The Table below illustrates that the
*PRIMES always emerge in the
same 8 positions of the Cycle (left).
*PRIMES always emerge in the
same 8 positions of the Cycle (left).
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*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).
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.
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
(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
Copyright (c) 2000-2005 by M.Winkler