) Z8 h% G# E3 }0 _* WRamanujan, Srinivasa (1887–1920).
 C0 r( E# p1 T R# Bhighly composite numbers.
' j2 c5 Q6 Z; E/ a" u- y# u/ u" x) Krandomness, of primes.
' D' E1 l' s4 s# Q, Z2 Y) KVon Sternach and a prime random walk. 4 Z. P6 R9 L3 K/ D9 ^$ P0 ^; c
record primes.
3 \& N1 Q* C$ @; I. Hsome records.
" n0 H7 l3 J7 W, Jrepunits, prime. * J4 O" }) m, W
Rhonda numbers. + }! z# E% s+ ]0 O* G
Riemann hypothesis.
2 i9 B0 U7 O- C5 H6 O( o& Q! uthe Farey sequence and the Riemann hypothesis. & h. K$ J) b+ c2 S# G
the Riemann hypothesis and σ(n), the sum of divisors function.
/ j* I6 N0 h7 s" _7 r* psquarefree and blue and red numbers. $ H3 w5 m9 j% E. m
the Mertens conjecture. ) }: o7 G c2 K8 U9 k2 J
Riemann hypothesis curiosities.
5 q) O$ m6 `8 ^ B: nRiesel number. / I% w1 a( z8 S; T
right-truncatable prime. 9 b+ \7 r# G0 x$ ]* Z; i
RSA algorithm.
/ t `1 u& z3 S, v j3 T0 E/ s7 {Martin Gardner’s challenge. 4 E1 i1 ]8 G ~9 Q5 a( C
RSA Factoring Challenge, the New.
. s7 i' d" A4 I7 n$ i: sRuth-Aaron numbers. - |3 V) P6 b" n" N, i
Scherk’s conjecture. " Z5 b& \7 O( I/ `8 o/ g
semi-primes.
; m7 m. D8 @: w5 H$ M) ^; Y**y primes. 4 \, l" n7 h7 f7 p
Shank’s conjecture.
1 e% K% s8 z1 r, gSiamese primes. 0 j# ^. Q5 z* z* @- T3 E' k7 X
Sierpinski numbers.
% U8 M2 H/ R/ H+ H: Q) uSierpinski strings.
; Y2 a3 a+ z( @& mSierpinski’s quadratic.
# e0 \& d$ G- B4 kSierpinski’s φ(n) conjecture. # B% i" @* K+ i& O. N7 w
Sloane’s On-Line Encyclopedia of Integer Sequences. 3 `* s' }% w# s7 J0 g ?& d" {
Smith numbers. & }2 W l3 {$ N
Smith brothers.
' {) k0 W$ y" z" Psmooth numbers. 4 }. i" p/ d/ t8 g
Sophie Germain primes.
# h% @( ^/ p8 `. v; isafe primes. 3 c4 \$ R |9 |, G
squarefree numbers. , A0 t, X: k' ]) {
Stern prime.
8 L( x2 Q. T, h# _" `- Y$ g$ j9 Kstrong law of small numbers.
" n* N4 m) N& N- f1 P* j8 ^triangular numbers. % }6 ^% X" q# ?2 |! [: ~4 R
trivia.
7 K% A) Y# b0 j) Q" a& N/ Btwin primes. ' [ `& T' R% k/ p
twin curiosities.
* P; e8 Z& w6 I1 BUlam spiral. 9 f( b% L! K1 _$ @# y
unitary divisors.
: _8 K% j9 m" }6 P! [unitary perfect.
" i# \" w4 }/ `% V5 muntouchable numbers. , h$ N; g0 ]: E% r: w' U* W
weird numbers. + Q4 Y" z& N; h' F5 r( H4 {- U
Wieferich primes.
5 [8 R/ ~4 ?: x$ h# p' GWilson’s theorem. 4 n/ ?& t: `! h" N. ?
twin primes.
8 o3 U- j4 ]/ l* {! NWilson primes.
4 q( B2 X) @4 I8 |# zWolstenholme’s numbers, and theorems.
6 D n0 a( y# V2 ~( ^6 lmore factors of Wolstenholme numbers.
+ m7 P0 a5 L9 a; XWoodall primes. - D. K; H( O; o8 X+ V( H
zeta mysteries: the quantum connection.