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.
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