Prime Numbers

594

Sierpi´nski

gasket, 428, 437 numbers, 76, 77 theorem, 77

Sierpi´nski, W., 17, 77

sieving, 76, 77, 121–125, 153–155, 169, 228, 259, 264, 267– 271, 275, 276, 278, 283, 294, 295, 298, 300, 437, 491, 492, 526

Silva, T., 19

Silver, R., 463

Silverman, J., 322, 358, 375, 434 Silverman, R., 343

simple continued fractions, 85 Skewes number, 59, 60 Skinner, C., 417

Sloan, I., 415 Slowinski, D., 23

Smarandache–Wellin numbers, 78 Smart, N., 392, 418

Smith, J., 269

Smith, J. (with Pomerance et al.), 276

smooth numbers, 48, 73, 120, 123, 124, 126, 128, 263–268, 270, 272–274, 276–286, 293, 295–298, 300–307, 335, 337– 339, 366, 377

Snow White and the seven dwarves, 430

Sobol, I., 414

Solinas, J., x, 376, 392, 523 Solovay, R., 166

Somer, L., x

Sophie Germain primes, 63, 71, 207 Sorenson method (for gcd), 381,

464

Sorenson, J., 381, 464, 483, 529 special number field sieve (SNFS),

299

special quadratic sieve (SQS), 276, 278

Spence, G., 23, 76

square roots, 99, 100, 102, 107, 112, 454

INDEX

squarefree number, 26 squaring, 444 Srassen, V., 166

Srinivasan probabilistic method, 250 Srinivasan, A., 250, 251

Stark, H., 368

Stehl´e, D., ix, x, 466, 470, 473 Stein, J., 463

Stinson, D. (with Gong et al.), 402, 438

Stirling formula, 54 Stoll, M., 417

Strassen recursion, 259

Strassen, V., 166, 238, 259, 490, 502

strong probable prime, 135

strong pseudoprime, 136, 137, 139, 140, 166

Stuart, I., 430

succinct certificate, 179

suitable numbers (in fast multiplication), 503

Sun, Z.-H., 32

Sun, Z.-W., 32 Sun-Zi, 87 Sundaram, G., 401 Sundquist, R., 24 Sutton, B., 487

Suyama theorem, 28, 219 Suyama, H., 219, 220, 341 Swarztrauber, P., 483 Symes, D., x, 316 Szemer´edi, E., 13, 14

Tang, M., 169

Tanner, J., 533 Tao, T., ix, 13, 14 Tardif, C., 28, 386 Tasche, M., 501 Tatuzawa, T., 247

Taylor expansion, 105 Taylor, R., 417

te Riele, H., 39

te Riele, H. (with Brent et al.), 25 te Riele, H. (with Deshouillers et

al.), 19

INDEX

te Riele, H. (with van de Lune et al.), 38, 67

Technology Review, 424 Teitelbaum, J., 270

ternary Goldbach problem, 19, 20, 62, 71

Terr, D., x, 236 Terzian, J., 463

Teske, E., x, 233, 235, 236

Teske, E. (with Buchmann et al.), 236

Teukolsky, S. (with Press et al.), 399, 402, 403

Tevanian, A., x Tezuka, S., 406, 415 Thomas, J., 465 Thompson, R., x

Thyssen, A. (with Pritchard et al.), 78

Tijdeman, R., 416, 417, 434 Titchmarsh, E., 43, 69, 170, 440 Tonelli, A., 100

Toom–Cook method, 472–476, 506, 524, 525, 536

Toplic, M., 78 Trabb Pardo, L., 163 Traub, J., 413, 415 Trevisan, V., 29

trial division, 117–120, 173 triangular numbers, 437, 515 Trott, M., x

Tsapakidis, D. (with Escott et al.), 234

Tucker, T., 417

Tuckerman, B. (with Brillhart et al.), 299

Tukey, J., 479

Tuler, R. (with Pomerance et al.), 276

Tur´an, P., 13, 14

Turing machine (TM), 419, 420, 423, 435, 436

twin-prime pairs, 14–16, 19, 38, 62, 80

twinkle device, 424

twist curve, 329, 377, 394, 395

595

Ullman, J. (with Aho et al.), 466, 509, 513

Underwood, P. (with Frind et al.), 78

unique factorization domain (UFD), 291

Vall´ee, B., 302

Valor, G., 23

van de Lune, J., 38, 67

van der Corput sequence, 408 van der Corput, J., 44, 407, 408 van der Hulst, M., 200

van der Pol, B., 428 van Halewyn, C., 346

van Halewyn, C. (with Brent et al.), 28, 321, 340–342, 347, 385, 456, 496, 528

Van Loan, C., 481, 483, 485, 530 van Oorschot, P., 234, 235

van Oorschot, P. (with Menezes et al.), 88, 91, 102, 104, 110, 390, 391, 402, 445, 450, 461, 522

van Zyl, B., 428

Vandewalle, J. (with Bosselaers et al.), 449, 452, 453

Vandiver conjecture, 492 Vanstone, S. (with Menezes et al.),

88, 91, 102, 104, 110, 390– 392, 402, 445, 450, 461, 522

Vaughan, R., 43, 47, 48, 57, 70, 537, 538

Veach, E., 415, 439 Vehka, T., 81 Venkatesan, R., 432

Vettering, W. (with Press et al.), 399, 402, 403

Vinogradov

equidistribution theorem, 58 estimates, 72 ternary-Goldbach theorem, 20,

71

Vinogradov, I., 19, 20, 45, 46, 48, 64, 538

596

Vladimirov, V., 429

Volovich, I. (with Vladimirov et al.), 429

von Koch, H., 37

von Mangoldt, H., 37, 171 von Neumann, J., 397 von zur Gathen, J., 95

Wada, H., 418

Wagon, S., x, 81, 107, 389, 396, 433 Wagsta Jr., S., x, 4, 5, 7, 25, 149, 165, 168, 343, 533

Wagsta Jr., S. (with Bateman et al.), 25

Wagsta Jr., S. (with Brillhart et al.), 299

Wall Street, 409, 413 Wall–Sun–Sun primes, 4, 32 Walsh–Hadamard transform, 478,

525 Wang, Y., 19 Wantzel, P., 210 Ware, A., 487

Waring problem, 538 Warren, B., 430 Washington, L., 76 Wassing, H., 14

Watkins, M., x, 247, 248, 361 Watt, N., 45

Weber variety, 361

Weber, D. (with Schirokauer et al.), 306, 387

Weber, K., 464 Wedeniwski, S., 39 Weierstrass

equations, 375

form, 320, 321, 329, 374 function, 375

Weiss, E., 288

Weisstein, E., 75, 78, 418 Wellin, P., x, 78

Welsh, Jr., L., 23

Western, A., 299 Weyl theorem, 44, 58 Weyl, H., 44

wheel, 119, 120

INDEX

Wheeler, N., x

Whiten, W., 414 Wiedemann, D., 269

Wiedmann method (for coordinate recurrence), 269

Wieferich primes, 4, 31, 32, 64, 416, 434

Wieferich, A., 31

Wiener, M., x, 234, 235, 431 Wiener, M. (with De Win et al.),

381, 453, 458, 536 Wiens, D., 418

Wieting, T., x

Wiles, A., 415, 417, 492, 532 Williams, C., 420, 423 Williams, D., 499

Williams, H., 174, 219, 220, 229, 385, 389

Williams, J., x, 251 Willmore, D., 23

Wilson primes, 4, 32, 33, 65, 81, 82, 514, 534

Wilson quotient, 32, 33, 65 Wilson theorem, 21, 33 Wilson–Lagrange theorem, 32, 64,

65, 238 Winkler, P., x

Winograd complexity, 525, 539 Winograd, S., 524

Winter, D. (with van de Lune et al.), 38, 67

Winterhof, A., 538 Wirth, T., 4

Wirth, T. (with Franke et al.), 374 Wolf, M., 429, 439

Wolfram, S., x

Woltman, G., 4

Woltman, G., x, 23, 24, 343, 345, 346, 453, 470, 496, 528

Wozniakowski, H., 406, 415 Wright, E., 36, 46, 87, 121, 227,

492, 527 Wu, P., 399, 400 Wylde, A., x

Yacobi, Y., 458, 536

INDEX

Yagle, A., 259, 499, 539 Yan, A., 426

Yan, B., 426

Yan, J., 426

Yerkes, A., x Yildirim, C., 38

Yokoyama, K. (with Izu et al.), 357 Yor, M. (with Balazard et al.), 440 Yoshimura, J., 425

Young J. (with Crandall et al.), 29, 456, 496, 528

Young, J., 24, 29, 30 Yu, G., 45

Zaccagnini, A., x

Zagier, D., 247, 417

597

Zelenov, E. (with Vladimirov et al.), 429

zero padding (of signals), 489, 490 Zhang’s special quadratic sieve,

276 Zhang, M., 276, 309

Zhang, Z., x, 151, 169 Ziegler, J., 454

Zimmermann, P., ix, x, 3, 5, 11, 343, 345, 346, 377, 466, 470, 473

Zimmermann, P. (with Dubner et al.), 78, 79

Zinoviev, D., 20

Zuckerman, H. (with Niven et al.), 282