Prime Numbers: A Computational PerspectivesSpringer Science & Business Media, 2001 - 545 pages Primes is a definitive presentation on the most modern computational ideas about prime numbers and factoring and will stand as an excellent reference for this kind of computation, of interest to both researchers and educators. The book is timely, because primes and factoring have reached a certain vogue, partly due to their use in cryptography. A final chapter presents applications to mathematical finance via quasi-Monte Carlo theory. Historical comments are also included throughout. Valuable enhancement files and program code will be available via the web. |
Table des matières
II | 1 |
IV | 2 |
V | 5 |
VI | 7 |
VII | 9 |
VIII | 12 |
X | 15 |
XI | 16 |
CI | 232 |
CII | 234 |
CIII | 236 |
CIV | 239 |
CV | 240 |
CVI | 242 |
CVII | 244 |
CVIII | 245 |
XII | 18 |
XIV | 19 |
XV | 20 |
XVI | 24 |
XVII | 28 |
XVIII | 30 |
XX | 35 |
XXI | 36 |
XXII | 40 |
XXIII | 44 |
XXIV | 45 |
XXV | 69 |
XXVI | 77 |
XXIX | 79 |
XXX | 81 |
XXXI | 83 |
XXXIII | 85 |
XXXIV | 89 |
XXXV | 93 |
XXXVI | 96 |
XXXVII | 99 |
XXXVIII | 101 |
XXXIX | 106 |
XL | 109 |
XLI | 110 |
XLII | 111 |
XLIII | 112 |
XLIV | 113 |
XLVI | 114 |
XLVIII | 115 |
L | 116 |
LI | 118 |
LII | 120 |
LIV | 122 |
LV | 123 |
LVI | 129 |
LVII | 130 |
LVIII | 131 |
LIX | 133 |
LX | 134 |
LXI | 138 |
LXII | 139 |
LXIII | 141 |
LXV | 146 |
LXVI | 150 |
LXVII | 156 |
LXVIII | 159 |
LXXI | 160 |
LXXII | 164 |
LXXIII | 167 |
LXXV | 170 |
LXXVI | 172 |
LXXVII | 175 |
LXXVIII | 180 |
LXXX | 185 |
LXXXI | 186 |
LXXXII | 189 |
LXXXIII | 191 |
LXXXIV | 193 |
LXXXV | 194 |
LXXXVI | 195 |
LXXXVIII | 197 |
LXXXIX | 199 |
XC | 200 |
XCI | 202 |
XCII | 204 |
XCV | 207 |
XCVI | 210 |
XCVII | 214 |
XCVIII | 216 |
XCIX | 220 |
C | 227 |
CIX | 246 |
CX | 251 |
CXI | 254 |
CXII | 257 |
CXIII | 258 |
CXIV | 260 |
CXV | 267 |
CXVI | 268 |
CXVII | 269 |
CXVIII | 271 |
CXIX | 272 |
CXX | 281 |
CXXI | 285 |
CXXII | 289 |
CXXIII | 299 |
CXXIV | 301 |
CXXV | 302 |
CXXVI | 305 |
CXXVII | 313 |
CXXIX | 317 |
CXXX | 323 |
CXXXI | 334 |
CXXXIII | 338 |
CXXXIV | 340 |
CXXXV | 346 |
CXXXVI | 353 |
CXXXVII | 355 |
CXXXVIII | 357 |
CXXXIX | 362 |
CXL | 363 |
CXLI | 364 |
CXLII | 370 |
CXLIV | 373 |
CXLV | 375 |
CXLVI | 381 |
CXLVII | 384 |
CXLVIII | 385 |
CXLIX | 388 |
CL | 390 |
CLI | 396 |
CLII | 400 |
CLIII | 407 |
CLVI | 408 |
CLVII | 409 |
CLVIII | 411 |
CLX | 414 |
CLXI | 418 |
CLXII | 421 |
CLXIII | 422 |
CLXIV | 424 |
CLXV | 427 |
CLXVII | 429 |
CLXVIII | 430 |
CLXIX | 433 |
CLXXI | 436 |
CLXXII | 445 |
CLXXIII | 450 |
CLXXIV | 456 |
CLXXV | 459 |
CLXXVI | 461 |
CLXXVII | 464 |
CLXXVIII | 465 |
CLXXIX | 467 |
CLXXXI | 468 |
CLXXXII | 471 |
CLXXXIII | 475 |
CLXXXIV | 491 |
CLXXXV | 497 |
503 | |
529 | |
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Expressions et termes fréquents
algebra arithmetic asymptotic B-smooth B₁ binary bound calculation coefficients complexity composite number computational congruence conjecture convolution coprime Crandall cryptography curve order cyclic denote digits discrete logarithm divisor elements elliptic curve estimate evaluation example Exercise explicit exponent vectors Fermat numbers field sieve finite field Frobenius function given heuristic idea implementation infinitely inverse irreducible polynomial Legendre symbol Lenstra loop matrix Mersenne prime method modulo Montgomery multiplication negacyclic nontrivial factorization Note number field number theory odd prime operations pairs parameters Pomerance positive integer primality test prime factor prime numbers primitive root probable prime problem proof prove pseudoprime quadratic quadratic forms quadratic nonresidue quadratic residues quadratic sieve random recursive representation residue result Riemann Riemann hypothesis Section sequence sieve signal square root Theorem values zero