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Prime Numbers

Prime Numbers Prime Numbers

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INDEX 587 Lehmer, D., 149, 152, 155, 164, 166, 174, 175, 186, 463, 464, 466 Lehmer, D. (with Brillhart et al.), 299 Lehmer, E., 164 Lenstra Jr., H., x, 31, 57, 76, 107, 128, 166, 186, 187, 189– 191, 194, 207, 209–212, 238, 251, 278, 302, 323, 333–336, 339 Lenstra Jr., H. (with Buhler et al.), 289, 290, 292, 297, 493, 532 Lenstra Jr., H. (with Lenstra et al.), 28, 280, 293, 299 Lenstra, A., x, 3, 28, 189, 272, 278, 280, 292, 293, 299, 301, 302 Leveque theorem, 439 Levich, M., x Levin,L.(withH˚astad et al.), 433 Levy flight, 428 Leyland,P.,3,4,374 lg, 26 li, 10 li0, 59 Li, S., 132, 169 Li, X., 441 Lichtblau, D., x, 311 Lieman, D., x Lifchitz, H., 14 Lim, C., 391 Lindelöf hypothesis, 45 Lindemann, I., x Lindqvist, L., 80 Littlewood, J., 46, 59, 78 Liu, Q., 487 Loebenberger, D., x Long, D., 389 Lovasz, L., 189 Lovasz, L. (with Lenstra et al.), 280, 293 Lovorn Bender, R., 306 Luby,M.(withH˚astad et al.), 433 Lucas chain, 147, 330, 345 numbers, 103, 112, 195 pseudoprimes, 142, 145, 146, 148–150, 166 theorem, 173, 174, 179 tree, 179, 181 Lucas, E., 28, 173, 174, 179 Lucas–Lehmer test, 4, 23, 24, 76, 181, 183, 184, 456, 496, 523, 528 Lyapunov exponents, 438 Lygeros, N. (with Dubner et al.), 78, 79 Lyne, A., 483 Müller, V., x, 392 Madisetti, V., 499 Maier, H., 38 Mairson, 126 Manasse, M., 272 Manasse, M. (with Lenstra et al.), 28, 299 Mann, X., 433 Marcus, D., 284 Marsaglia theorem, 401 Marsaglia, G., 400, 438 Martin, M., x Masser, D., 417 Mathematica, viii, 311, 541, 543 Mathematical Games, 2 Matijasevič, Y., 418 matrix, 151, 304 and random numbers, 400 determinant, 239 fast methods, 259, 265, 268 GUE, 427 Hessenberg, 427 in convolution, 538 in FFT, 483, 484 in golden-section transform, 529 in NFS, 293 in QS, 266 in recursive gcd, 469 operators, 421 random, 426

588 INDEX reduction, 263 structured Gauss methods, 269 transpose, 485, 530 Mauldin, R., 417 Mayer, E., x, 4, 23, 30, 218, 485, 488, 538 Mayer, E. (with Crandall et al.), 30, 219, 456, 485, 491, 496, 528, 531, 538 Mayer, E. (with Crandall et al.), 218 McClellan, J., 524 McCurley, K., 251 McGuckin, F., x McIntosh, R., 28, 32, 386 McIntosh–Tardif factor, 256, 385 McIntosh–Wagstaff probable prime, 384 McKee, J., 242, 255 measure theory (of continued fractions), 85 Meissel, E., 152, 155 Mellin transform, 160–162, 168 Menezes, A., 88, 91, 102, 104, 110, 390–392, 394, 402, 445, 450, 461, 522 Merel, L., 417 Mersenne numbers, 4, 22, 25–28, 52, 63, 64, 76, 79, 109, 181, 183, 256, 307, 308, 455, 496– 498, 523 primes, 3, 22–25, 31, 52, 63, 64, 76, 79, 113, 183, 184, 363, 373, 399, 438, 454– 456, 466, 496, 500–502, 524, 528, 530–532, 539 Mersenne, M., 25 Mertens conjecture, 39 constant, 35, 36, 79, 80 function, 36, 37 theorem, 27, 35, 127, 163 Mestre theorems, 378 Mestre, J., 349 Metsänkylä, T., 416 Micali scenario, 397 Micali, S., 397 Mignotte, M., x, 416 Mihăilescu, P., ix, x, 214, 215, 416 Miller, G., 137, 141, 200 Miller, K., 399 Miller, V., x, 152, 391, 402 Miller, V. (with Lagarias et al.), 152, 155, 158 Miller, W.(with Dimitrov et al.), 530 Mills constant, 75 Mills, W., 21, 75 Mister, S. (with De Win et al.), 381, 453, 458, 536 Mitchell, D., x Mitchell, V., x Mitra, T., x Miyaji, A. (with Cohen et al.), 333, 460 Mizony, M. (with Dubner et al.), 78, 79 Möbius function µ, 36, 37, 39, 94, 155, 425 Moenck, R., 513 mole rule, 5 Monico, C., 394 Monier, L., 136, 151, 165 Monier–Rabin theorem, 151 Monte Carlo, 229, 397, 404, 405, 409, 412, 413 Montgomery coordinates, 324, 370 curve, 374 method (for div/mod), 447 parameterization, 330, 370, 432 powering, 448 Montgomery, H., 43, 426 Montgomery, H. (with Niven et al.), 282 Montgomery, P., x, 147, 238, 254, 256, 270, 273, 292, 299, 317, 321, 329, 330, 332, 340–343, 345, 346, 374, 375, 380, 383, 384, 395,

588 INDEX<br />

reduction, 263<br />

structured Gauss methods, 269<br />

transpose, 485, 530<br />

Mauldin, R., 417<br />

Mayer, E., x, 4, 23, 30, 218, 485,<br />

488, 538<br />

Mayer, E. (with Crandall et al.),<br />

30, 219, 456, 485, 491,<br />

496, 528, 531, 538<br />

Mayer, E. (with Crandall et al.),<br />

218<br />

McClellan, J., 524<br />

McCurley, K., 251<br />

McGuckin, F., x<br />

McIntosh, R., 28, 32, 386<br />

McIntosh–Tardif factor, 256, 385<br />

McIntosh–Wagstaff probable prime,<br />

384<br />

McKee, J., 242, 255<br />

measure theory (of continued fractions),<br />

85<br />

Meissel, E., 152, 155<br />

Mellin transform, 160–162, 168<br />

Menezes, A., 88, 91, 102, 104, 110,<br />

390–392, 394, 402, 445,<br />

450, 461, 522<br />

Merel, L., 417<br />

Mersenne<br />

numbers, 4, 22, 25–28, 52, 63,<br />

64, 76, 79, 109, 181, 183,<br />

256, 307, 308, 455, 496–<br />

498, 523<br />

primes, 3, 22–25, 31, 52, 63,<br />

64, 76, 79, 113, 183, 184,<br />

363, 373, 399, 438, 454–<br />

456, 466, 496, 500–502,<br />

524, 528, 530–532, 539<br />

Mersenne, M., 25<br />

Mertens<br />

conjecture, 39<br />

constant, 35, 36, 79, 80<br />

function, 36, 37<br />

theorem, 27, 35, 127, 163<br />

Mestre theorems, 378<br />

Mestre, J., 349<br />

Metsänkylä, T., 416<br />

Micali scenario, 397<br />

Micali, S., 397<br />

Mignotte, M., x, 416<br />

Mihăilescu, P., ix, x, 214, 215, 416<br />

Miller, G., 137, 141, 200<br />

Miller, K., 399<br />

Miller, V., x, 152, 391, 402<br />

Miller, V. (with Lagarias et al.),<br />

152, 155, 158<br />

Miller, W.(with Dimitrov et al.),<br />

530<br />

Mills constant, 75<br />

Mills, W., 21, 75<br />

Mister, S. (with De Win et al.),<br />

381, 453, 458, 536<br />

Mitchell, D., x<br />

Mitchell, V., x<br />

Mitra, T., x<br />

Miyaji, A. (with Cohen et al.), 333,<br />

460<br />

Mizony, M. (with Dubner et al.),<br />

78, 79<br />

Möbius function µ, 36, 37, 39, 94,<br />

155, 425<br />

Moenck, R., 513<br />

mole rule, 5<br />

Monico, C., 394<br />

Monier, L., 136, 151, 165<br />

Monier–Rabin theorem, 151<br />

Monte Carlo, 229, 397, 404, 405,<br />

409, 412, 413<br />

Montgomery<br />

coordinates, 324, 370<br />

curve, 374<br />

method (for div/mod), 447<br />

parameterization, 330, 370, 432<br />

powering, 448<br />

Montgomery, H., 43, 426<br />

Montgomery, H. (with Niven et<br />

al.), 282<br />

Montgomery, P., x, 147, 238, 254,<br />

256, 270, 273, 292, 299,<br />

317, 321, 329, 330, 332,<br />

340–343, 345, 346, 374,<br />

375, 380, 383, 384, 395,

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