素数.rar
(1.44 MB, 下载次数: 12)
Entries A to Z.
abc conjecture.
abundant number.
AKS algorithm for primality testing.
aliquot sequences (sociable chains).
almost-primes.
amicable numbers. 4 K) B9 L. I6 a3 }- G9 c( W& A
amicable curiosities.
Andrica’s conjecture.
arithmetic progressions, of primes. 5 [6 l. R. E/ @9 @8 d* o
Aurifeuillian factorization.
average prime. Z9 ]* d) @- t6 b; } L( [
Bang’s theorem.
Bateman’s conjecture.
Beal’s conjecture, and prize. : f+ _8 E7 w8 e. A
Benford’s law.
Bernoulli numbers. . ?$ C/ C, H' ~( Z, ~2 A; ~! @! T) ~
Bernoulli number curiosities.
Bertrand’s postulate.
Bonse’s inequality. + j) S; u x/ S& V: p8 g
Brier numbers.
Brocard’s conjecture. ' F, x, k6 ~; X% j' d# K/ h/ u
Brun’s constant.
Buss’s function.
Carmichael numbers.
Catalan’s conjecture.
Catalan’s Mersenne conjecture.
Champernowne’s constant.
champion numbers. 2 i ?! x( B l. b i1 {$ d
Chinese remainder theorem.
cicadas and prime periods.
circle, prime.
circular prime.
Clay prizes, the.
compositorial.
concatenation of primes. 7 p/ V% n: d, {! ^- d
conjectures. \1 x1 n7 B+ n! T
consecutive integer sequence.
consecutive numbers.
consecutive primes, sums of. $ u! X: T/ K3 J/ o! A+ ~+ t$ d* z
Conway’s prime-producing machine.
cousin primes.
Cullen primes. + v: I+ k" I( D* f' L
Cunningham project. 7 Y4 W. R; {& D8 L% Y' T% \! H
Cunningham chains.
decimals, recurring (periodic).
the period of 1/13.
cyclic numbers.
Artin’s conjecture.
the repunit connection.
magic squares.
deficient number. " K4 J1 G! _# P' E0 c- e: t! h
deletable and truncatable primes. - q" Z! |5 L4 a$ V7 _$ l4 {) H
Demlo numbers. 1 e: s) n( H% w9 a) _0 t% b
descriptive primes. ( U7 t' Q. x* r& {9 v
Dickson’s conjecture.
digit properties. 0 o% k3 f" `7 ]( h
Diophantus (c. AD 200; d. 284). & ]% O. p7 q; o3 P, D( Y
Dirichlet’s theorem and primes in arithmetic series.
primes in polynomials. . j9 A1 x2 T: u
distributed computing. 9 y; T6 E2 d7 Q7 L1 [% y: X, @
divisibility tests.
divisors (factors).
how many divisors? how big is d(n)? 0 v1 N2 G3 z) [$ N6 ?* H
record number of divisors. ) w: m7 m4 h$ k# ?
curiosities of d(n).
divisors and congruences. & N* o; x) T1 I& P9 ?5 x
the sum of divisors function. 1 R+ }2 ?- j5 P6 d
the size of σ(n). 9 U4 t3 \0 C$ r* o0 N7 i/ ~
a recursive formula.
divisors and partitions.
curiosities of σ(n). + _$ ?5 f, {& `; j
prime factors. * Z d4 @/ x( c" Y8 P
divisor curiosities.
economical numbers.
Electronic Frontier Foundation.
elliptic curve primality proving. + f1 N$ o1 O) g9 b( t- E$ s7 a3 K+ [
emirp.
Eratosthenes of Cyrene, the sieve of.
Erd?s, Paul (1913–1996). 3 h8 ~2 r' {9 v% x8 C$ z# m
his collaborators and Erd?s numbers. 4 Z/ ^4 f1 Q7 M j) W4 Y$ t
errors. 0 t: N4 |7 H7 P( s$ r
Euclid (c. 330–270 BC). ! S0 U" \6 f+ ] R9 T1 p
unique factorization.
&Radic;2 is irrational. 2 ~ g7 ]5 O7 O; P: ^" g
Euclid and the infinity of primes. 1 K. O: t8 `% J
consecutive composite numbers. 3 \ H2 l) Y, B2 _& L
primes of the form 4n +3. ( k- u" J+ ?1 B0 l
a recursive sequence.
Euclid and the first perfect number. 7 Z. y" @, ?0 i' U1 ^% b$ [
Euclidean algorithm.
Euler, Leonhard (1707–1783).
Euler’s convenient numbers.
the Basel problem. ! x" X: }9 g+ ?+ b
Euler’s constant.
Euler and the reciprocals of the primes.
Euler’s totient (phi) function.
Carmichael’s totient function conjecture. 5 y( H8 H( G3 E+ G
curiosities of φ(n).
Euler’s quadratic.
the Lucky Numbers of Euler.
factorial.
factors of factorials.
factorial primes. * `2 R5 K/ i3 N, {9 B0 k$ r6 g
factorial sums.
factorials, double, triple . . . . 7 g+ _+ T% r4 y% F
factorization, methods of.
factors of particular forms.
Fermat’s algorithm.
Legendre’s method.
congruences and factorization.
how difficult is it to factor large numbers?
quantum computation.
Feit-Thompson conjecture.
Fermat, Pierre de (1607–1665).
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. 7 ~' N* C) Y$ e) F6 m
Fermat factorization, from F<sub>5</sub> to F<sub>30</sub>. D: I$ V" t$ R# Z# e; b
Generalized Fermat numbers. 6 x8 W* q4 d- A3 V& d# D( P! H& {
Fermat’s Last Theorem.
the first case of Fermat’s Last Theorem. 3 |1 B% o% Q" g2 T8 H/ K. z
Wall-Sun-Sun primes. , v7 \( K9 ?7 c3 |& p
Fermat-Catalan equation and conjecture. 3 n/ H9 v K7 j" K0 n% d
Fibonacci numbers. ' c+ O; l% q/ Q" ]0 \! z6 b
divisibility properties. ; R' T; @2 e& F5 N
Fibonacci curiosities.
édouard Lucas and the Fibonacci numbers.
Fibonacci composite sequences.
formulae for primes.
Fortunate numbers and Fortune’s conjecture.
gaps between primes and composite runs. ' ~+ O) _" Q, ^0 s' P9 m9 v+ I+ \" G
Gauss, Johann Carl Friedrich (1777–1855).
Gauss and the distribution of primes.
Gaussian primes. " q4 ^: `! K; Y& d+ i5 e `4 h
Gauss’s circle problem. # [( v8 u: r+ ^( A
Gilbreath’s conjecture.
GIMPS—Great Internet Mersenne Prime Search. @1 E2 U' y. J k Z' U- G) J) e
Giuga’s conjecture.
Giuga numbers. * d* C- h2 C G3 B7 d) C+ n
Goldbach’s conjecture.
good primes. 5 e5 G4 J5 _% r
Grimm’s problem. 3 V1 O4 q9 e, C/ v3 i9 E3 L! N
Hardy, G. H. (1877–1947). 7 c, }/ t! J9 g: k- W
Hardy-Littlewood conjectures.
heuristic reasoning. ! c( v1 B3 @4 W5 J; O) z) Y
a heuristic argument by George Pólya.
Hilbert’s 23 problems. # x# M9 o7 z- O6 w
home prime. / G3 k, d6 |8 n/ |: V1 o* o
hypothesis H.
illegal prime. / ]9 D4 D9 @/ d O) R
inconsummate number. " L" T8 _' e# G
induction.
jumping champion. 8 v) L( \7 j* k- r3 x$ B3 l' {
k-tuples conjecture, prime. ' G8 T n) H1 d$ O
knots, prime and composite.
Landau, Edmund (1877–1938).
left-truncatable prime. . ?. _/ c! z/ u: B
Legendre, A. M. (1752–1833). ) j* g: C% Q9 A" _
Lehmer, Derrick Norman (1867–1938). ! J/ S$ R; o0 L# J! l
Lehmer, Derrick Henry (1905–1991).
Linnik’s constant. - p9 F" N3 y, i/ {' \
Liouville, Joseph (1809–1882).
Littlewood’s theorem. 9 [' e2 X8 A$ R
the prime numbers race.
Lucas, édouard (1842–1891).
the Lucas sequence.
primality testing.
Lucas’s game of calculation. : ~: Y- M* W8 j9 c
the Lucas-Lehmer test.
lucky numbers. " f9 |& z- B5 p4 U2 I7 Q) l
the number of lucky numbers and primes.
“random” primes. 6 ^2 Z, v! H8 K: t8 L
magic squares.
Matijasevic and Hilbert’s 10th problem.
Mersenne numbers and Mersenne primes.
Mersenne numbers.
hunting for Mersenne primes.
the coming of electronic computers. ! E: r( A: w2 i/ q+ ?# s. b
Mersenne prime conjectures.
the New Mersenne conjecture. $ N) V G$ d: }; l# [: G7 E4 r( r
how many Mersenne primes? 3 \, J& T4 t9 |* G3 B3 ^- L( m; o: i
Eberhart’s conjecture. }& m1 ]; O0 X. D1 k0 m
factors of Mersenne numbers.
Lucas-Lehmer test for Mersenne primes. ' f4 A; ?3 Y* t4 I4 }; ]5 ^6 `
Mertens constant. 1 C$ a6 {3 n& D) a0 I0 o% I
Mertens theorem.
Mills’ theorem. 4 v) e% a- u. ?6 L7 S
Wright’s theorem.
mixed bag.
multiplication, fast. ! |4 A2 J$ w8 _
Niven numbers.
odd numbers as p + 2a<sup>2</sup>.
Opperman’s conjecture. + v& C+ j# c- B2 S
palindromic primes. - G7 e7 T; ?( a: ]
pandigital primes.
Pascal’s ** and the binomial coefficients. : H: a! }' P8 g. m
Pascal’s ** and Sierpinski’s gasket. 1 O I" q+ S5 v9 w- o2 Z" W
Pascal ** curiosities.
patents on prime numbers. % X" K+ T1 g7 S2 v6 ^! H
Pépin’s test for Fermat numbers.
perfect numbers. + I4 p$ M- c5 o J# }+ D& u% }. D* }( b
odd perfect numbers. , r7 p& @5 J" B& |4 w& {
perfect, multiply.
permutable primes.
π, primes in the decimal expansion of.
Pocklington’s theorem. ' R1 N8 J9 ~5 u% a
Polignac’s conjectures.
Polignac or obstinate numbers. / a) |) E+ i2 \3 p; q) C
powerful numbers.
primality testing. % n) S! s0 E( A" D' w6 Z& r) S
probabilistic methods. 8 ?; r; h% t0 a( p$ ~: M c; Y3 N* e# d
prime number graph. 2 O% U5 q/ V# z8 y3 j( w6 \
prime number theorem and the prime counting function.
history.
elementary proof. ) ` E! \. G" n4 p) x ]
record calculations. 0 \$ ~6 P4 I# ^6 L- M) X
estimating p(n).
calculating p(n).
a curiosity.
prime pretender. 4 A: |" X5 _' m ^ ]( F& [, l
primitive prime factor.
primitive roots. 3 P+ H6 y" Z2 p6 F8 N1 o% Z
Artin’s conjecture.
a curiosity.
primordial.
primorial primes.
Proth’s theorem.
pseudoperfect numbers.
pseudoprimes.
bases and pseudoprimes.
pseudoprimes, strong. & o5 i. C3 ]1 w8 n
public key encryption. 6 g6 X5 n" p8 Y, L! Q
pyramid, prime.
Pythagorean **s, prime.
quadratic residues. 5 M# O' h' f" P4 u3 X8 w
residual curiosities. 6 e: B1 r# z9 s. i7 V
polynomial congruences. g# H/ S$ z" Q. S2 W2 ?" \
quadratic reciprocity, law of.
Euler’s criterion. - f) }7 t7 e( b- B+ Q
Ramanujan, Srinivasa (1887–1920). & V# \3 e0 b0 ?
highly composite numbers. ) h7 V: ]6 v- E7 u, Q/ k8 ~0 }
randomness, of primes. 6 ~( g- m( l `$ X
Von Sternach and a prime random walk.
record primes. 9 Y+ ^( W: n2 I. u3 x: [
some records.
repunits, prime.
Rhonda numbers.
Riemann hypothesis. 7 R6 W+ Q J* M' i& v1 v
the Farey sequence and the Riemann hypothesis.
the Riemann hypothesis and σ(n), the sum of divisors function. * U2 B: y2 y& v3 ]
squarefree and blue and red numbers. 3 z+ y9 }4 \; j; k* W8 {; ~9 O" o
the Mertens conjecture.
Riemann hypothesis curiosities.
Riesel number. 0 D: K4 A2 o+ u: D
right-truncatable prime. ( C& }8 [$ V2 v2 G* u4 p
RSA algorithm.
Martin Gardner’s challenge.
RSA Factoring Challenge, the New.
Ruth-Aaron numbers. - P/ T y2 y! B$ k0 m5 v
Scherk’s conjecture. * X' l8 F. E8 S- x" C- r# z: g
semi-primes. ; C7 d5 F. ^* N
**y primes. * u# A* [4 z: P8 ^/ Z$ E
Shank’s conjecture.
Siamese primes. 8 I8 W1 v. n0 A$ `# h2 ?
Sierpinski numbers. ; r5 s% r9 X- F+ }$ b1 p$ S7 W
Sierpinski strings. ! }$ D z* \) w1 V0 ^
Sierpinski’s quadratic. 2 z# c5 P. |+ K# o3 w! r4 U8 P; c, e$ N
Sierpinski’s φ(n) conjecture. 9 O; e; R8 a) z* Z O2 N; A2 Z
Sloane’s On-Line Encyclopedia of Integer Sequences. ' m+ @5 T) f( g" T5 I8 E
Smith numbers.
Smith brothers. + N$ Q q7 T( h1 o
smooth numbers. 4 B5 @1 B) T L1 t. d* y; k
Sophie Germain primes. # n2 B, X! h+ t) }
safe primes.
squarefree numbers. ! _+ n4 n0 a: Y
Stern prime. 8 D7 O9 K2 \& c/ `4 U
strong law of small numbers.
triangular numbers.
trivia.
twin primes.
twin curiosities.
Ulam spiral. & l7 l7 O% j1 _/ ]: [6 @( A
unitary divisors.
unitary perfect.
untouchable numbers.
weird numbers. 8 @2 [) O V) T' a+ ?* s
Wieferich primes. 6 a5 y% _; X& m i; E
Wilson’s theorem. 3 H' h2 i6 x5 K! ]$ y1 R- P
twin primes.
Wilson primes. * y) z8 w6 E$ s
Wolstenholme’s numbers, and theorems. / r7 C, X S" N5 {& f
more factors of Wolstenholme numbers.
Woodall primes. 8 F Z4 z9 D4 R ]
zeta mysteries: the quantum connection.
素数.rar
(1.44 MB, 下载次数: 12)
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