| Description |
xv, 272 pages ; 25 cm |
| Bibliography |
Includes bibliographical references (pages 253-264) and index. |
| Summary |
A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erdős, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know-and much more that you never suspected-about prime numbers, including: the unproven Riemann hypothesis and the power of the zeta function, the "Primes is in P" algorithm, the sieve of Eratosthenes of Cyrene, Fermat and Fibonacci numbers, the Great Internet Mersenne Prime Search, and much, much more. |
| Contents |
Machine derived contents note: Table of Contents -- Introduction -- List Of Entries: -- abc conjecture -- abundant number -- AKS algorithm for primality testing -- aliquot sequences (sociable chains) -- almost-primes -- amicable numbers -- amicable curiosities -- Andrica's conjecture -- arithmetic progressions, of primes -- Aurifeuillian factorization -- average prime -- Bang's theorem -- Bateman's conjecture -- Beal's conjecture, and prize -- Benford's law -- Bernoulli numbers -- Bernoulli number curiosities -- Bertrand's postulate -- Bonse's inequality -- Brier numbers -- Brocard's conjecture -- Brun's constant -- Buss's function -- Carmichael numbers -- Catalan's conjecture -- Catalan's Mersenne conjecture -- Champion numbers -- Chinese remainder theorem -- cicadas and prime periods -- circle, prime -- circular prime -- Clay prizes, the -- compositorial -- concatenation of primes -- conjectures -- consecutive integer sequence -- consecutive numbers -- consecutive primes, sums of -- Conway's prime-producing machine -- cousin primes -- Cullen primes -- Cunningham project -- Cunningham chains -- decimals, recurring (periodic) -- deficient number -- deletable and truncatable primes -- Demlo numbers -- descriptive primes -- Dickson's conjecture -- digit properties -- Diophantus (c.200: died 284) -- Dirichlet's theorem and primes in arithmetic series -- distributed computing -- divisibility tests -- divisors (factors) -- economical numbers -- Electronic Frontier Foundation -- elliptic curve primality proving -- emirp -- Eratosthenes of Cyrene, the sieve of -- Erdos, Paul (1913-1996) -- errors -- Euclid -- Unique factorisation -- í2 is irrational -- Euclid and the infinity of primes. -- Consecutive composite numbers -- Primes of the form 4n+3 -- 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 -- Euler and the reciprocals of the primes -- Euler's phi [totient] function -- Carmichael's totient function conjecture -- Curiosities of w(n) -- Euler's quadratic -- The Lucky Numbers of Euler. -- factorial -- factors of factorials -- factorial primes -- factorial sums -- factorials, double, triple -- factorization, methods of -- factors of particular forms -- Fermat's algorithm -- Legendre's method -- 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 x2 + y2 -- Fermat's conjecture, Fermat numbers and Fermat primes -- Fermat factorisation, from F6 to F30 -- Generalized Fermat numbers -- Fermat's Last Theorem -- The first case of Fermat's Last Theorem: -- Wall-Sun-Sun primes -- Fermat-Catalan equation and conjecture -- Fibonacci numbers -- divisibility properties -- 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 -- Gauss Johann Carl Friedrich (1777-1855) -- Gauss and the distribution of primes -- Gaussian primes -- Gauss's circle problem -- Gilbreath conjecture -- GIMPS = Great Internet Mersenne Primes Search -- Giuga's conjecture -- Giuga numbers -- Goldbach's conjecture -- good primes -- graph, prime number -- Grimm's problem -- Hardy G H (1877-1947) -- Hardy-Littlewood conjectures -- heuristic reasoning -- Hilbert's 23 problems -- home prime -- hypothesis H -- illegal prime -- inconsummate number -- induction jumping champion -- k-tuples conjecture, prime -- knots, prime and composite -- Landau, Edmund (1877-1938) -- left-truncatable prime -- Legendre A.M. (1752-1833) -- Legendre's theorem (1808) -- Lehmer, Derrick Norman (1867-1938) -- Lehmer, Derrick Henry (1905-1991) -- Linnik's constant -- Liouville, Joseph (1809-1882) -- Littlewood's theorem -- the prime numbers race -- Look and Say sequence -- Lucas, Édouard (1842-1891) -- the Lucas sequence -- primality testing -- Lucas's game of calculation -- the Lucas-Lehmer test -- lucky numbers -- the number of Lucky numbers and primes -- 'random' primes' -- magic squares -- Matijasevic and Hilbert's 10th problem -- Mersenne numbers and Mersenne primes -- Mersenne numbers -- hunting for Mersenne primes -- the coming of electronic computers -- Mersenne prime conjectures -- the New Mersenne Conjecture -- how many Mersenne primes ? -- Eberhart's conjecture -- factors of Mersenne Numbers -- Lucas-Lehmer test for Mersenne primes -- Mertens' theorem -- Mertens' constant -- Mill's theorem -- Wright's theorem -- mixed bag -- multiplication, fast -- Niven Numbers -- odd numbers as p + 2a2 -- Opperman's conjecture -- palindromic primes -- pandigital primes -- Pascal's Triangle and the binomial coefficients -- Pascal's triangle and Sierpinski's gasket -- Pascal triangle curiosities -- patents on prime numbers -- Pépin's test for Fermat numbers -- perfect numbers -- odd perfect numbers -- perfect, multiply -- permutable primes -- o, primes in the decimal expansion of -- Pocklington's theorem -- Polignac's conjectures -- Polignac or obstinate numbers -- powerful numbers -- consecutive powerful numbers -- primality testing -- probabilistic methods -- prime number graph -- prime number theorem and the prime counting function -- history -- elementary proof -- record calculations -- estimating p(n) -- calculating p(n) -- a curiosity -- prime pretender -- primitive prime factor -- primitive roots -- Artin's conjecture -- a curiosity -- primorial -- primorial primes -- Proth's Theorem -- pseudoperfect numbers -- bases and pseudpoprimes -- pseudoprimes, strong -- public key encryption -- pyramid, prime -- Pythagorean triangles, prime -- quadratic residues -- residual curiosities -- 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 -- record primes -- some records -- repunits, prime -- Rhonda numbers -- Riemann hypothesis -- Farey series and Riemann's Hypothesis -- Riemann's hypothesis and r(n), the sum of divisor function -- squarefree and blue and red numbers -- the Mertens conjecture -- Riemann Hypothesis curiosities -- Riesel number -- right-truncatable prime -- RSA algorithm -- Martin Gardner's challenge -- RSA Factoring Challenge, The New -- Ruth-Aaron numbers -- Scherk's conjecture -- semi-primes -- sexy primes -- Shank's Conjecture -- Siamese primes -- Sierpinski numbers -- Sierpinski strings -- Sierpinski's quadratic -- Sierpinski's phi(n) conjecture -- Sloane's On-Line Encyclopedia of Integer Sequences -- Smith numbers -- Smith Brothers -- smooth numbers -- Sophie Germain primes -- safe primes -- square-free numbers -- Stern prime -- strong law of small numbers -- triangular numbers -- trivia -- twin primes -- twin curiosities -- Ulam spiral -- unitary divisors -- unitary perfect -- untouchable numbers -- weird numbers -- Wieferich primes -- Wilson's theorem -- twin primes -- Wilson's quotient -- Wilson primes -- Wolstenholme's numbers, and theorems -- more factors of Wolstenholme numbers -- Woodall primes -- zeta mysteries: the quantum connection -- Appendices -- Glossary -- Bibliography -- Index. |
| Subject |
Numbers, Prime.
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Numbers, Prime. (OCoLC)fst01041241
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Priemgetallen.
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| Genre/Form |
Nonfiction.
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| ISBN |
0471462349 (acid-free paper) |
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9780471462347 (acid-free paper) |
| Standard No. |
9780471462347 |
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723812605255 |
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