Entries A to Z.0 l, F" {' q3 x) y% `( x
abc conjecture.
abundant number.
AKS algorithm for primality testing. & F5 Q0 Z$ D! A
aliquot sequences (sociable chains).
almost-primes. & @$ b8 P$ M" o4 s+ z O
amicable numbers. " _0 n) e* I" k4 a% c$ r; b
amicable curiosities. ; m/ x& Z" Q4 F: C7 F; V
Andrica’s conjecture. : }7 ~7 r6 r$ C8 g: D x6 H# q+ \
arithmetic progressions, of primes. - T1 ?5 x( I# w
Aurifeuillian factorization.
average prime.
Bang’s theorem.
Bateman’s conjecture. / }. P& \: G5 B B) C2 d9 A* z; Q
Beal’s conjecture, and prize.
Benford’s law.
Bernoulli numbers.
Bernoulli number curiosities. / _6 s6 r5 w# }3 P% w' [% T
Bertrand’s postulate. ' \) q+ G) }. z+ k
Bonse’s inequality.
Brier numbers. % y. \$ R: Q$ y" R7 D
Brocard’s conjecture. 9 g- A4 }$ F5 A4 L
Brun’s constant. + |; }# J7 ~. P" M- L4 L+ j
Buss’s function.
Carmichael numbers. - e y) }" x% e- s6 X6 C
Catalan’s conjecture.
Catalan’s Mersenne conjecture.
Champernowne’s constant. 1 u7 T. ~9 S7 N6 z8 {2 w1 ?1 R9 w @8 c
champion numbers. 4 _5 w# l$ K7 X# P x7 ~
Chinese remainder theorem. ( p) x1 t' g( m8 S8 H
cicadas and prime periods. ; a* E/ P, E# _
circle, prime. 7 K% b) K8 g" k6 I; q, X4 }: h
circular prime. 2 H- f {* V$ p3 U
Clay prizes, the. ' Y' S# |1 e4 ]2 U7 Z7 U, \) L
compositorial. ' Y; [7 I% F, m( K' C4 G% W0 n
concatenation of primes.
conjectures. " Z( f( j9 K% C; L, T
consecutive integer sequence.
consecutive numbers. & h" s. A' @ |# q
consecutive primes, sums of. & a! t. H9 Q: H' u+ p) [- W) d2 k
Conway’s prime-producing machine. 4 ^( ?( B4 I( \" q7 D+ N5 U6 T G" V
cousin primes. 6 C. p: y2 b# l$ t% \4 u& t! q" e
Cullen primes. q; u" J% Z3 W3 V9 O8 ]3 F0 H
Cunningham project. . D. A: d5 B7 Y! {$ {, Y4 p a
Cunningham chains.
decimals, recurring (periodic).
the period of 1/13. 6 q1 c) [7 R* k' {4 m0 Q4 `2 i
cyclic numbers.
Artin’s conjecture.
the repunit connection. 5 I; w3 V9 \. T7 f) T
magic squares.
deficient number. 9 ^5 w3 T1 R! C! }6 Z e
deletable and truncatable primes. - t+ a% k; I0 R
Demlo numbers. ! Q( q# t% P& g2 Q6 `4 L
descriptive primes.
Dickson’s conjecture.
digit properties.
Diophantus (c. AD 200; d. 284).
Dirichlet’s theorem and primes in arithmetic series.
primes in polynomials.
distributed computing. & o" q" i( G! d& {( z
divisibility tests. ' d( M8 `/ c) |2 R5 Z' Z' b/ ]
divisors (factors).
how many divisors? how big is d(n)?
record number of divisors.
curiosities of d(n).
divisors and congruences. 4 @3 u- C' D9 t3 [+ ?8 o' j, Z! M
the sum of divisors function.
the size of σ(n). 4 H: L4 ~+ i; o4 R$ T6 {7 W0 P
a recursive formula.
divisors and partitions. 5 R1 `) B1 l3 G& w0 M
curiosities of σ(n).
prime factors.
divisor curiosities.
economical numbers.
Electronic Frontier Foundation. & w7 q" L; F" K6 O* U$ F, q
elliptic curve primality proving. 5 M- ]9 y2 Y# c0 H, j6 \
emirp. ' k1 c, g' C- Z* L
Eratosthenes of Cyrene, the sieve of.
Erd?s, Paul (1913–1996).
his collaborators and Erd?s numbers.
errors.
Euclid (c. 330–270 BC).
unique factorization. ?7 X* @5 J9 k+ D2 I, J* f
&Radic;2 is irrational. 2 z a: g8 e' Z: M/ o9 I& J
Euclid and the infinity of primes.
consecutive composite numbers.
primes of the form 4n +3. 4 I* ?& m4 Z Z9 V( X8 M
a recursive sequence.
Euclid and the first perfect number. 0 w. x6 w* X! W' W0 v1 b( [! E
Euclidean algorithm.
Euler, Leonhard (1707–1783). ! E7 n6 R N6 E7 C; o
Euler’s convenient numbers.
the Basel problem.
Euler’s constant.
Euler and the reciprocals of the primes. , q! a% f( m$ k0 G4 x8 u
Euler’s totient (phi) function. % u+ E1 \3 e. l L6 X3 B& `6 \% I) [
Carmichael’s totient function conjecture.
curiosities of φ(n).
Euler’s quadratic.
the Lucky Numbers of Euler.
factorial. / `& b0 W/ _+ L; r1 r, o2 \8 [
factors of factorials.
factorial primes.
factorial sums.
factorials, double, triple . . . .
factorization, methods of. ' m! T* w4 s! R/ Q$ f1 M, R7 F/ V
factors of particular forms. ' a+ \1 L9 J$ l8 U2 d i3 p4 b
Fermat’s algorithm. 8 F4 {! {7 n1 \7 h5 P/ u
Legendre’s method. : T; w# `, R. M E3 S; B; C
congruences and factorization. 3 p. ~8 v% {" S2 `' S
how difficult is it to factor large numbers? 3 {. g7 ` m1 l/ l2 C. X
quantum computation. J" h$ Q% s0 }- ]
Feit-Thompson conjecture. 0 o7 `2 A( \& a9 V
Fermat, Pierre de (1607–1665).
Fermat’s Little Theorem. - C) p0 l* A* M0 t& u3 @2 u4 w; R
Fermat quotient.
Fermat and primes of the form x<sup>2</sup> + y<sup>2</sup>. ( Z. t2 K$ V* B" d$ Y. _" z( Q
Fermat’s conjecture, Fermat numbers, and Fermat primes. . G# J, L/ m& N- G) _! q
Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>. ' x% b. T6 t; @& V% j! C
Generalized Fermat numbers. 9 T2 W: {; R0 Y+ `
Fermat’s Last Theorem. . u- G2 x$ m0 j
the first case of Fermat’s Last Theorem. ) ?& R- H/ }( e/ O# U, h
Wall-Sun-Sun primes.
Fermat-Catalan equation and conjecture. Q6 n) j2 i4 \9 f: c3 F s' P9 h
Fibonacci numbers.
divisibility properties.
Fibonacci curiosities. 9 O# a4 U% D# Z7 @3 `- k* h9 X* b
édouard Lucas and the Fibonacci numbers. 9 K- `1 Y) l5 N: x
Fibonacci composite sequences.
formulae for primes. 2 j/ U5 k2 O+ ]( w$ e, T$ A { _9 g
Fortunate numbers and Fortune’s conjecture.
gaps between primes and composite runs.
Gauss, Johann Carl Friedrich (1777–1855). 9 ?* u2 q& Y6 \
Gauss and the distribution of primes.
Gaussian primes. 8 g+ i& ^. \, t+ f2 c. o+ P; c0 q9 N$ ]
Gauss’s circle problem. - C2 h# x1 x) ^# v
Gilbreath’s conjecture.
GIMPS—Great Internet Mersenne Prime Search.
Giuga’s conjecture. ' D+ H$ L2 n' l; F" o# ?
Giuga numbers.
Goldbach’s conjecture.
good primes. 8 l' u8 n) d+ Y9 O- _3 P
Grimm’s problem. ( t1 F+ K I3 i! |/ p w u
Hardy, G. H. (1877–1947). " l0 l5 m& |/ ^9 \6 v- ^
Hardy-Littlewood conjectures. ! F" u, q8 m+ Q" ?
heuristic reasoning. " P, } Q0 J" J
a heuristic argument by George Pólya.
Hilbert’s 23 problems.
home prime.
hypothesis H.
illegal prime. : e$ Q* W3 C e: ^
inconsummate number.
induction. " n; j6 x' _( c: ^) g3 l( F
jumping champion.
k-tuples conjecture, prime.
knots, prime and composite. ) E) ?; o& ?5 u+ o0 G, Z
Landau, Edmund (1877–1938). 6 o9 p: V7 P" o
left-truncatable prime. ! o0 F& g0 O' e. p' y4 O
Legendre, A. M. (1752–1833).
Lehmer, Derrick Norman (1867–1938). 9 Q& H& u/ f! v
Lehmer, Derrick Henry (1905–1991). ) l$ f. [" Z- d" X
Linnik’s constant. ) I6 f0 u) R; Z! Q% F0 K
Liouville, Joseph (1809–1882). 1 Z" k) a7 Y# t0 |8 n
Littlewood’s theorem.
the prime numbers race. 0 Q$ W4 X% r: b
Lucas, édouard (1842–1891).
the Lucas sequence. ' z& H, y* k! `: i! l; s6 `3 o
primality testing.
Lucas’s game of calculation. 2 l/ V# Y6 f8 B: p) @" X* u
the Lucas-Lehmer test.
lucky numbers.
the number of lucky numbers and primes. ' E% N0 g& i* e# j; i" z% w
“random” primes.
magic squares. % Q2 x/ {# o( E" g
Matijasevic and Hilbert’s 10th problem.
Mersenne numbers and Mersenne primes.
Mersenne numbers.
hunting for Mersenne primes. ' s9 A. s7 s& K# H) Q
the coming of electronic computers.
Mersenne prime conjectures.
the New Mersenne conjecture. ' ?, D9 Y: h, K7 i1 b8 m
how many Mersenne primes?
Eberhart’s conjecture.
factors of Mersenne numbers. * {! G+ i9 M1 p% T4 G$ B
Lucas-Lehmer test for Mersenne primes.
Mertens constant.
Mertens theorem.
Mills’ theorem.
Wright’s theorem. $ y" ?4 ?% ?% i1 \
mixed bag. 1 O% W$ A; D3 @4 X, g3 {
multiplication, fast. 9 _/ x* F2 f) _. a) Q0 ?; b
Niven numbers. ' F f0 y& u* I% B
odd numbers as p + 2a<sup>2</sup>. + Q8 s5 }% l6 h! |: V$ q. f
Opperman’s conjecture.
palindromic primes. 0 i# r% ?. f& i0 [8 _7 q1 @
pandigital primes. ' C9 a" T5 P7 ~) f. W0 K0 ]5 L3 W
Pascal’s ** and the binomial coefficients.
Pascal’s ** and Sierpinski’s gasket. 9 j8 F7 B2 T1 Z5 X
Pascal ** curiosities. ! p0 s: U3 H5 \- ~ x
patents on prime numbers.
Pépin’s test for Fermat numbers. 8 f4 M: I$ d$ a! M+ a3 O
perfect numbers. * N* X* T: u6 q+ M
odd perfect numbers.
perfect, multiply.
permutable primes.
π, primes in the decimal expansion of. ' e! C6 Z$ A$ `9 B$ z! {0 B
Pocklington’s theorem. 7 c! W* F/ ]: l, T7 E
Polignac’s conjectures.
Polignac or obstinate numbers. 3 P4 e* f9 m9 H! e
powerful numbers.
primality testing. 1 s( X3 i! j3 l) S: Y; L
probabilistic methods.
prime number graph. # f- f& M$ R0 U7 G
prime number theorem and the prime counting function.
history.
elementary proof.
record calculations.
estimating p(n). - @( C; l m" q L% ^, X
calculating p(n). ' I2 `$ g5 u2 n6 S* S; Q5 `; d/ q
a curiosity. ; I' w' o" Q: t+ R, H
prime pretender. , t$ [: U; c: c; ]8 g# U0 c5 h/ T
primitive prime factor.
primitive roots. 0 ]! q- S" A3 Z2 W5 h$ B& a5 e
Artin’s conjecture. e. S( m# {# t
a curiosity. / G7 V, e5 n5 J, Q
primordial. 3 X. T y+ S2 d; t" Z, |- O
primorial primes. 6 U5 m; D& V E
Proth’s theorem. 3 o+ y, {' q) X1 N
pseudoperfect numbers.
pseudoprimes.
bases and pseudoprimes. 5 L/ q: @7 n( @% J0 J( U
pseudoprimes, strong. 4 ?! f: H7 A# S" C6 k
public key encryption.
pyramid, prime. ; N9 O( c8 {& T
Pythagorean **s, prime.
quadratic residues.
residual curiosities. 2 v0 ^. X# t7 X$ b4 |
polynomial congruences.
quadratic reciprocity, law of.
Euler’s criterion.
Ramanujan, Srinivasa (1887–1920).
highly composite numbers.
randomness, of primes.
Von Sternach and a prime random walk. * G5 G# @; d9 a& O
record primes.
some records. 4 {! h: {( x: x d6 G; ?
repunits, prime.
Rhonda numbers.
Riemann hypothesis. 4 A* n- C) A# H4 N( q2 u2 |9 Q' A
the Farey sequence and the Riemann hypothesis.
the Riemann hypothesis and σ(n), the sum of divisors function. + n# S$ ?& G# j. r- ^. W% j" t
squarefree and blue and red numbers. 6 y/ Q1 A; | @* ^5 P+ v4 w" j
the Mertens conjecture. ! k$ S9 J* v+ r
Riemann hypothesis curiosities.
Riesel number.
right-truncatable prime. # n$ K; x1 D4 r# |; u4 M) p
RSA algorithm.
Martin Gardner’s challenge.
RSA Factoring Challenge, the New.
Ruth-Aaron numbers. 4 W* ]7 G" Q* A! p
Scherk’s conjecture. : q5 `. Y. w+ n1 O
semi-primes. U7 W4 ^, Q2 c7 T
**y primes. % W* L! d6 R& C2 Q
Shank’s conjecture.
Siamese primes. 9 O9 v$ c" V% b# H7 a
Sierpinski numbers.
Sierpinski strings. P ~5 }2 L% h
Sierpinski’s quadratic. 3 ~# l9 c1 Q0 C! S8 i5 e
Sierpinski’s φ(n) conjecture.
Sloane’s On-Line Encyclopedia of Integer Sequences.
Smith numbers. + j" [( s3 |7 x( A9 H" Y' t
Smith brothers.
smooth numbers. 8 t" I/ _, f; d( j9 b( t2 m
Sophie Germain primes. ' N5 j" C3 u% {2 ]! U; f
safe primes.
squarefree numbers.
Stern prime. 1 u+ P! f- _5 R! g: v
strong law of small numbers. ; p+ Z4 F# \; ]( J0 Z. H" z: G
triangular numbers.
trivia. * q `; ^9 ~; Z2 r- J2 F3 r$ ]
twin primes. 7 M8 r4 m5 l1 w! H9 ?
twin curiosities. 9 k+ U- \8 C' q
Ulam spiral. 4 v2 @/ A% j) M5 Q+ t
unitary divisors. . u9 q$ k# j! J H3 e4 k
unitary perfect.
untouchable numbers.
weird numbers. ) i/ T2 e' m. l D$ F; J- O6 |
Wieferich primes. - n N* K5 p& B: D4 D! h" U
Wilson’s theorem. 6 G, ^4 o& ?1 Y7 A) N
twin primes. ) C, t9 ] ~9 ], ?4 f
Wilson primes.
Wolstenholme’s numbers, and theorems.
more factors of Wolstenholme numbers.
Woodall primes.
zeta mysteries: the quantum connection.
素数.rar
(1.44 MB, 下载次数: 12)
| 欢迎光临 数学建模社区-数学中国 (http://www.madio.net/) | Powered by Discuz! X2.5 |