素数.rar
(1.44 MB, 下载次数: 12)
Entries A to Z.
abc conjecture. 7 J' U2 Z" d. T; U
abundant number.
AKS algorithm for primality testing.
aliquot sequences (sociable chains). : O5 N; d% S% S" \
almost-primes.
amicable numbers. , ^( d3 L4 O1 J
amicable curiosities. U: y( [% ]! ?, ^* ^
Andrica’s conjecture.
arithmetic progressions, of primes. b9 q' s& Z* o3 B; E# [& g% p8 m
Aurifeuillian factorization.
average prime. ! \ t4 I1 N5 L( {) E3 ~ \. O
Bang’s theorem. 0 A& B% k7 r0 P6 g4 v# B N, ~
Bateman’s conjecture.
Beal’s conjecture, and prize. ; q5 w7 P. @ j" |5 T4 z
Benford’s law. + ^/ `% s0 ~7 I; I, M6 h3 O
Bernoulli numbers. - H. ]9 H# f& _. y1 z
Bernoulli number curiosities.
Bertrand’s postulate.
Bonse’s inequality. 8 b( t- G$ d) n! [1 o5 i
Brier numbers. ) f* ]$ c* n0 E3 I5 z
Brocard’s conjecture. 8 ]1 A M3 f: v N0 W
Brun’s constant. ! \6 m/ L$ n0 g3 G N+ S
Buss’s function. * F( g7 C8 S% N
Carmichael numbers.
Catalan’s conjecture.
Catalan’s Mersenne conjecture.
Champernowne’s constant. / F* n1 C/ D+ F: T
champion numbers. % t0 z6 P: D! h0 f
Chinese remainder theorem. W# C+ a; f0 E% L
cicadas and prime periods.
circle, prime.
circular prime.
Clay prizes, the. 5 Z4 v' r, [ H8 ?; e
compositorial. G. i3 X9 N2 |
concatenation of primes. " e0 P/ w/ d! q! }
conjectures. ( C- ~4 g- y* I7 e7 v
consecutive integer sequence.
consecutive numbers. ! ~# F9 D2 d0 q, R$ h/ r! G+ E3 j
consecutive primes, sums of. , T/ e1 P& N( ^, t1 b
Conway’s prime-producing machine. ! ~/ H) n( m( R7 u" R3 k1 M
cousin primes. 1 G! L8 N' e4 h% Z9 h
Cullen primes.
Cunningham project. ' A' R' b+ Y4 G
Cunningham chains.
decimals, recurring (periodic). # g; Z% V$ ^' r8 [
the period of 1/13. 7 B: ~4 l0 R. Q* g' [" t
cyclic numbers. 9 {5 W1 g& C5 _8 L6 C4 `$ }
Artin’s conjecture. ! t( d3 i2 J# B" z
the repunit connection.
magic squares. 2 k# }) V1 }( o2 V4 H. {
deficient number.
deletable and truncatable primes.
Demlo numbers.
descriptive primes.
Dickson’s conjecture. " l& g* F4 T3 c" I1 r" c; ^2 b4 m {
digit properties.
Diophantus (c. AD 200; d. 284). . j6 q/ U8 A" ]& }8 u, Z4 V
Dirichlet’s theorem and primes in arithmetic series. ' x; p5 P6 G9 o0 [7 U8 v
primes in polynomials. & b M' k& j% y
distributed computing.
divisibility tests. * o$ ~" J( e, u$ J. u2 e4 {1 ~
divisors (factors).
how many divisors? how big is d(n)?
record number of divisors. 8 h" T/ ?, @# [$ K
curiosities of d(n). 3 Z/ e: V/ A( P! d
divisors and congruences. 7 \1 i1 C( n6 \0 B( ~
the sum of divisors function.
the size of σ(n).
a recursive formula.
divisors and partitions.
curiosities of σ(n).
prime factors.
divisor curiosities. ) V- G; c9 T' L, b5 }
economical numbers. 2 P+ R* R" b) K1 {6 A+ ?1 t
Electronic Frontier Foundation.
elliptic curve primality proving. 0 m( G7 {$ b; f9 u6 f1 L
emirp.
Eratosthenes of Cyrene, the sieve of. + K# h) G6 J" W9 F/ n% V- T8 l
Erd?s, Paul (1913–1996).
his collaborators and Erd?s numbers.
errors. % U# a! {- J2 C: V; y% q
Euclid (c. 330–270 BC).
unique factorization.
&Radic;2 is irrational.
Euclid and the infinity of primes.
consecutive composite numbers.
primes of the form 4n +3. ' X9 v5 e" \4 P S2 q
a recursive sequence.
Euclid and the first perfect number.
Euclidean algorithm.
Euler, Leonhard (1707–1783).
Euler’s convenient numbers.
the Basel problem.
Euler’s constant. $ b- i; y* p9 V. |# O
Euler and the reciprocals of the primes.
Euler’s totient (phi) function. 8 i: r$ O* e) l( S" Q
Carmichael’s totient function conjecture.
curiosities of φ(n). , v+ G6 s7 L% Z: Q$ e/ j% e% X
Euler’s quadratic.
the Lucky Numbers of Euler. ' o. P% @2 F' X( j" w2 H) v8 z
factorial.
factors of factorials.
factorial primes. e; ?; H( D' Q5 C5 U1 {& o( S+ ~5 C" u
factorial sums.
factorials, double, triple . . . .
factorization, methods of.
factors of particular forms.
Fermat’s algorithm. & l5 \+ d! @3 X
Legendre’s method. 0 |9 D+ y8 s. F, x5 I) Q
congruences and factorization.
how difficult is it to factor large numbers?
quantum computation. 9 |; d. H% a7 E H4 Z
Feit-Thompson conjecture.
Fermat, Pierre de (1607–1665). 0 J' o4 K3 Y: f9 }7 H5 b2 i
Fermat’s Little Theorem.
Fermat quotient.
Fermat and primes of the form x<sup>2</sup> + y<sup>2</sup>.
Fermat’s conjecture, Fermat numbers, and Fermat primes. 2 g4 t* E5 O5 S
Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>.
Generalized Fermat numbers. W9 @8 b& u! V, D8 c
Fermat’s Last Theorem. 6 {, x$ ?6 a# R: L
the first case of Fermat’s Last Theorem. / F5 ?8 |0 J7 l1 D% b
Wall-Sun-Sun primes.
Fermat-Catalan equation and conjecture. 0 n4 h0 U: `) D" E
Fibonacci numbers.
divisibility properties. , p- x) m8 p+ F0 h- ~
Fibonacci curiosities. $ I! {2 V2 `! r8 R
édouard Lucas and the Fibonacci numbers.
Fibonacci composite sequences. 1 C% B, P& _, k; O! v. _* d5 R+ R
formulae for primes. % X9 q1 X c; \0 {
Fortunate numbers and Fortune’s conjecture. " n' k! J$ e4 Z1 Z9 _6 f: D4 ~( H6 [
gaps between primes and composite runs.
Gauss, Johann Carl Friedrich (1777–1855). 5 x" U8 J6 D+ m
Gauss and the distribution of primes.
Gaussian primes.
Gauss’s circle problem.
Gilbreath’s conjecture.
GIMPS—Great Internet Mersenne Prime Search.
Giuga’s conjecture.
Giuga numbers. - J/ H* }! a* c8 t' R
Goldbach’s conjecture. 7 R1 _: o+ f6 @( P! i
good primes.
Grimm’s problem. {9 @- S5 L. {; t! ]1 O
Hardy, G. H. (1877–1947). ) _! Y& F G2 J: t E/ v9 W; B
Hardy-Littlewood conjectures. 1 K2 j+ s1 ~3 i
heuristic reasoning. : B$ h t8 q& J& M3 O3 h" R
a heuristic argument by George Pólya. . Y0 V) Q) E* H
Hilbert’s 23 problems.
home prime. 6 m! N" U2 ^6 ?" l7 y( X+ \6 r
hypothesis H.
illegal prime.
inconsummate number.
induction. 0 j' S; A* x/ l0 _& U% P: k* b$ ~
jumping champion.
k-tuples conjecture, prime.
knots, prime and composite.
Landau, Edmund (1877–1938). 1 i( [' c+ Q+ g9 `. a" ]
left-truncatable prime. / s3 y+ ^- s3 u9 f* e/ c
Legendre, A. M. (1752–1833). # K7 B+ g8 u2 d& k, @
Lehmer, Derrick Norman (1867–1938).
Lehmer, Derrick Henry (1905–1991).
Linnik’s constant.
Liouville, Joseph (1809–1882). ! K" ~6 k" {9 K& A% J) ^; ^; E J
Littlewood’s theorem.
the prime numbers race.
Lucas, édouard (1842–1891).
the Lucas sequence.
primality testing.
Lucas’s game of calculation. , @: B. w% f' K! o- k! r
the Lucas-Lehmer test.
lucky numbers. . o1 ^. m# ^9 N1 a* v
the number of lucky numbers and primes. ' X+ i' J- b& n- n* G
“random” primes.
magic squares.
Matijasevic and Hilbert’s 10th problem. : I0 m8 V/ k# v1 K1 g. S0 q5 h
Mersenne numbers and Mersenne primes. @ h2 T H# F, e% n
Mersenne numbers.
hunting for Mersenne primes.
the coming of electronic computers.
Mersenne prime conjectures. $ g* a) F# i' g6 [
the New Mersenne conjecture. % V5 K! P& i4 A- `: _6 o; r& v
how many Mersenne primes?
Eberhart’s conjecture.
factors of Mersenne numbers.
Lucas-Lehmer test for Mersenne primes.
Mertens constant.
Mertens theorem. + n( h: ^- b9 Q3 u1 r/ _0 e
Mills’ theorem. . ]7 c/ V8 b( Q( x
Wright’s theorem. 9 y( t9 Y7 u, I( W- i9 L
mixed bag. / }& c1 X9 I( ~8 k! B( O/ |
multiplication, fast. - U, y( A, A+ z3 y6 S! t% f0 Z
Niven numbers. $ Y& S: d* K+ O: x# {. `! ^% E7 I( z
odd numbers as p + 2a<sup>2</sup>. u( g8 O& \8 z7 V
Opperman’s conjecture. # Q! O- E9 M+ h$ D( d4 R3 b
palindromic primes. / ]) V8 s& [) h' R$ M N$ v: S
pandigital primes.
Pascal’s ** and the binomial coefficients. 8 s E+ U: t" |! ?* I! W
Pascal’s ** and Sierpinski’s gasket. * v1 @' v! J9 F, b4 h- ^' L. {
Pascal ** curiosities. 2 h! _) l2 w9 ^0 W8 Y
patents on prime numbers.
Pépin’s test for Fermat numbers.
perfect numbers. 2 ~& {7 n: }& `- |
odd perfect numbers.
perfect, multiply.
permutable primes.
π, primes in the decimal expansion of.
Pocklington’s theorem.
Polignac’s conjectures. 5 p4 @3 r8 R* f& ?/ ?" r. l3 w+ D
Polignac or obstinate numbers. ' d5 ^2 F+ d9 ?( P2 x! x- o, c0 F
powerful numbers.
primality testing.
probabilistic methods. 4 N5 L5 q" |' y/ u
prime number graph.
prime number theorem and the prime counting function. / J4 E3 T+ W% H# v
history.
elementary proof. 3 j+ }8 }5 V4 l. G$ e- F- K
record calculations.
estimating p(n).
calculating p(n). : ]3 }' U# w8 k5 Y3 X* P' f8 u
a curiosity. " {9 G0 d6 P# q: `6 ]
prime pretender.
primitive prime factor.
primitive roots.
Artin’s conjecture. $ X$ Y8 n7 h. }8 _) r1 E9 f
a curiosity. , x- `+ L( `& p
primordial. z7 s9 r) P9 X1 N6 [! J
primorial primes. * H3 ~6 S3 A$ j& K8 _; a
Proth’s theorem. 2 y, s* P1 I2 Z8 Y& S
pseudoperfect numbers. / |% L; w2 |( k! Y L
pseudoprimes.
bases and pseudoprimes.
pseudoprimes, strong. 7 s9 D1 n) m; P2 o; p& `$ {
public key encryption.
pyramid, prime.
Pythagorean **s, prime.
quadratic residues.
residual curiosities.
polynomial congruences.
quadratic reciprocity, law of. . s% u% t6 ~- _5 f4 p0 |) \/ o0 Q* Q
Euler’s criterion. * C- K2 b4 T0 ^0 n6 c
Ramanujan, Srinivasa (1887–1920). 7 B$ E6 X1 {9 S3 R. i
highly composite numbers. 9 `- }: [+ t# {" Z; K/ B3 C/ {
randomness, of primes. + T2 ~' U& x0 X
Von Sternach and a prime random walk. # z" U7 q. J7 G% D) v
record primes. 1 K' R/ N P+ z" U7 W2 E. a) x
some records.
repunits, prime. : l2 b% l" |3 C) O/ e1 y
Rhonda numbers.
Riemann hypothesis.
the Farey sequence and the Riemann hypothesis.
the Riemann hypothesis and σ(n), the sum of divisors function. 8 h, Q3 I0 I4 p
squarefree and blue and red numbers.
the Mertens conjecture.
Riemann hypothesis curiosities. ; e1 B0 X1 @2 E
Riesel number.
right-truncatable prime. + M. r0 {- v8 z8 ^
RSA algorithm.
Martin Gardner’s challenge. 2 w3 e: l, F/ R- V1 Z. V0 p
RSA Factoring Challenge, the New. # s# b. s/ Y$ p& u" r% ^
Ruth-Aaron numbers.
Scherk’s conjecture. ( {8 ~8 g' x& l; k- P# O# k. x4 j
semi-primes. 5 [, t: ?2 Q1 H5 c1 ?0 ]# D& d# ~
**y primes. }* ]! u" N7 K4 P2 O. X) w
Shank’s conjecture. " _' O) I5 D' u$ _; I3 J* w! u
Siamese primes. * y) p/ S! ^ R+ j
Sierpinski numbers.
Sierpinski strings. ; D* T+ A1 H- B
Sierpinski’s quadratic.
Sierpinski’s φ(n) conjecture. 4 b0 w. g* l& ^7 C7 N: h: h$ G
Sloane’s On-Line Encyclopedia of Integer Sequences. 6 H2 f! @. p5 p1 h$ o) `
Smith numbers.
Smith brothers. ; `+ r6 d# U! e9 v5 R+ a
smooth numbers. : w7 R1 W6 r; W5 \$ P' v; @! a
Sophie Germain primes.
safe primes. ( H: C, V* F4 @1 j* s9 h, i! B% J. ?" `
squarefree numbers.
Stern prime. * e( g" q& b% D" e- Q2 _$ I( ?, W
strong law of small numbers.
triangular numbers.
trivia. ) ]+ G; e( \/ e P# Y
twin primes. : X1 h$ K9 X: S% L: n
twin curiosities. . }+ y; i; M" `* x, j0 g
Ulam spiral. , Q& ~) a3 e3 j1 c, t. L6 v
unitary divisors.
unitary perfect. ) t* m& n1 x. ]. z; F! X% H2 R
untouchable numbers. ( d: j1 z! c. }( s. |% `6 `
weird numbers. : v q5 `% g/ U9 n k# Q+ K
Wieferich primes.
Wilson’s theorem.
twin primes.
Wilson primes.
Wolstenholme’s numbers, and theorems.
more factors of Wolstenholme numbers. + `% a7 L& F& U. q' B' i) y
Woodall primes. . D! |; o5 C+ y3 ^/ L
zeta mysteries: the quantum connection.
素数.rar
(1.44 MB, 下载次数: 12)
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