The Table below illustrates that the
*PRIMES always emerge in the
same 8 positions of the Cycle (left).  
0
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
90
 91
 92
 93
 94
 95
 96
 97
 98
 99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 ...
*With  the exception of the Elemental Numbers, '2', '3', and '5'.
The Calculations shown below illustrate that all composites in the same 8 positions
as the primes are products of previously emerging primes (the products of the
primes in the 1st cycle account for all composites in the 2nd through 7th cycles).
7 x 7 = 49   7 x 11 = 77   7 x 13 = 91   7 x 17 = 119   7 x 19 = 133   7 x 23 = 161   7 x 29 = 203   7 x 31 = 217   7 x 37 = 259   7 x 41 = 287   7 x 43 = 301   7 x 47 = 329   7 x 53 = 371  7 x 59 = 413  ...

11 x 11 = 121   11 x 13 = 143   11 x 17 = 187   11 x 19 = 209   11 x 23 = 253   11 x 29 = 319   11 x 31 = 341   11 x 37 = 407  ...

13 x 13 = 169   13 x 17 = 221   13 x 19 = 247   13 x 23 = 299   13 x 29 = 377   13 x 31 = 403  ...

17 x 17 = 289   17 x 19 = 323   17 x 23 = 391  ...

19 x 19 = 361   19 x 23 = 437  ...

Etc.
Using knowledge of the Mechanism of Distribution to generate the primes
(Demonstrated to an "arbitrary" limit of 350)


   1
  7  ------------7x7=49............................................................................................................................. (delete 49 when it appears)
11  ------------7x11=77,11x11=121..................................................................................................... (delete: 77, 121)
13  ------------7x13=91,11x13=143,13x13=169................................................................................ (delete: 91, 143, 169)
17  ------------7x17=119,11x17=187,13x17=221,17x17=289........................................................ (delete: 119, 187, 221, 289)
19  ------------7x19=133,11x19=209,13x19=247,17x19=323,19x19=above limit...................... (delete: 133, 209, 247, 323)
23  ------------7x23=161,11x23=253,13x23=299,17x23=above limit........................................... (delete: 161, 253, 299)
29  ------------7x29=203,11x29=319,13x29=above limit................................................................. (delete: 203, 319)

  1+30=31  --7x31=217,11x31=341,13x31=above limit................................................................. (delete: 217, 341)
  7+30=37  --7x37=259,11x37=above limit...................................................................................... (delete: 259)
11+30=41  --7x41=287,11x41=above limit...................................................................................... (delete: 287)
13+30=43  --7x43=301,11x43=above limit...................................................................................... (delete: 301)
17+30=47  --7x47=329,11x47=above limit...................................................................................... (delete: 329)
19+30=(49 is deleated)
23+30=53  --7x53=above limit--we have found all composites to be deleated to our arbitrary limit of 350.
 29+30=59

  1+(2x30)=61  
  7+(2x30)=67  
11+(2x30)=71  
13+(2x30)=73  
17+(2x30)=(77 is deleted)
19+(2x30)=79
23+(2x30)=83
29+(2x30)=89

  1+(3x30)=(91 is deleted)
  7+(3x30)=97
11+(3x30)=101
13+(3x30)=103
17+(3x30)=107
19+(3x30)=109
23+(3x30)=113
29+(3x30)=(119 is deleted)

  1+(4x30)=(121 is deleted)
  7+(4x30)=127
11+(4x30)=131
13+(4x30)=(133 is deleted)
17+(4x30)=137
19+(4x30)=139
23+(4x30)=(143 is deleted)
29+(4x30)=149

  1+(5x30)=151
  7+(5x30)=157
11+(5x30)=(161 is deleted)
13+(5x30)=163
17+(5x30)=167
19+(5x30)=(169 is deleted)
23+(5x30)=173
29+(5x30)=179

  1+(6x30)=181
  7+(6x30)=(187 is deleted)
11+(6x30)=191
13+(6x30)=193
17+(6x30)=197
19+(6x30)=199
23+(6x30)=(203 is deleted)
29+(6x30)=(209 is deleted)

  1+(7x30)=211
  7+(7x30)=(217 is deleted)
11+(7x30)=(221 is deleted)
13+(7x30)=223
17+(7x30)=227
19+(7x30)=229
23+(7x30)=233
29+(7x30)=239

  1+(8x30)=241
  7+(8x30)=(247 is deleted)
11+(8x30)=251
13+(8x30)=(253 is deleted)
17+(8x30)=257
19+(8x30)=(259 is deleted)
23+(8x30)=263
29+(8x30)=269

  1+(9x30)=271
  7+(9x30)=277
11+(9x30)=281
13+(9x30)=283
17+(9x30)=(287 is deleted)
19+(9x30)=(289 is deleted)
23+(9x30)=293
29+(9x30)=(299 is deleted)

  1+(10x30)=(301 is deleted)
  7+(10x30)=307
11+(10x30)=311
13+(10x30)=313
17+(10x30)=317
19+(10x30)=(319 is deleted)
23+(10x30)=(323 is deleted)
29+(10x30)=(329 is deleted)

  1+(11x30)=331
  7+(11x30)=337
11+(11x30)=(341 is deleted)
13+(11x30)=(343 is deleted)
17+(11x30)=347
19+(11x30)=349
23+(11x30)=353---above the arbitrary limit of 350
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Copyright (c) 2000-2005 by M.Winkler