One can download here the computer results described in the paper On the diffusion of the Improved Generalized Feistel, to appear in Advances in Mathematics of Communications.

The paper considers the Improved Generalized Feistel Structure (IGFS) suggested by Suzaki and Minematsu (LNCS, 2010). It is a generalization of the classical Feistel cipher. The message is divided into k subblocks, a Feistel transformation is applied to each pair of successive subblocks, and then a permutation of the subblocks follows. This permutation affects the diffusion property of the cypher. IGFS with relatively big k and good diffusion are of particular interest for light weight applications. Suzaki and Minematsu (LNCS, 2010) study the case when one and the same permutation is applied at each round, while we consider IGFS with possibly different permutations at the different rounds. In this case we present permutation sequences yielding IGFS with the best known by now diffusion for all even k ≤ 2048. For k ≤ 16 they are found by a computer-aided search, while for 18 ≤ k ≤ 2048 we first consider several recursive constructions of a permutation sequence for k subblocks from two permutation sequences for ka< k and kb< k subblocks respectively. Using computer, we apply these constructions to obtain permutation sequences with good diffusion for each even k ≤ 2048. Finally we obtain infinite families of permutation sequences for k>2048.

The results for different k are in different files. The file DiffeeK_R_B.txt contains the results for k=K. Here R is the diffusion round of IGFS with the permutation sequence presented in the file, and B is the lower bound for the diffusion round of IGFS with k subblocks for even-odd permutations. Our results attain this bound for k = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 28, 30, 32, 48, 50, 70, 80, 112, 128, and are quite close to it for the other values of k ≤ 2048. For each even k ≤ 2048 we present here information for the results in the file DiffeeK_R_B.txt (explanations are given in the file too). Consider, for instance, the row for k=22 below: 9 8 means that the diffusion round of IGFS with the permutation sequence presented in Diffee22_9_8.txt is 9, while 8 is the lower bound, and the permutation sequence is obtained by construction 5 using the sequences for k=10 and k=12 subblocks.

k R B Construction Remark

2 2 - 2 computer computer

4 4 - 4 computer computer

6 5 - 5 computer computer

8 6 - 6 computer computer

10 6 - 6 computer computer

12 7 - 7 computer computer

14 7 - 7 computer computer

16 7 - 7 computer computer

18 8 - 8 2 2.3.3

20 8 - 8 1 2.10

22 9 - 8 5 10+12

24 9 - 8 1 2.12

26 10 - 8 3 12+14

28 9 - 9 1 2.14

30 9 - 9 2 2.3.5

32 9 - 9 1 2.16

34 10 - 9 4 16+18

36 10 - 9 1 2.18

38 11 - 9 3 18+20

40 10 - 9 1 2.20

42 10 - 9 2 2.3.7

44 11 - 10 1 2.22

46 12 - 10 3 22+24

48 10 - 10 2 2.3.8

50 10 - 10 2 2.5.5

52 12 - 10 1 2.26

54 11 - 10 2 2.3.9

56 11 - 10 1 2.28

58 12 - 10 3 28+30

60 11 - 10 1 2.30

62 12 - 10 3 30+32

64 11 - 10 1 2.32

66 12 - 10 2 2.3.11

68 12 - 10 1 2.34

70 11 - 11 2 2.5.7

72 12 - 11 1 2.36

74 13 - 11 4 36+38

76 13 - 11 1 2.38

78 13 - 11 2 2.3.13

80 11 - 11 2 2.5.8

82 13 - 11 3 40+42

84 12 - 11 1 2.42

86 13 - 11 5 42+44

88 13 - 11 1 2.44

90 12 - 11 2 2.3.15

92 14 - 11 1 2.46

94 14 - 11 6 46+48

96 12 - 11 1 2.48

98 12 - 11 2 2.7.7

100 12 - 11 1 2.50

102 13 - 11 2 2.3.17

104 14 - 11 1 2.52

106 15 - 11 3 52+54

108 13 - 11 1 2.54

110 13 - 11 2 2.5.11

112 12 - 12 2 2.7.8

114 14 - 12 2 2.3.19

116 14 - 12 1 2.58

118 14 - 12 6 58+60

120 13 - 12 1 2.60

122 14 - 12 4 60+62

124 14 - 12 1 2.62

126 13 - 12 2 2.3.21

128 12 - 12 2 2.8.8

130 14 - 12 2 2.5.13

132 14 - 12 1 2.66

134 15 - 12 3 66+68

136 14 - 12 1 2.68

138 15 - 12 3 68+70

140 13 - 12 1 2.70

142 14 - 12 5 70+72

144 13 - 12 2 2.3.24

146 15 - 12 4 72+74

148 15 - 12 1 2.74

150 13 - 12 2 2.3.25

152 15 - 12 1 2.76

154 14 - 12 2 2.7.11

156 15 - 12 1 2.78

158 15 - 12 6 78+80

160 13 - 12 1 2.80

162 14 - 12 2 2.3.27

164 15 - 12 1 2.82

166 15 - 12 6 82+84

168 14 - 12 1 2.84

170 14 - 12 2 2.5.17

172 15 - 12 1 2.86

174 15 - 12 2 2.3.29

176 14 - 12 2 2.8.11

178 16 - 12 3 88+90

180 14 - 13 1 2.90

182 15 - 13 2 2.7.13

184 16 - 13 1 2.92

186 15 - 13 2 2.3.31

188 16 - 13 1 2.94

190 15 - 13 2 2.5.19

192 14 - 13 1 2.96

194 15 - 13 3 96+98

196 14 - 13 1 2.98

198 15 - 13 3 98+100

200 14 - 13 1 2.100

202 15 - 13 4 100+102

204 15 - 13 1 2.102

206 16 - 13 5 102+104

208 15 - 13 2 2.8.13

210 14 - 13 2 2.3.35

212 17 - 13 1 2.106

214 17 - 13 6 106+108

216 15 - 13 1 2.108

218 16 - 13 3 108+110

220 15 - 13 1 2.110

222 16 - 13 3 110+112

224 14 - 13 1 2.112

226 16 - 13 4 112+114

228 16 - 13 1 2.114

230 16 - 13 2 2.5.23

232 16 - 13 1 2.116

234 16 - 13 2 2.3.39

236 16 - 13 1 2.118

238 15 - 13 2 2.7.17

240 14 - 13 2 2.3.40

242 16 - 13 2 2.11.11

244 16 - 13 1 2.122

246 16 - 13 2 2.3.41

248 16 - 13 1 2.124

250 14 - 13 2 2.5.25

252 15 - 13 1 2.126

254 16 - 13 3 126+128

256 14 - 13 1 2.128

258 16 - 13 2 2.3.43

260 16 - 13 1 2.130

262 16 - 13 7 130+132

264 16 - 13 1 2.132

266 16 - 13 2 2.7.19

268 17 - 13 1 2.134

270 15 - 13 2 2.3.45

272 15 - 13 2 2.8.17

274 17 - 13 4 136+138

276 17 - 13 1 2.138

278 17 - 13 6 138+140

280 15 - 13 1 2.140

282 16 - 13 7 140+142

284 16 - 13 1 2.142

286 17 - 13 3 142+144

288 15 - 13 1 2.144

290 16 - 14 2 2.5.29

292 17 - 14 1 2.146

294 15 - 14 2 2.3.49

296 17 - 14 1 2.148

298 18 - 14 3 148+150

300 15 - 14 1 2.150

302 17 - 14 5 150+152

304 16 - 14 2 2.8.19

306 16 - 14 2 2.3.51

308 16 - 14 1 2.154

310 16 - 14 2 2.5.31

312 17 - 14 1 2.156

314 18 - 14 3 156+158

316 17 - 14 1 2.158

318 17 - 14 7 158+160

320 15 - 14 1 2.160

322 16 - 14 4 160+162

324 16 - 14 1 2.162

326 17 - 14 5 162+164

328 17 - 14 1 2.164

330 16 - 14 2 2.3.55

332 17 - 14 1 2.166

334 17 - 14 7 166+168

336 15 - 14 2 2.3.56

338 17 - 14 3 168+170

340 16 - 14 1 2.170

342 17 - 14 2 2.3.57

344 17 - 14 1 2.172

346 18 - 14 3 172+174

348 17 - 14 1 2.174

350 15 - 14 2 2.5.35

352 16 - 14 1 2.176

354 17 - 14 2 2.3.59

356 18 - 14 1 2.178

358 18 - 14 6 178+180

360 16 - 14 1 2.180

362 17 - 14 4 180+182

364 17 - 14 1 2.182

366 17 - 14 2 2.3.61

368 17 - 14 2 2.8.23

370 17 - 14 2 2.5.37

372 17 - 14 1 2.186

374 17 - 14 2 2.11.17

376 18 - 14 1 2.188

378 16 - 14 2 2.3.63

380 17 - 14 1 2.190

382 17 - 14 6 190+192

384 15 - 14 2 2.3.64

386 17 - 14 4 192+194

388 17 - 14 1 2.194

390 17 - 14 2 2.3.65

392 16 - 14 1 2.196

394 17 - 14 4 196+198

396 17 - 14 1 2.198

398 17 - 14 6 198+200

400 15 - 14 2 2.5.40

402 17 - 14 4 200+202

404 17 - 14 1 2.202

406 17 - 14 2 2.7.29

408 17 - 14 1 2.204

410 17 - 14 2 2.5.41

412 18 - 14 1 2.206

414 18 - 14 2 2.3.69

416 17 - 14 1 2.208

418 17 - 14 6 208+210

420 16 - 14 1 2.210

422 19 - 14 5 210+212

424 19 - 14 1 2.212

426 17 - 14 2 2.3.71

428 19 - 14 1 2.214

430 17 - 14 2 2.5.43

432 16 - 14 2 2.3.72

434 17 - 14 2 2.7.31

436 18 - 14 1 2.218

438 18 - 14 2 2.3.73

440 17 - 14 1 2.220

442 18 - 14 2 2.13.17

444 18 - 14 1 2.222

446 18 - 14 6 222+224

448 16 - 14 1 2.224

450 16 - 14 2 2.3.75

452 18 - 14 1 2.226

454 18 - 14 7 226+228

456 18 - 14 1 2.228

458 19 - 14 3 228+230

460 18 - 14 1 2.230

462 17 - 14 2 2.3.77

464 17 - 14 2 2.8.29

466 19 - 14 3 232+234

468 18 - 15 1 2.234

470 18 - 15 2 2.5.47

472 18 - 15 1 2.236

474 18 - 15 2 2.3.79

476 17 - 15 1 2.238

478 18 - 15 3 238+240

480 16 - 15 1 2.240

482 18 - 15 7 240+242

484 18 - 15 1 2.242

486 17 - 15 2 2.3.81

488 18 - 15 1 2.244

490 16 - 15 2 2.5.49

492 18 - 15 1 2.246

494 18 - 15 7 246+248

496 17 - 15 2 2.8.31

498 18 - 15 2 2.3.83

500 16 - 15 1 2.250

502 17 - 15 5 250+252

504 17 - 15 1 2.252

506 18 - 15 4 252+254

508 18 - 15 1 2.254

510 17 - 15 2 2.3.85

512 16 - 15 1 2.256

514 18 - 15 7 256+258

516 18 - 15 1 2.258

518 18 - 15 2 2.7.37

520 18 - 15 1 2.260

522 18 - 15 2 2.3.87

524 18 - 15 1 2.262

526 19 - 15 3 262+264

528 17 - 15 2 2.3.88

530 19 - 15 3 264+266

532 18 - 15 1 2.266

534 19 - 15 2 2.3.89

536 19 - 15 1 2.268

538 20 - 15 3 268+270

540 17 - 15 1 2.270

542 18 - 15 3 270+272

544 17 - 15 1 2.272

546 18 - 15 2 2.3.91

548 19 - 15 1 2.274

550 17 - 15 2 2.5.55

552 19 - 15 1 2.276

554 20 - 15 3 276+278

556 19 - 15 1 2.278

558 18 - 15 2 2.3.93

560 16 - 15 2 2.5.56

562 18 - 15 7 280+282

564 18 - 15 1 2.282

566 18 - 15 7 282+284

568 18 - 15 1 2.284

570 18 - 15 2 2.3.95

572 19 - 15 1 2.286

574 18 - 15 2 2.7.41

576 17 - 15 1 2.288

578 18 - 15 2 2.17.17

580 18 - 15 1 2.290

582 18 - 15 2 2.3.97

584 19 - 15 1 2.292

586 20 - 15 3 292+294

588 17 - 15 1 2.294

590 18 - 15 2 2.5.59

592 18 - 15 2 2.8.37

594 18 - 15 2 2.3.99

596 20 - 15 1 2.298

598 20 - 15 2 2.13.23

600 17 - 15 1 2.300

602 18 - 15 2 2.7.43

604 19 - 15 1 2.302

606 18 - 15 2 2.3.101

608 18 - 15 1 2.304

610 18 - 15 2 2.5.61

612 18 - 15 1 2.306

614 19 - 15 3 306+308

616 18 - 15 1 2.308

618 19 - 15 3 308+310

620 18 - 15 1 2.310

622 19 - 15 5 310+312

624 18 - 15 2 2.3.104

626 20 - 15 4 312+314

628 20 - 15 1 2.314

630 17 - 15 2 2.3.105

632 19 - 15 1 2.316

634 20 - 15 3 316+318

636 19 - 15 1 2.318

638 19 - 15 2 2.11.29

640 16 - 15 2 2.5.64

642 18 - 15 4 320+322

644 18 - 15 1 2.322

646 19 - 15 3 322+324

648 18 - 15 1 2.324

650 18 - 15 2 2.5.65

652 19 - 15 1 2.326

654 19 - 15 2 2.3.109

656 18 - 15 2 2.8.41

658 19 - 15 2 2.7.47

660 18 - 15 1 2.330

662 19 - 15 5 330+332

664 19 - 15 1 2.332

666 19 - 15 2 2.3.111

668 19 - 15 1 2.334

670 19 - 15 2 2.5.67

672 17 - 15 1 2.336

674 19 - 15 4 336+338

676 19 - 15 1 2.338

678 19 - 15 2 2.3.113

680 18 - 15 1 2.340

682 19 - 15 2 2.11.31

684 19 - 15 1 2.342

686 17 - 15 2 2.7.49

688 18 - 15 2 2.8.43

690 19 - 15 2 2.3.115

692 20 - 15 1 2.346

694 20 - 15 6 346+348

696 19 - 15 1 2.348

698 20 - 15 3 348+350

700 17 - 15 1 2.350

702 18 - 15 5 350+352

704 18 - 15 1 2.352

706 19 - 15 7 352+354

708 19 - 15 1 2.354

710 18 - 15 2 2.5.71

712 20 - 15 1 2.356

714 18 - 15 2 2.3.119

716 20 - 15 1 2.358

718 20 - 15 7 358+360

720 17 - 15 2 2.3.120

722 19 - 15 4 360+362

724 19 - 15 1 2.362

726 19 - 15 2 2.3.121

728 19 - 15 1 2.364

730 19 - 15 2 2.5.73

732 19 - 15 1 2.366

734 19 - 15 7 366+368

736 19 - 15 1 2.368

738 19 - 15 2 2.3.123

740 19 - 15 1 2.370

742 19 - 15 7 370+372

744 19 - 15 1 2.372

746 20 - 15 3 372+374

748 19 - 15 1 2.374

750 17 - 15 2 2.3.125

752 19 - 15 2 2.8.47

754 20 - 15 2 2.13.29

756 18 - 16 1 2.378

758 19 - 16 5 378+380

760 19 - 16 1 2.380

762 19 - 16 2 2.3.127

764 19 - 16 1 2.382

766 19 - 16 7 382+384

768 17 - 16 1 2.384

770 18 - 16 2 2.5.77

772 19 - 16 1 2.386

774 19 - 16 2 2.3.129

776 19 - 16 1 2.388

778 20 - 16 3 388+390

780 19 - 16 1 2.390

782 19 - 16 6 390+392

784 17 - 16 2 2.7.56

786 19 - 16 2 2.3.131

788 19 - 16 1 2.394

790 19 - 16 2 2.5.79

792 19 - 16 1 2.396

794 20 - 16 3 396+398

796 19 - 16 1 2.398

798 19 - 16 2 2.3.133

800 17 - 16 1 2.400

802 19 - 16 4 400+402

804 19 - 16 1 2.402

806 20 - 16 3 402+404

808 19 - 16 1 2.404

810 18 - 16 2 2.3.135

812 19 - 16 1 2.406

814 19 - 16 7 406+408

816 18 - 16 2 2.3.136

818 20 - 16 3 408+410

820 19 - 16 1 2.410

822 20 - 16 2 2.3.137

824 20 - 16 1 2.412

826 19 - 16 2 2.7.59

828 20 - 16 1 2.414

830 19 - 16 2 2.5.83

832 19 - 16 1 2.416

834 20 - 16 3 416+418

836 19 - 16 1 2.418

838 19 - 16 7 418+420

840 18 - 16 1 2.420

842 21 - 16 7 420+422

844 21 - 16 1 2.422

846 19 - 16 2 2.3.141

848 20 - 16 2 2.8.53

850 18 - 16 2 2.5.85

852 19 - 16 1 2.426

854 19 - 16 2 2.7.61

856 21 - 16 1 2.428

858 20 - 16 2 2.3.143

860 19 - 16 1 2.430

862 20 - 16 3 430+432

864 18 - 16 1 2.432

866 19 - 16 4 432+434

868 19 - 16 1 2.434

870 19 - 16 2 2.3.145

872 20 - 16 1 2.436

874 21 - 16 3 436+438

876 20 - 16 1 2.438

878 20 - 16 6 438+440

880 18 - 16 2 2.5.88

882 18 - 16 2 2.3.147

884 20 - 16 1 2.442

886 21 - 16 3 442+444

888 20 - 16 1 2.444

890 20 - 16 2 2.5.89

892 20 - 16 1 2.446

894 20 - 16 7 446+448

896 17 - 16 2 2.7.64

898 19 - 16 3 448+450

900 18 - 16 1 2.450

902 20 - 16 2 2.11.41

904 20 - 16 1 2.452

906 20 - 16 2 2.3.151

908 20 - 16 1 2.454

910 19 - 16 2 2.5.91

912 19 - 16 2 2.3.152

914 21 - 16 4 456+458

916 21 - 16 1 2.458

918 19 - 16 2 2.3.153

920 20 - 16 1 2.460

922 21 - 16 3 460+462

924 19 - 16 1 2.462

926 20 - 16 3 462+464

928 19 - 16 1 2.464

930 19 - 16 2 2.3.155

932 21 - 16 1 2.466

934 21 - 16 6 466+468

936 20 - 16 1 2.468

938 20 - 16 2 2.7.67

940 20 - 16 1 2.470

942 20 - 16 7 470+472

944 19 - 16 2 2.8.59

946 20 - 16 2 2.11.43

948 20 - 16 1 2.474

950 19 - 16 2 2.5.95

952 19 - 16 1 2.476

954 20 - 16 2 2.3.159

956 20 - 16 1 2.478

958 20 - 16 6 478+480

960 18 - 16 1 2.480

962 20 - 16 7 480+482

964 20 - 16 1 2.482

966 19 - 16 2 2.3.161

968 20 - 16 1 2.484

970 19 - 16 2 2.5.97

972 19 - 16 1 2.486

974 20 - 16 5 486+488

976 19 - 16 2 2.8.61

978 20 - 16 2 2.3.163

980 18 - 16 1 2.490

982 20 - 16 5 490+492

984 20 - 16 1 2.492

986 20 - 16 2 2.17.29

988 20 - 16 1 2.494

990 19 - 16 2 2.3.165

992 19 - 16 1 2.496

994 19 - 16 2 2.7.71

996 20 - 16 1 2.498

998 20 - 16 7 498+500

1000 18 - 16 1 2.500

1002 19 - 16 7 500+502

1004 19 - 16 1 2.502

1006 20 - 16 3 502+504

1008 18 - 16 2 2.3.168

1010 19 - 16 2 2.5.101

1012 20 - 16 1 2.506

1014 20 - 16 2 2.3.169

1016 20 - 16 1 2.508

1018 21 - 16 3 508+510

1020 19 - 16 1 2.510

1022 20 - 16 3 510+512

1024 17 - 16 2 2.8.64

1026 20 - 16 2 2.3.171

1028 20 - 16 1 2.514

1030 20 - 16 2 2.5.103

1032 20 - 16 1 2.516

1034 21 - 16 3 516+518

1036 20 - 16 1 2.518

1038 20 - 16 7 518+520

1040 19 - 16 2 2.5.104

1042 21 - 16 3 520+522

1044 20 - 16 1 2.522

1046 20 - 16 7 522+524

1048 20 - 16 1 2.524

1050 18 - 16 2 2.3.175

1052 21 - 16 1 2.526

1054 20 - 16 2 2.17.31

1056 19 - 16 1 2.528

1058 21 - 16 4 528+530

1060 21 - 16 1 2.530

1062 20 - 16 2 2.3.177

1064 20 - 16 1 2.532

1066 21 - 16 2 2.13.41

1068 21 - 16 1 2.534

1070 21 - 16 2 2.5.107

1072 20 - 16 2 2.8.67

1074 21 - 16 2 2.3.179

1076 22 - 16 1 2.538

1078 19 - 16 2 2.7.77

1080 19 - 16 1 2.540

1082 20 - 16 4 540+542

1084 20 - 16 1 2.542

1086 20 - 16 2 2.3.181

1088 19 - 16 1 2.544

1090 20 - 16 2 2.5.109

1092 20 - 16 1 2.546

1094 21 - 16 5 546+548

1096 21 - 16 1 2.548

1098 20 - 16 2 2.3.183

1100 19 - 16 1 2.550

1102 21 - 16 2 2.19.29

1104 20 - 16 2 2.3.184

1106 20 - 16 2 2.7.79

1108 22 - 16 1 2.554

1110 20 - 16 2 2.3.185

1112 21 - 16 1 2.556

1114 22 - 16 3 556+558

1116 20 - 16 1 2.558

1118 20 - 16 6 558+560

1120 18 - 16 1 2.560

1122 20 - 16 2 2.3.187

1124 20 - 16 1 2.562

1126 21 - 16 3 562+564

1128 20 - 16 1 2.564

1130 20 - 16 2 2.5.113

1132 20 - 16 1 2.566

1134 19 - 16 2 2.3.189

1136 19 - 16 2 2.8.71

1138 21 - 16 3 568+570

1140 20 - 16 1 2.570

1142 21 - 16 5 570+572

1144 21 - 16 1 2.572

1146 20 - 16 2 2.3.191

1148 20 - 16 1 2.574

1150 20 - 16 2 2.5.115

1152 18 - 16 2 2.3.192

1154 20 - 16 4 576+578

1156 20 - 16 1 2.578

1158 20 - 16 2 2.3.193

1160 20 - 16 1 2.580

1162 20 - 16 2 2.7.83

1164 20 - 16 1 2.582

1166 21 - 16 5 582+584

1168 20 - 16 2 2.8.73

1170 20 - 16 2 2.3.195

1172 22 - 16 1 2.586

1174 22 - 16 6 586+588

1176 19 - 16 1 2.588

1178 20 - 16 7 588+590

1180 20 - 16 1 2.590

1182 20 - 16 2 2.3.197

1184 20 - 16 1 2.592

1186 20 - 16 7 592+594

1188 20 - 16 1 2.594

1190 19 - 16 2 2.5.119

1192 22 - 16 1 2.596

1194 20 - 16 2 2.3.199

1196 22 - 16 1 2.598

1198 22 - 16 6 598+600

1200 18 - 16 2 2.3.200

1202 20 - 16 7 600+602

1204 20 - 16 1 2.602

1206 20 - 16 2 2.3.201

1208 21 - 16 1 2.604

1210 20 - 16 2 2.5.121

1212 20 - 16 1 2.606

1214 21 - 16 3 606+608

1216 20 - 16 1 2.608

1218 20 - 16 2 2.3.203

1220 20 - 16 1 2.610

1222 20 - 17 7 610+612

1224 20 - 17 1 2.612

1226 21 - 17 4 612+614

1228 21 - 17 1 2.614

1230 20 - 17 2 2.3.205

1232 19 - 17 2 2.7.88

1234 21 - 17 4 616+618

1236 21 - 17 1 2.618

1238 21 - 17 6 618+620

1240 20 - 17 1 2.620

1242 21 - 17 2 2.3.207

1244 21 - 17 1 2.622

1246 21 - 17 2 2.7.89

1248 20 - 17 1 2.624

1250 18 - 17 2 2.5.125

1252 22 - 17 1 2.626

1254 20 - 17 2 2.3.209

1256 22 - 17 1 2.628

1258 21 - 17 2 2.17.37

1260 19 - 17 1 2.630

1262 21 - 17 5 630+632

1264 20 - 17 2 2.8.79

1266 22 - 17 2 2.3.211

1268 22 - 17 1 2.634

1270 20 - 17 2 2.5.127

1272 21 - 17 1 2.636

1274 20 - 17 2 2.7.91

1276 21 - 17 1 2.638

1278 20 - 17 2 2.3.213

1280 18 - 17 1 2.640

1282 20 - 17 4 640+642

1284 20 - 17 1 2.642

1286 21 - 17 3 642+644

1288 20 - 17 1 2.644

1290 20 - 17 2 2.3.215

1292 21 - 17 1 2.646

1294 21 - 17 6 646+648

1296 19 - 17 2 2.3.216

1298 21 - 17 3 648+650

1300 20 - 17 1 2.650

1302 20 - 17 2 2.3.217

1304 21 - 17 1 2.652

1306 22 - 17 3 652+654

1308 21 - 17 1 2.654

1310 20 - 17 2 2.5.131

1312 20 - 17 1 2.656

1314 21 - 17 2 2.3.219

1316 21 - 17 1 2.658

1318 21 - 17 7 658+660

1320 20 - 17 1 2.660

1322 21 - 17 7 660+662

1324 21 - 17 1 2.662

1326 21 - 17 2 2.3.221

1328 20 - 17 2 2.8.83

1330 20 - 17 2 2.5.133

1332 21 - 17 1 2.666

1334 21 - 17 7 666+668

1336 21 - 17 1 2.668

1338 21 - 17 2 2.3.223

1340 21 - 17 1 2.670

1342 21 - 17 2 2.11.61

1344 19 - 17 1 2.672

1346 21 - 17 4 672+674

1348 21 - 17 1 2.674

1350 19 - 17 2 2.3.225

1352 21 - 17 1 2.676

1354 22 - 17 3 676+678

1356 21 - 17 1 2.678

1358 20 - 17 2 2.7.97

1360 19 - 17 2 2.5.136

1362 21 - 17 2 2.3.227

1364 21 - 17 1 2.682

1366 21 - 17 7 682+684

1368 21 - 17 1 2.684

1370 21 - 17 2 2.5.137

1372 19 - 17 1 2.686

1374 20 - 17 7 686+688

1376 20 - 17 1 2.688

1378 21 - 17 4 688+690

1380 21 - 17 1 2.690

1382 22 - 17 5 690+692

1384 22 - 17 1 2.692

1386 20 - 17 2 2.3.231

1388 22 - 17 1 2.694

1390 21 - 17 2 2.5.139

1392 20 - 17 2 2.3.232

1394 21 - 17 2 2.17.41

1396 22 - 17 1 2.698

1398 22 - 17 2 2.3.233

1400 19 - 17 1 2.700

1402 20 - 17 7 700+702

1404 20 - 17 1 2.702

1406 21 - 17 3 702+704

1408 19 - 17 2 2.8.88

1410 20 - 17 2 2.5.141

1412 21 - 17 1 2.706

1414 20 - 17 2 2.7.101

1416 21 - 17 1 2.708

1418 22 - 17 3 708+710

1420 20 - 17 1 2.710

1422 21 - 17 2 2.3.237

1424 21 - 17 2 2.8.89

1426 22 - 17 2 2.23.31

1428 20 - 17 1 2.714

1430 21 - 17 2 2.5.143

1432 22 - 17 1 2.716

1434 21 - 17 2 2.3.239

1436 22 - 17 1 2.718

1438 22 - 17 7 718+720

1440 19 - 17 1 2.720

1442 21 - 17 2 2.7.103

1444 21 - 17 1 2.722

1446 21 - 17 2 2.3.241

1448 21 - 17 1 2.724

1450 20 - 17 2 2.5.145

1452 21 - 17 1 2.726

1454 22 - 17 3 726+728

1456 20 - 17 2 2.7.104

1458 20 - 17 2 2.3.243

1460 21 - 17 1 2.730

1462 21 - 17 2 2.17.43

1464 21 - 17 1 2.732

1466 22 - 17 3 732+734

1468 21 - 17 1 2.734

1470 19 - 17 2 2.3.245

1472 21 - 17 1 2.736

1474 22 - 17 3 736+738

1476 21 - 17 1 2.738

1478 21 - 17 7 738+740

1480 21 - 17 1 2.740

1482 21 - 17 2 2.3.247

1484 21 - 17 1 2.742

1486 22 - 17 3 742+744

1488 20 - 17 2 2.3.248

1490 22 - 17 2 2.5.149

1492 22 - 17 1 2.746

1494 21 - 17 2 2.3.249

1496 21 - 17 1 2.748

1498 22 - 17 3 748+750

1500 19 - 17 1 2.750

1502 21 - 17 7 750+752

1504 21 - 17 1 2.752

1506 20 - 17 2 2.3.251

1508 22 - 17 1 2.754

1510 21 - 17 2 2.5.151

1512 20 - 17 1 2.756

1514 21 - 17 7 756+758

1516 21 - 17 1 2.758

1518 21 - 17 2 2.3.253

1520 20 - 17 2 2.5.152

1522 22 - 17 3 760+762

1524 21 - 17 1 2.762

1526 21 - 17 2 2.7.109

1528 21 - 17 1 2.764

1530 20 - 17 2 2.3.255

1532 21 - 17 1 2.766

1534 21 - 17 7 766+768

1536 19 - 17 1 2.768

1538 20 - 17 7 768+770

1540 20 - 17 1 2.770

1542 21 - 17 2 2.3.257

1544 21 - 17 1 2.772

1546 22 - 17 3 772+774

1548 21 - 17 1 2.774

1550 20 - 17 2 2.5.155

1552 20 - 17 2 2.8.97

1554 21 - 17 2 2.3.259

1556 22 - 17 1 2.778

1558 22 - 17 2 2.19.41

1560 21 - 17 1 2.780

1562 21 - 17 2 2.11.71

1564 21 - 17 1 2.782

1566 21 - 17 2 2.3.261

1568 19 - 17 1 2.784

1570 21 - 17 7 784+786

1572 21 - 17 1 2.786

1574 22 - 17 3 786+788

1576 21 - 17 1 2.788

1578 22 - 17 3 788+790

1580 21 - 17 1 2.790

1582 21 - 17 2 2.7.113

1584 20 - 17 2 2.3.264

1586 22 - 17 2 2.13.61

1588 22 - 17 1 2.794

1590 21 - 17 2 2.5.159

1592 21 - 17 1 2.796

1594 22 - 17 3 796+798

1596 21 - 17 1 2.798

1598 21 - 17 6 798+800

1600 19 - 17 1 2.800

1602 21 - 17 4 800+802

1604 21 - 17 1 2.802

1606 22 - 17 3 802+804

1608 21 - 17 1 2.804

1610 20 - 17 2 2.5.161

1612 22 - 17 1 2.806

1614 22 - 17 6 806+808

1616 20 - 17 2 2.8.101

1618 22 - 17 3 808+810

1620 20 - 17 1 2.810

1622 21 - 17 5 810+812

1624 21 - 17 1 2.812

1626 21 - 17 2 2.3.271

1628 21 - 17 1 2.814

1630 21 - 17 2 2.5.163

1632 20 - 17 1 2.816

1634 22 - 17 2 2.19.43

1636 22 - 17 1 2.818

1638 21 - 17 2 2.3.273

1640 21 - 17 1 2.820

1642 22 - 17 4 820+822

1644 22 - 17 1 2.822

1646 22 - 17 7 822+824

1648 21 - 17 2 2.8.103

1650 20 - 17 2 2.3.275

1652 21 - 17 1 2.826

1654 22 - 17 5 826+828

1656 22 - 17 1 2.828

1658 23 - 17 3 828+830

1660 21 - 17 1 2.830

1662 21 - 17 7 830+832

1664 20 - 17 2 2.8.104

1666 20 - 17 2 2.7.119

1668 22 - 17 1 2.834

1670 21 - 17 2 2.5.167

1672 21 - 17 1 2.836

1674 21 - 17 2 2.3.279

1676 21 - 17 1 2.838

1678 21 - 17 7 838+840

1680 19 - 17 2 2.3.280

1682 22 - 17 2 2.29.29

1684 23 - 17 1 2.842

1686 21 - 17 2 2.3.281

1688 23 - 17 1 2.844

1690 21 - 17 2 2.5.169

1692 21 - 17 1 2.846

1694 21 - 17 2 2.7.121

1696 22 - 17 1 2.848

1698 21 - 17 2 2.3.283

1700 20 - 17 1 2.850

1702 21 - 17 5 850+852

1704 21 - 17 1 2.852

1706 22 - 17 3 852+854

1708 21 - 17 1 2.854

1710 21 - 17 2 2.3.285

1712 22 - 17 2 2.8.107

1714 24 - 17 3 856+858

1716 22 - 17 1 2.858

1718 22 - 17 6 858+860

1720 21 - 17 1 2.860

1722 21 - 17 2 2.3.287

1724 22 - 17 1 2.862

1726 22 - 17 6 862+864

1728 20 - 17 1 2.864

1730 21 - 17 4 864+866

1732 21 - 17 1 2.866

1734 21 - 17 2 2.3.289

1736 21 - 17 1 2.868

1738 22 - 17 3 868+870

1740 21 - 17 1 2.870

1742 22 - 17 5 870+872

1744 21 - 17 2 2.8.109

1746 21 - 17 2 2.3.291

1748 23 - 17 1 2.874

1750 19 - 17 2 2.5.175

1752 22 - 17 1 2.876

1754 23 - 17 3 876+878

1756 22 - 17 1 2.878

1758 22 - 17 7 878+880

1760 20 - 17 1 2.880

1762 21 - 17 3 880+882

1764 20 - 17 1 2.882

1766 22 - 17 5 882+884

1768 22 - 17 1 2.884

1770 21 - 17 2 2.3.295

1772 23 - 17 1 2.886

1774 23 - 17 6 886+888

1776 21 - 17 2 2.3.296

1778 21 - 17 2 2.7.127

1780 22 - 17 1 2.890

1782 21 - 17 2 2.3.297

1784 22 - 17 1 2.892

1786 23 - 17 3 892+894

1788 22 - 17 1 2.894

1790 22 - 17 2 2.5.179

1792 19 - 17 1 2.896

1794 21 - 17 4 896+898

1796 21 - 17 1 2.898

1798 21 - 17 6 898+900

1800 20 - 17 1 2.900

1802 22 - 17 4 900+902

1804 22 - 17 1 2.902

1806 21 - 17 2 2.3.301

1808 21 - 17 2 2.8.113

1810 21 - 17 2 2.5.181

1812 22 - 17 1 2.906

1814 23 - 17 3 906+908

1816 22 - 17 1 2.908

1818 21 - 17 2 2.3.303

1820 21 - 17 1 2.910

1822 21 - 17 7 910+912

1824 21 - 17 1 2.912

1826 22 - 17 2 2.11.83

1828 23 - 17 1 2.914

1830 21 - 17 2 2.3.305

1832 23 - 17 1 2.916

1834 21 - 17 2 2.7.131

1836 21 - 17 1 2.918

1838 22 - 17 5 918+920

1840 21 - 17 2 2.5.184

1842 22 - 17 2 2.3.307

1844 23 - 17 1 2.922

1846 22 - 17 2 2.13.71

1848 21 - 17 1 2.924

1850 21 - 17 2 2.5.185

1852 22 - 17 1 2.926

1854 22 - 17 2 2.3.309

1856 21 - 17 1 2.928

1858 22 - 17 3 928+930

1860 21 - 17 1 2.930

1862 21 - 17 2 2.7.133

1864 23 - 17 1 2.932

1866 22 - 17 2 2.3.311

1868 23 - 17 1 2.934

1870 21 - 17 2 2.5.187

1872 21 - 17 2 2.3.312

1874 23 - 17 3 936+938

1876 22 - 17 1 2.938

1878 22 - 17 7 938+940

1880 22 - 17 1 2.940

1882 23 - 17 3 940+942

1884 22 - 17 1 2.942

1886 23 - 17 3 942+944

1888 21 - 17 1 2.944

1890 20 - 17 2 2.3.315

1892 22 - 17 1 2.946

1894 23 - 17 3 946+948

1896 22 - 17 1 2.948

1898 23 - 17 3 948+950

1900 21 - 17 1 2.950

1902 21 - 17 7 950+952

1904 20 - 17 2 2.7.136

1906 22 - 17 7 952+954

1908 22 - 17 1 2.954

1910 21 - 17 2 2.5.191

1912 22 - 17 1 2.956

1914 22 - 17 2 2.3.319

1916 22 - 17 1 2.958

1918 22 - 17 2 2.7.137

1920 19 - 17 2 2.3.320

1922 22 - 17 2 2.31.31

1924 22 - 17 1 2.962

1926 21 - 17 2 2.3.321

1928 22 - 17 1 2.964

1930 21 - 17 2 2.5.193

1932 21 - 17 1 2.966

1934 22 - 17 5 966+968

1936 21 - 17 2 2.8.121

1938 22 - 17 2 2.3.323

1940 21 - 17 1 2.970

1942 21 - 17 7 970+972

1944 21 - 17 1 2.972

1946 22 - 17 2 2.7.139

1948 22 - 17 1 2.974

1950 21 - 17 2 2.3.325

1952 21 - 17 1 2.976

1954 22 - 17 7 976+978

1956 22 - 17 1 2.978

1958 23 - 17 3 978+980

1960 20 - 17 1 2.980

1962 22 - 17 2 2.3.327

1964 22 - 17 1 2.982

1966 23 - 17 3 982+984

1968 21 - 17 2 2.3.328

1970 21 - 17 2 2.5.197

1972 22 - 17 1 2.986

1974 21 - 17 2 2.7.141

1976 22 - 18 1 2.988

1978 23 - 18 3 988+990

1980 21 - 18 1 2.990

1982 22 - 18 3 990+992

1984 21 - 18 1 2.992

1986 22 - 18 3 992+994

1988 21 - 18 1 2.994

1990 21 - 18 2 2.5.199

1992 22 - 18 1 2.996

1994 23 - 18 3 996+998

1996 22 - 18 1 2.998

1998 22 - 18 2 2.3.333

2000 19 - 18 2 2.5.200

2002 21 - 18 7 1000+1002

2004 21 - 18 1 2.1002

2006 21 - 18 7 1002+1004

2008 21 - 18 1 2.1004

2010 21 - 18 2 2.5.201

2012 22 - 18 1 2.1006

2014 22 - 18 6 1006+1008

2016 20 - 18 1 2.1008

2018 21 - 18 4 1008+1010

2020 21 - 18 1 2.1010

2022 22 - 18 2 2.3.337

2024 22 - 18 1 2.1012

2026 23 - 18 3 1012+1014

2028 22 - 18 1 2.1014

2030 21 - 18 2 2.5.203

2032 21 - 18 2 2.8.127

2034 22 - 18 2 2.3.339

2036 23 - 18 1 2.1018

2038 23 - 18 6 1018+1020

2040 21 - 18 1 2.1020

2042 22 - 18 4 1020+1022

2044 22 - 18 1 2.1022

2046 22 - 18 2 2.3.341

2048 19 - 18 1 2.1024