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