User:BudjarnLambeth/Basal subgroup: Difference between revisions
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m BudjarnLambeth moved page Basal subgroup to User:BudjarnLambeth/Basal subgroup |
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''Example'': | ''Example'': | ||
The basal subgroup of '''[[edo|ed2/1]]''' | The basal subgroup of '''[[edo|ed2/1]]''' - - - BSG2/1 - - - is 2.3.5.7.11.13... ''a.k.a.'' 2/1 . 3/1 . 5/1 . 7/1 . 11/1 . 13/1... | ||
== Prime basal subgroups == | == Prime basal subgroups == | ||
| Line 18: | Line 18: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[edt|ed3/1]]''' | * The basal subgroup of '''[[edt|ed3/1]]''' - - - BSG3/1 - - - is 3/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed5|ed5/1]]''' | * The basal subgroup of '''[[ed5|ed5/1]]''' - - - BSG5/1 - - - is 5/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1... | ||
* The basal subgroup of '''[[ed7|ed7/1]]''' | * The basal subgroup of '''[[ed7|ed7/1]]''' - - - BSG7/1 - - - is 7/1 . 11/1 . 13/1 . 17/1 . 19/1 . 23/1... | ||
* The basal subgroup of '''[[ed11|ed11/1]]''' | * The basal subgroup of '''[[ed11|ed11/1]]''' - - - BSG11/1 - - - is 11/1 . 13/1 . 17/1 . 19/1 . 23/1 . 29/1... | ||
* The basal subgroup of '''[[ed13|ed13/1]]''' | * The basal subgroup of '''[[ed13|ed13/1]]''' - - - BSG13/1 - - - is 13/1 . 17/1 . 19/1 . 23/1 . 29/1 . 31/1... | ||
* The basal subgroup of '''[[ed17|ed17/1]]''' | * The basal subgroup of '''[[ed17|ed17/1]]''' - - - BSG17/1 - - - is 17/1 . 19/1 . 23/1 . 29/1 . 31/1 . 37/1... | ||
* The basal subgroup of '''[[ed19|ed19/1]]''' | * The basal subgroup of '''[[ed19|ed19/1]]''' - - - BSG19/1 - - - is 19/1 . 23/1 . 29/1 . 31/1 . 37/1 . 41/1... | ||
* The basal subgroup of '''[[ed23|ed23/1]]''' | * The basal subgroup of '''[[ed23|ed23/1]]''' - - - BSG23/1 - - - is 23/1 . 29/1 . 31/1 . 37/1 . 41/1 . 43/1... | ||
* The basal subgroup of '''[[ed29|ed29/1]]''' | * The basal subgroup of '''[[ed29|ed29/1]]''' - - - BSG29/1 - - - is 29/1 . 31/1 . 37/1 . 41/1 . 43/1 . 47/1... | ||
''and so on...'' | ''and so on...'' | ||
=== ed3/2, ed5/2, ed7/2, ed11/2... === | === ed3/2, ed5/2, ed7/2, ed11/2... === | ||
A.k.a. "[[half-prime subgroup]]s". | A.k.a. "[[half-prime subgroup]]s". | ||
To find BSGn/2: | To find BSGn/2: | ||
| Line 39: | Line 38: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed3/2]]''' | * The basal subgroup of '''[[ed3/2]]''' - - - BSG3/2 - - - is 3/2 . 5/2 . 7/2 . 11/2 . 13/2 . 17/2... | ||
* The basal subgroup of '''[[ed5/2]]''' | * The basal subgroup of '''[[ed5/2]]''' - - - BSG5/2 - - - is 5/2 . 7/2 . 11/2 . 13/2 . 17/2 . 19/2... | ||
* The basal subgroup of '''[[ed7/2]]''' | * The basal subgroup of '''[[ed7/2]]''' - - - BSG7/2 - - - is 7/2 . 11/2 . 13/2 . 17/2 . 19/2 . 23/2... | ||
* The basal subgroup of '''[[ed11/2]]''' | * The basal subgroup of '''[[ed11/2]]''' - - - BSG11/2 - - - is 11/2 . 13/2 . 17/2 . 19/2 . 23/2 . 29/2... | ||
* The basal subgroup of '''[[ed13/2]]''' | * The basal subgroup of '''[[ed13/2]]''' - - - BSG13/2 - - - is 13/2 . 17/2 . 19/2 . 23/2 . 29/2 . 31/2... | ||
* The basal subgroup of '''[[ed17/2]]''' | * The basal subgroup of '''[[ed17/2]]''' - - - BSG17/2 - - - is 17/2 . 19/2 . 23/2 . 29/2 . 31/2 . 37/2... | ||
* The basal subgroup of '''[[ed19/2]]''' | * The basal subgroup of '''[[ed19/2]]''' - - - BSG19/2 - - - is 19/2 . 23/2 . 29/2 . 31/2 . 37/2 . 41/2... | ||
* The basal subgroup of '''[[ed23/2]]''' | * The basal subgroup of '''[[ed23/2]]''' - - - BSG23/2 - - - is 23/2 . 29/2 . 31/2 . 37/2 . 41/2 . 43/2... | ||
* The basal subgroup of '''[[ed29/2]]''' | * The basal subgroup of '''[[ed29/2]]''' - - - BSG29/2 - - - is 29/2 . 31/2 . 37/2 . 41/2 . 43/2 . 47/2... | ||
''and so on...'' | ''and so on...'' | ||
=== ed5/3, ed7/3, ed11/3, ed17/3... === | === ed5/3, ed7/3, ed11/3, ed17/3... === | ||
A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | ||
To find BSGn/3: | To find BSGn/3: | ||
| Line 60: | Line 58: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed5/3]]''' | * The basal subgroup of '''[[ed5/3]]''' - - - BSG5/3 - - - is 5/3 . 7/3 . 11/3 . 13/3 . 17/3 . 19/3... | ||
* The basal subgroup of '''[[ed7/3]]''' | * The basal subgroup of '''[[ed7/3]]''' - - - BSG7/3 - - - is 7/3 . 11/3 . 13/3 . 17/3 . 19/3 . 23/3... | ||
* The basal subgroup of '''[[ed11/3]]''' | * The basal subgroup of '''[[ed11/3]]''' - - - BSG11/3 - - - is 11/3 . 13/3 . 17/3 . 19/3 . 23/3 . 29.3... | ||
* The basal subgroup of '''[[ed13/3]]''' | * The basal subgroup of '''[[ed13/3]]''' - - - BSG13/3 - - - is 13/3 . 17/3 . 19/3 . 23/3 . 29/3 . 31/3... | ||
* The basal subgroup of '''[[ed17/3]]''' | * The basal subgroup of '''[[ed17/3]]''' - - - BSG17/3 - - - is 17/3 . 19/3 . 23/3 . 29/3 . 31/3 . 37/3... | ||
* The basal subgroup of '''[[ed19/3]]''' | * The basal subgroup of '''[[ed19/3]]''' - - - BSG19/3 - - - is 19/3 . 23/3 . 29/3 . 31/3 . 37/3 . 41/3... | ||
* The basal subgroup of '''[[ed23/3]]''' | * The basal subgroup of '''[[ed23/3]]''' - - - BSG23/3 - - - is 23/3 . 29/3 . 31/3 . 37/3 . 41/3 . 43/3... | ||
* The basal subgroup of '''[[ed29/3]]''' | * The basal subgroup of '''[[ed29/3]]''' - - - BSG29/3 - - - is 29/3 . 31/3 . 37/3 . 41/3 . 43/3 . 47/3... | ||
''and so on...'' | ''and so on...'' | ||
=== ed5/4, ed7/4, ed11/4, ed17/4... === | === ed5/4, ed7/4, ed11/4, ed17/4... === | ||
A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | ||
To find BSGn/4: | To find BSGn/4: | ||
| Line 80: | Line 77: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed5/4]]''' | * The basal subgroup of '''[[ed5/4]]''' - - - BSG5/4 - - - is 5/4 . 7/4 . 11/4 . 13/4 . 17/4 . 19/4... | ||
* The basal subgroup of '''[[ed7/4]]''' | * The basal subgroup of '''[[ed7/4]]''' - - - BSG7/4 - - - is 7/4 . 11/4 . 13/4 . 17/4 . 19/4 . 23/4... | ||
* The basal subgroup of '''[[ed11/4]]''' | * The basal subgroup of '''[[ed11/4]]''' - - - BSG11/4 - - - is 11/4 . 13/4 . 17/4 . 19/4 . 23/4 . 29/4... | ||
* The basal subgroup of '''[[ed13/4]]''' | * The basal subgroup of '''[[ed13/4]]''' - - - BSG13/4 - - - is 13/4 . 17/4 . 19/4 . 23/4 . 29/4 . 31/4... | ||
* The basal subgroup of '''[[ed17/4]]''' | * The basal subgroup of '''[[ed17/4]]''' - - - BSG17/4 - - - is 17/4 . 19/4 . 23/4 . 29/4 . 31/4 . 37/4... | ||
* The basal subgroup of '''[[ed19/4]]''' | * The basal subgroup of '''[[ed19/4]]''' - - - BSG19/4 - - - is 19/4 . 23/4 . 29/4 . 31/4 . 37/4 . 41/4... | ||
* The basal subgroup of '''[[ed23/4]]''' | * The basal subgroup of '''[[ed23/4]]''' - - - BSG23/4 - - - is 23/4 . 29/4 . 31/4 . 37/4 . 41/4 . 43/4... | ||
* The basal subgroup of '''[[ed29/4]]''' | * The basal subgroup of '''[[ed29/4]]''' - - - BSG29/4 - - - is 29/4 . 31/4 . 37/4 . 41/4 . 43/4 . 47/4... | ||
''and so on...'' | ''and so on...'' | ||
=== ed7/5, ed11/5, ed17/5, ed19/5... === | === ed7/5, ed11/5, ed17/5, ed19/5... === | ||
A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | ||
To find BSGn/5: | To find BSGn/5: | ||
| Line 100: | Line 96: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed7/5]]''' | * The basal subgroup of '''[[ed7/5]]''' - - - BSG7/5 - - - is 7/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
* The basal subgroup of '''[[ed11/5]]''' | * The basal subgroup of '''[[ed11/5]]''' - - - BSG11/5 - - - is 11/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5... | ||
* The basal subgroup of '''[[ed13/5]]''' | * The basal subgroup of '''[[ed13/5]]''' - - - BSG13/5 - - - is 13/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5... | ||
* The basal subgroup of '''[[ed17/5]]''' | * The basal subgroup of '''[[ed17/5]]''' - - - BSG17/5 - - - is 17/5 . 19/5 . 23/5 . 29/5 . 31/5 . 37/5... | ||
* The basal subgroup of '''[[ed19/5]]''' | * The basal subgroup of '''[[ed19/5]]''' - - - BSG19/5 - - - is 19/5 . 23/5 . 29/5 . 31/5 . 37/5 . 41/5... | ||
* The basal subgroup of '''[[ed23/5]]''' | * The basal subgroup of '''[[ed23/5]]''' - - - BSG23/5 - - - is 23/5 . 29/5 . 31/5 . 37/5 . 41/5 . 43/5... | ||
* The basal subgroup of '''[[ed29/5]]''' | * The basal subgroup of '''[[ed29/5]]''' - - - BSG29/5 - - - is 29/5 . 31/5 . 37/5 . 41/5 . 43/5 . 47/5... | ||
''and so on...'' | ''and so on...'' | ||
=== ed7/6, ed11/6, ed17/6, ed19/6... === | === ed7/6, ed11/6, ed17/6, ed19/6... === | ||
A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | ||
To find BSGn/6: | To find BSGn/6: | ||
| Line 119: | Line 114: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed7/6]]''' | * The basal subgroup of '''[[ed7/6]]''' - - - BSG7/6 - - - is 7/6 . 11/6 . 13/6 . 17/6 . 19/6 . 23/6... | ||
* The basal subgroup of '''[[ed11/6]]''' | * The basal subgroup of '''[[ed11/6]]''' - - - BSG11/6 - - - is 11/6 . 13/6 . 17/6 . 19/6 . 23/6 . 29/6... | ||
* The basal subgroup of '''[[ed13/6]]''' | * The basal subgroup of '''[[ed13/6]]''' - - - BSG13/6 - - - is 13/6 . 17/6 . 19/6 . 23/6 . 29/6 . 31/6... | ||
* The basal subgroup of '''[[ed17/6]]''' | * The basal subgroup of '''[[ed17/6]]''' - - - BSG17/6 - - - is 17/6 . 19/6 . 23/6 . 29/6 . 31/6 . 37/6... | ||
* The basal subgroup of '''[[ed19/6]]''' | * The basal subgroup of '''[[ed19/6]]''' - - - BSG19/6 - - - is 19/6 . 23/6 . 29/6 . 31/6 . 37/6 . 41/6... | ||
* The basal subgroup of '''[[ed23/6]]''' | * The basal subgroup of '''[[ed23/6]]''' - - - BSG23/6 - - - is 23/6 . 29/6 . 31/6 . 37/6 . 41/6 . 43/6... | ||
* The basal subgroup of '''[[ed29/6]]''' | * The basal subgroup of '''[[ed29/6]]''' - - - BSG29/6 - - - is 29/6 . 31/6 . 37/6 . 41/6 . 43/6 . 47/6... | ||
''and so on...'' | ''and so on...'' | ||
=== ed11/7, ed17/7, ed19/7, ed23/7... === | === ed11/7, ed17/7, ed19/7, ed23/7... === | ||
A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | ||
To find BSGn/7: | To find BSGn/7: | ||
| Line 138: | Line 132: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed11/7]]''' | * The basal subgroup of '''[[ed11/7]]''' - - - BSG11/7 - - - is 11/7 . 13/7 . 17/7 . 19/7 . 23/7 . 29/7... | ||
* The basal subgroup of '''[[ed13/7]]''' | * The basal subgroup of '''[[ed13/7]]''' - - - BSG13/7 - - - is 13/7 . 17/7 . 19/7 . 23/7 . 29/7 . 31/7... | ||
* The basal subgroup of '''[[ed17/7]]''' | * The basal subgroup of '''[[ed17/7]]''' - - - BSG17/7 - - - is 17/7 . 19/7 . 23/7 . 29/7 . 31/7 . 37/7... | ||
* The basal subgroup of '''[[ed19/7]]''' | * The basal subgroup of '''[[ed19/7]]''' - - - BSG19/7 - - - is 19/7 . 23/7 . 29/7 . 31/7 . 37/7 . 41/7... | ||
* The basal subgroup of '''[[ed23/7]]''' | * The basal subgroup of '''[[ed23/7]]''' - - - BSG23/7 - - - is 23/7 . 29/7 . 31/7 . 37/7 . 41/7 . 43/7... | ||
* The basal subgroup of '''[[ed29/7]]''' | * The basal subgroup of '''[[ed29/7]]''' - - - BSG29/7 - - - is 29/7 . 31/7 . 37/7 . 41/7 . 43/7 . 47/7... | ||
''and so on...'' | ''and so on...'' | ||
=== ed11/8, ed17/8, ed19/8, ed23/8... === | === ed11/8, ed17/8, ed19/8, ed23/8... === | ||
A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | ||
To find BSGn/8: | To find BSGn/8: | ||
| Line 156: | Line 149: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed11/8]]''' | * The basal subgroup of '''[[ed11/8]]''' - - - BSG11/8 - - - is 11/8 . 13/8 . 17/8 . 19/8 . 23/8 . 29/8... | ||
* The basal subgroup of '''[[ed13/8]]''' | * The basal subgroup of '''[[ed13/8]]''' - - - BSG13/8 - - - is 13/8 . 17/8 . 19/8 . 23/8 . 29/8 . 31/8... | ||
* The basal subgroup of '''[[ed17/8]]''' | * The basal subgroup of '''[[ed17/8]]''' - - - BSG17/8 - - - is 17/8 . 19/8 . 23/8 . 29/8 . 31/8 . 37/8... | ||
* The basal subgroup of '''[[ed19/8]]''' | * The basal subgroup of '''[[ed19/8]]''' - - - BSG19/8 - - - is 19/8 . 23/8 . 29/8 . 31/8 . 37/8 . 41/8... | ||
* The basal subgroup of '''[[ed23/8]]''' | * The basal subgroup of '''[[ed23/8]]''' - - - BSG23/8 - - - is 23/8 . 29/8 . 31/8 . 37/8 . 41/8 . 43/8... | ||
* The basal subgroup of '''[[ed29/8]]''' | * The basal subgroup of '''[[ed29/8]]''' - - - BSG29/8 - - - is 29/8 . 31/8 . 37/8 . 41/8 . 43/8 . 47/8... | ||
''and so on...'' | ''and so on...'' | ||
=== ed11/9, ed17/9, ed19/9, ed23/9... === | === ed11/9, ed17/9, ed19/9, ed23/9... === | ||
A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | ||
To find BSGn/9: | To find BSGn/9: | ||
| Line 174: | Line 166: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed11/9]]''' | * The basal subgroup of '''[[ed11/9]]''' - - - BSG11/9 - - - is 11/9 . 13/9 . 17/9 . 19/9 . 23/9 . 29/9... | ||
* The basal subgroup of '''[[ed13/9]]''' | * The basal subgroup of '''[[ed13/9]]''' - - - BSG13/9 - - - is 13/9 . 17/9 . 19/9 . 23/9 . 29/9 . 31/9... | ||
* The basal subgroup of '''[[ed17/9]]''' | * The basal subgroup of '''[[ed17/9]]''' - - - BSG17/9 - - - is 17/9 . 19/9 . 23/9 . 29/9 . 31/9 . 37/9... | ||
* The basal subgroup of '''[[ed19/9]]''' | * The basal subgroup of '''[[ed19/9]]''' - - - BSG19/9 - - - is 19/9 . 23/9 . 29/9 . 31/9 . 37/9 . 41/9... | ||
* The basal subgroup of '''[[ed23/9]]''' | * The basal subgroup of '''[[ed23/9]]''' - - - BSG23/9 - - - is 23/9 . 29/9 . 31/9 . 37/9 . 41/9 . 43/9... | ||
* The basal subgroup of '''[[ed29/9]]''' | * The basal subgroup of '''[[ed29/9]]''' - - - BSG29/9 - - - is 29/9 . 31/9 . 37/9 . 41/9 . 43/9 . 47/9... | ||
''and so on...'' | ''and so on...'' | ||
=== ed11/10, ed17/10, ed19/10, ed23/10... === | === ed11/10, ed17/10, ed19/10, ed23/10... === | ||
A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | ||
To find BSGn/10: | To find BSGn/10: | ||
| Line 192: | Line 183: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed11/10]]''' | * The basal subgroup of '''[[ed11/10]]''' - - - BSG11/10 - - - is 11/10 . 13/10 . 17/10 . 19/10 . 23/10 . 29/10... | ||
* The basal subgroup of '''[[ed13/10]]''' | * The basal subgroup of '''[[ed13/10]]''' - - - BSG13/10 - - - is 13/10 . 17/10 . 19/10 . 23/10 . 29/10 . 31/10... | ||
* The basal subgroup of '''[[ed17/10]]''' | * The basal subgroup of '''[[ed17/10]]''' - - - BSG17/10 - - - is 17/10 . 19/10 . 23/10 . 29/10 . 31/10 . 37/10... | ||
* The basal subgroup of '''[[ed19/10]]''' | * The basal subgroup of '''[[ed19/10]]''' - - - BSG19/10 - - - is 19/10 . 23/10 . 29/10 . 31/10 . 37/10 . 41/10... | ||
* The basal subgroup of '''[[ed23/10]]''' | * The basal subgroup of '''[[ed23/10]]''' - - - BSG23/10 - - - is 23/10 . 29/10 . 31/10 . 37/10 . 41/10 . 43/10... | ||
* The basal subgroup of '''[[ed29/10]]''' | * The basal subgroup of '''[[ed29/10]]''' - - - BSG29/10 - - - is 29/10 . 31/10 . 37/10 . 41/10 . 43/10 . 47/10... | ||
''and so on...'' | ''and so on...'' | ||
=== ed13/11, ed17/11, ed19/11, ed23/11... === | === ed13/11, ed17/11, ed19/11, ed23/11... === | ||
A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | ||
To find BSGn/11: | To find BSGn/11: | ||
| Line 210: | Line 200: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed13/11]]''' | * The basal subgroup of '''[[ed13/11]]''' - - - BSG13/11 - - - is 13/11 . 17/11 . 19/11 . 23/11 . 29/11 . 31/11... | ||
* The basal subgroup of '''[[ed17/11]]''' | * The basal subgroup of '''[[ed17/11]]''' - - - BSG17/11 - - - is 17/11 . 19/11 . 23/11 . 29/11 . 31/11 . 37/11... | ||
* The basal subgroup of '''[[ed19/11]]''' | * The basal subgroup of '''[[ed19/11]]''' - - - BSG19/11 - - - is 19/11 . 23/11 . 29/11 . 31/11 . 37/11 . 41/11... | ||
* The basal subgroup of '''[[ed23/11]]''' | * The basal subgroup of '''[[ed23/11]]''' - - - BSG23/11 - - - is 23/11 . 29/11 . 31/11 . 37/11 . 41/11 . 43/11... | ||
* The basal subgroup of '''[[ed29/11]]''' | * The basal subgroup of '''[[ed29/11]]''' - - - BSG29/11 - - - is 29/11 . 31/11 . 37/11 . 41/11 . 43/11 . 47/11... | ||
''and so on...'' | ''and so on...'' | ||
=== ed13/12, ed17/12, ed29/12, ed23/12... === | === ed13/12, ed17/12, ed29/12, ed23/12... === | ||
A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | ||
To find BSGn/12: | To find BSGn/12: | ||
| Line 227: | Line 216: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed13/12]]''' | * The basal subgroup of '''[[ed13/12]]''' - - - BSG13/12 - - - is 13/12 . 17/12 . 19/12 . 23/12 . 29/12 . 31/12... | ||
* The basal subgroup of '''[[ed17/12]]''' | * The basal subgroup of '''[[ed17/12]]''' - - - BSG17/12 - - - is 17/12 . 19/12 . 23/12 . 29/12 . 31/12 . 37/12... | ||
* The basal subgroup of '''[[ed19/12]]''' | * The basal subgroup of '''[[ed19/12]]''' - - - BSG19/12 - - - is 19/12 . 23/12 . 29/12 . 31/12 . 37/12 . 41/12... | ||
* The basal subgroup of '''[[ed23/12]]''' | * The basal subgroup of '''[[ed23/12]]''' - - - BSG23/12 - - - is 23/12 . 29/12 . 31/12 . 37/12 . 41/12 . 43/12... | ||
* The basal subgroup of '''[[ed29/12]]''' | * The basal subgroup of '''[[ed29/12]]''' - - - BSG29/12 - - - is 29/12 . 31/12 . 37/12 . 41/12 . 43/12 . 47/12... | ||
''and so on...'' | ''and so on...'' | ||
=== ed17/13, ed19/13, ed23/13, ed29/13... === | === ed17/13, ed19/13, ed23/13, ed29/13... === | ||
A.k.a. "[[half-prime subgroup|thirteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|thirteenth-prime subgroups]]". | ||
To find BSGn/13: | To find BSGn/13: | ||
| Line 244: | Line 232: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed17/13]]''' | * The basal subgroup of '''[[ed17/13]]''' - - - BSG17/13 - - - is 17/13 . 19/13 . 23/13 . 29/13 . 31/13 . 37/13... | ||
* The basal subgroup of '''[[ed19/13]]''' | * The basal subgroup of '''[[ed19/13]]''' - - - BSG19/13 - - - is 19/13 . 23/13 . 29/13 . 31/13 . 37/13 . 41/13... | ||
* The basal subgroup of '''[[ed23/13]]''' | * The basal subgroup of '''[[ed23/13]]''' - - - BSG23/13 - - - is 23/13 . 29/13 . 31/13 . 37/13 . 41/13 . 43/13... | ||
* The basal subgroup of '''[[ed29/13]]''' | * The basal subgroup of '''[[ed29/13]]''' - - - BSG29/13 - - - is 29/13 . 31/13 . 37/13 . 41/13 . 43/13 . 47/13... | ||
''and so on...'' | ''and so on...'' | ||
=== ed17/14, ed19/14, ed23/14, ed29/14... === | === ed17/14, ed19/14, ed23/14, ed29/14... === | ||
A.k.a. "[[half-prime subgroup|fourteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fourteenth-prime subgroups]]". | ||
To find BSGn/14: | To find BSGn/14: | ||
| Line 260: | Line 247: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed17/14]]''' | * The basal subgroup of '''[[ed17/14]]''' - - - BSG17/14 - - - is 17/14 . 19/14 . 23/14 . 29/14 . 31/14 . 37/14... | ||
* The basal subgroup of '''[[ed19/14]]''' | * The basal subgroup of '''[[ed19/14]]''' - - - BSG19/14 - - - is 19/14 . 23/14 . 29/14 . 31/14 . 37/14 . 41/14... | ||
* The basal subgroup of '''[[ed23/14]]''' | * The basal subgroup of '''[[ed23/14]]''' - - - BSG23/14 - - - is 23/14 . 29/14 . 31/14 . 37/14 . 41/14 . 43/14... | ||
* The basal subgroup of '''[[ed29/14]]''' | * The basal subgroup of '''[[ed29/14]]''' - - - BSG29/14 - - - is 29/14 . 31/14 . 37/14 . 41/14 . 43/14 . 47/14... | ||
''and so on...'' | ''and so on...'' | ||
=== ed17/15, ed19/15, ed23/15, ed29/15... === | === ed17/15, ed19/15, ed23/15, ed29/15... === | ||
A.k.a. "[[half-prime subgroup|fifteenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifteenth-prime subgroups]]". | ||
To find BSGn/15: | To find BSGn/15: | ||
| Line 276: | Line 262: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed17/15]]''' | * The basal subgroup of '''[[ed17/15]]''' - - - BSG17/15 - - - is 17/15 . 19/15 . 23/15 . 29/15 . 31/15 . 37/15... | ||
* The basal subgroup of '''[[ed19/15]]''' | * The basal subgroup of '''[[ed19/15]]''' - - - BSG19/15 - - - is 19/15 . 23/15 . 29/15 . 31/15 . 37/15 . 41/15... | ||
* The basal subgroup of '''[[ed23/15]]''' | * The basal subgroup of '''[[ed23/15]]''' - - - BSG23/15 - - - is 23/15 . 29/15 . 31/15 . 37/15 . 41/15 . 43/15... | ||
* The basal subgroup of '''[[ed29/15]]''' | * The basal subgroup of '''[[ed29/15]]''' - - - BSG29/15 - - - is 29/15 . 31/15 . 37/15 . 41/15 . 43/15 . 47/15... | ||
''and so on...'' | ''and so on...'' | ||
| Line 292: | Line 278: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed4|ed4/1]]''' | * The basal subgroup of '''[[ed4|ed4/1]]''' - - - BSG4/1 - - - is 4/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed6|ed6/1]]''' | * The basal subgroup of '''[[ed6|ed6/1]]''' - - - BSG6/1 - - - is 6/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed8|ed8/1]]''' | * The basal subgroup of '''[[ed8|ed8/1]]''' - - - BSG8/1 - - - is 8/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed9|ed9/1]]''' | * The basal subgroup of '''[[ed9|ed9/1]]''' - - - BSG9/1 - - - is 9/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed10|ed10/1]]''' | * The basal subgroup of '''[[ed10|ed10/1]]''' - - - BSG10/1 - - - is 10/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1... | ||
* The basal subgroup of '''[[ed12|ed12/1]]''' | * The basal subgroup of '''[[ed12|ed12/1]]''' - - - BSG12/1 - - - is 12/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed14|ed14/1]]''' | * The basal subgroup of '''[[ed14|ed14/1]]''' - - - BSG14/1 - - - is 14/1 . 11/1 . 13/1 . 17/1 . 19/1 . 23/1... | ||
* The basal subgroup of '''[[ed15|ed15/1]]''' | * The basal subgroup of '''[[ed15|ed15/1]]''' - - - BSG15/1 - - - is 15/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1... | ||
* The basal subgroup of '''[[ed16|ed16/1]]''' | * The basal subgroup of '''[[ed16|ed16/1]]''' - - - BSG16/1 - - - is 16/1 . 3/1 . 5/1 . 7/1 . 11/1 . 13/1... | ||
* The basal subgroup of '''[[ed18|ed18/1]]''' | * The basal subgroup of '''[[ed18|ed18/1]]''' - - - BSG18/1 - - - is 18/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed20|ed20/1]]''' | * The basal subgroup of '''[[ed20|ed20/1]]''' - - - BSG20/1 - - - is 20/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1... | ||
* The basal subgroup of '''[[ed21|ed21/1]]''' | * The basal subgroup of '''[[ed21|ed21/1]]''' - - - BSG21/1 - - - is 21/1 . 11/1 . 13/1 . 17/1 . 19/1 . 23/1... | ||
* The basal subgroup of '''[[ed22|ed22/1]]''' | * The basal subgroup of '''[[ed22|ed22/1]]''' - - - BSG22/1 - - - is 22/1 . 13/1 . 17/1 . 19/1 . 23/1 . 29/1... | ||
* The basal subgroup of '''[[ed24|ed24/1]]''' | * The basal subgroup of '''[[ed24|ed24/1]]''' - - - BSG24/1 - - - is 24/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed25|ed25/1]]''' | * The basal subgroup of '''[[ed25|ed25/1]]''' - - - BSG25/1 - - - is 25/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1... | ||
* The basal subgroup of '''[[ed26|ed26/1]]''' | * The basal subgroup of '''[[ed26|ed26/1]]''' - - - BSG26/1 - - - is 26/1 . 17/1 . 19/1 . 23/1 . 29/1 . 31/1... | ||
* The basal subgroup of '''[[ed27|ed27/1]]''' | * The basal subgroup of '''[[ed27|ed27/1]]''' - - - BSG27/1 - - - is 27/1 . 5/1 . 7/1 . 11/1 . 13/1 . 17/1... | ||
* The basal subgroup of '''[[ed28|ed28/1]]''' | * The basal subgroup of '''[[ed28|ed28/1]]''' - - - BSG28/1 - - - is 28/1 . 11/1 . 13/1 . 17/1 . 19/1 . 23/1... | ||
* The basal subgroup of '''[[ed30|ed30/1]]''' | * The basal subgroup of '''[[ed30|ed30/1]]''' - - - BSG30/1 - - - is 30/1 . 7/1 . 11/1 . 13/1 . 17/1 . 19/1 ... | ||
''and so on...'' | ''and so on...'' | ||
| Line 322: | Line 308: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/2 | |||
# Add n/2 to the start of the subgroup | # Add n/2 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 327: | Line 314: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed9/2]]''' | * The basal subgroup of '''[[ed9/2]]''' - - - BSG9/2 - - - is 9/2 . 5/2 . 7/2 . 11/2 . 13/2 . 17/2... | ||
* The basal subgroup of '''[[ed15/2]]''' | * The basal subgroup of '''[[ed15/2]]''' - - - BSG15/2 - - - is 15/2 . 7/2 . 11/2 . 13/2 . 17/2 . 19/2... | ||
* The basal subgroup of '''[[ed21/2]]''' | * The basal subgroup of '''[[ed21/2]]''' - - - BSG21/2 - - - is 21/2 . 11/2 . 13/2 . 17/2 . 19/2 . 23/2... | ||
* The basal subgroup of '''[[ed25/2]]''' | * The basal subgroup of '''[[ed25/2]]''' - - - BSG25/2 - - - is 25/2 . 7/2 . 11/2 . 13/2 . 17/2 . 19/2... | ||
* The basal subgroup of '''[[ed27/2]]''' | * The basal subgroup of '''[[ed27/2]]''' - - - BSG27/2 - - - is 27/2 . 5/2 . 7/2 . 11/2 . 13/2 . 17/2... | ||
''and so on...'' | ''and so on...'' | ||
=== ed4/3, ed8/3, ed10/3, ed14/3... === | === ed4/3, ed8/3, ed10/3, ed14/3... === | ||
A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | A.k.a. "[[half-prime subgroup|third-prime subgroups]]". | ||
To find BSGn/3: | To find BSGn/3: | ||
| Line 343: | Line 329: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/3 | |||
# Add n/3 to the start of the subgroup | # Add n/3 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 348: | Line 335: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed4/3]]''' | * The basal subgroup of '''[[ed4/3]]''' - - - BSG4/3 - - - is 4/3 . 5/3 . 7/3 . 11/3 . 13/3 . 17/3... | ||
* The basal subgroup of '''[[ed8/3]]''' | * The basal subgroup of '''[[ed8/3]]''' - - - BSG8/3 - - - is 8/3 . 5/3 . 7/3 . 11/3 . 13/3 . 17/3... | ||
* The basal subgroup of '''[[ed10/3]]''' | * The basal subgroup of '''[[ed10/3]]''' - - - BSG10/3 - - - is 10/3 . 7/3 . 11/3 . 13/3 . 17/3 . 19/3... | ||
* The basal subgroup of '''[[ed14/3]]''' | * The basal subgroup of '''[[ed14/3]]''' - - - BSG14/3 - - - is 14/3 . 11/3 . 13/3 . 17/3 . 19/3 . 23/3... | ||
* The basal subgroup of '''[[ed16/3]]''' | * The basal subgroup of '''[[ed16/3]]''' - - - BSG16/3 - - - is 16/3 . 3/3 . 5/3 . 7/3 . 11/3 . 13/3... | ||
* The basal subgroup of '''[[ed18/3]]''' | * The basal subgroup of '''[[ed18/3]]''' - - - BSG18/3 - - - is 18/3 . 5/3 . 7/3 . 11/3 . 13/3 . 17/3... | ||
* The basal subgroup of '''[[ed20/3]]''' | * The basal subgroup of '''[[ed20/3]]''' - - - BSG20/3 - - - is 20/3 . 7/3 . 11/3 . 13/3 . 17/3 . 19/3... | ||
* The basal subgroup of '''[[ed22/3]]''' | * The basal subgroup of '''[[ed22/3]]''' - - - BSG22/3 - - - is 22/3 . 13/3 . 17/3 . 19/3 . 23/3 . 29/3... | ||
* The basal subgroup of '''[[ed25/3]]''' | * The basal subgroup of '''[[ed25/3]]''' - - - BSG25/3 - - - is 25/3 . 7/3 . 11/3 . 13/3 . 17/3 . 19/3... | ||
* The basal subgroup of '''[[ed26/3]]''' | * The basal subgroup of '''[[ed26/3]]''' - - - BSG26/3 - - - is 26/3 . 17/3 . 19/3 . 23/3 . 29/3 . 31/3... | ||
* The basal subgroup of '''[[ed28/3]]''' | * The basal subgroup of '''[[ed28/3]]''' - - - BSG28/3 - - - is 28/3 . 11/3 . 13/3 . 17/3 . 19/3 . 23/3... | ||
''and so on...'' | ''and so on...'' | ||
=== ed9/4, ed15/4, ed21/4, ed25/4... === | === ed9/4, ed15/4, ed21/4, ed25/4... === | ||
A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | A.k.a. "[[half-prime subgroup|quarter-prime subgroups]]". | ||
To find BSGn/4: | To find BSGn/4: | ||
| Line 370: | Line 356: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/4 | |||
# Add n/4 to the start of the subgroup | # Add n/4 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 375: | Line 362: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed9/4]]''' | * The basal subgroup of '''[[ed9/4]]''' - - - BSG9/4 - - - is 9/4 . 5/4 . 7/4 . 11/4 . 13/4 . 17/4... | ||
* The basal subgroup of '''[[ed15/4]]''' | * The basal subgroup of '''[[ed15/4]]''' - - - BSG15/4 - - - is 15/4 . 7/4 . 11/4 . 13/4 . 17/4 . 19/4... | ||
* The basal subgroup of '''[[ed21/4]]''' | * The basal subgroup of '''[[ed21/4]]''' - - - BSG21/4 - - - is 21/4 . 11/4 . 13/4 . 17/4 . 19/4 . 23/4... | ||
* The basal subgroup of '''[[ed25/4]]''' | * The basal subgroup of '''[[ed25/4]]''' - - - BSG25/4 - - - is 25/4 . 7/4 . 11/4 . 13/4 . 17/4 . 19/4... | ||
* The basal subgroup of '''[[ed27/4]]''' | * The basal subgroup of '''[[ed27/4]]''' - - - BSG27/4 - - - is 27/4 . 5/4 . 7/4 . 11/4 . 13/4 . 17/4... | ||
''and so on...'' | ''and so on...'' | ||
=== ed6/5, ed8/5, ed9/5, ed12/5... === | === ed6/5, ed8/5, ed9/5, ed12/5... === | ||
A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|fifth-prime subgroups]]". | ||
To find BSGn/5: | To find BSGn/5: | ||
| Line 391: | Line 377: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/5 | |||
# Add n/5 to the start of the subgroup | # Add n/5 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 396: | Line 383: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed6/5]]''' | * The basal subgroup of '''[[ed6/5]]''' - - - BSG6/5 - - - is 6/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed8/5]]''' | * The basal subgroup of '''[[ed8/5]]''' - - - BSG8/5 - - - is 8/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed9/5]]''' | * The basal subgroup of '''[[ed9/5]]''' - - - BSG9/5 - - - is 9/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed12/5]]''' | * The basal subgroup of '''[[ed12/5]]''' - - - BSG12/5 - - - is 12/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed14/5]]''' | * The basal subgroup of '''[[ed14/5]]''' - - - BSG14/5 - - - is 14/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
* The basal subgroup of '''[[ed16/5]]''' | * The basal subgroup of '''[[ed16/5]]''' - - - BSG16/5 - - - is 16/5 . 3/5 . 7/5 . 11/5 . 13/5 . 17/5... | ||
* The basal subgroup of '''[[ed18/5]]''' | * The basal subgroup of '''[[ed18/5]]''' - - - BSG18/5 - - - is 18/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed21/5]]''' | * The basal subgroup of '''[[ed21/5]]''' - - - BSG21/5 - - - is 21/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
* The basal subgroup of '''[[ed22/5]]''' | * The basal subgroup of '''[[ed22/5]]''' - - - BSG22/5 - - - is 22/5 . 13/5 . 17/5 . 19/5 . 23/5 . 29/5... | ||
* The basal subgroup of '''[[ed24/5]]''' | * The basal subgroup of '''[[ed24/5]]''' - - - BSG24/5 - - - is 24/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed26/5]]''' | * The basal subgroup of '''[[ed26/5]]''' - - - BSG26/5 - - - is 26/5 . 17/5 . 19/5 . 23/5 . 29/5 . 31/5... | ||
* The basal subgroup of '''[[ed27/5]]''' | * The basal subgroup of '''[[ed27/5]]''' - - - BSG27/5 - - - is 27/5 . 7/5 . 11/5 . 13/5 . 17/5 . 19/5... | ||
* The basal subgroup of '''[[ed28/5]]''' | * The basal subgroup of '''[[ed28/5]]''' - - - BSG28/5 - - - is 28/5 . 11/5 . 13/5 . 17/5 . 19/5 . 23/5... | ||
''and so on...'' | ''and so on...'' | ||
=== ed35/6, ed55/6, ed65/6, ed77/6... === | === ed35/6, ed55/6, ed65/6, ed77/6... === | ||
A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|sixth-prime subgroups]]". | ||
To find BSGn/6: | To find BSGn/6: | ||
| Line 420: | Line 406: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/6 | |||
# Add n/6 to the start of the subgroup | # Add n/6 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 425: | Line 412: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed35/6]]''' | * The basal subgroup of '''[[ed35/6]]''' - - - BSG35/6 - - - is 35/6 . 11/6 . 13/6 . 17/6 . 19/6 . 23/6... | ||
* The basal subgroup of '''[[ed55/6]]''' | * The basal subgroup of '''[[ed55/6]]''' - - - BSG55/6 - - - is 55/6 . 13/6 . 17/6 . 19/6 . 23/6 . 29/6... | ||
* The basal subgroup of '''[[ed65/6]]''' | * The basal subgroup of '''[[ed65/6]]''' - - - BSG65/6 - - - is 65/6 . 17/6 . 19/6 . 23/6 . 29/6 . 31/6... | ||
* The basal subgroup of '''[[ed77/6]]''' | * The basal subgroup of '''[[ed77/6]]''' - - - BSG77/6 - - - is 77/6 . 13/6 . 17/6 . 19/6 . 23/6 . 29/6... | ||
''and so on...'' | ''and so on...'' | ||
=== ed8/7, ed9/7, ed10/7, ed12/7... === | === ed8/7, ed9/7, ed10/7, ed12/7... === | ||
A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | A.k.a. "[[half-prime subgroup|seventh-prime subgroups]]". | ||
To find BSGn/7: | To find BSGn/7: | ||
| Line 440: | Line 426: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/7 | |||
# Add n/7 to the start of the subgroup | # Add n/7 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 445: | Line 432: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed8/7]]''' | * The basal subgroup of '''[[ed8/7]]''' - - - BSG8/7 - - - is 8/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed9/7]]''' | * The basal subgroup of '''[[ed9/7]]''' - - - BSG9/7 - - - is 9/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed10/7]]''' | * The basal subgroup of '''[[ed10/7]]''' - - - BSG10/7 - - - is 10/7 . 11/7 . 13/7 . 17/7 . 19/7 . 23/7... | ||
* The basal subgroup of '''[[ed12/7]]''' | * The basal subgroup of '''[[ed12/7]]''' - - - BSG12/7 - - - is 12/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed15/7]]''' | * The basal subgroup of '''[[ed15/7]]''' - - - BSG15/7 - - - is 15/7 . 11/7 . 13/7 . 17/7 . 19/7 . 23/7... | ||
* The basal subgroup of '''[[ed16/7]]''' | * The basal subgroup of '''[[ed16/7]]''' - - - BSG16/7 - - - is 16/7 . 12/7 . 10/7 . 11/7 . 13/7 . 17/7... | ||
* The basal subgroup of '''[[ed18/7]]''' | * The basal subgroup of '''[[ed18/7]]''' - - - BSG18/7 - - - is 18/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed20/7]]''' | * The basal subgroup of '''[[ed20/7]]''' - - - BSG20/7 - - - is 20/7 . 11/7 . 13/7 . 17/7 . 19/7 . 23/7... | ||
* The basal subgroup of '''[[ed22/7]]''' | * The basal subgroup of '''[[ed22/7]]''' - - - BSG22/7 - - - is 22/7 . 13/7 . 17/7 . 19/7 . 23/7 . 29/7... | ||
* The basal subgroup of '''[[ed24/7]]''' | * The basal subgroup of '''[[ed24/7]]''' - - - BSG24/7 - - - is 24/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed25/7]]''' | * The basal subgroup of '''[[ed25/7]]''' - - - BSG25/7 - - - is 25/7 . 11/7 . 13/7 . 17/7 . 19/7 . 23/7... | ||
* The basal subgroup of '''[[ed26/7]]''' | * The basal subgroup of '''[[ed26/7]]''' - - - BSG26/7 - - - is 26/7 . 17/7 . 19/7 . 23/7 . 29/7 . 31/7... | ||
* The basal subgroup of '''[[ed27/7]]''' | * The basal subgroup of '''[[ed27/7]]''' - - - BSG27/7 - - - is 27/7 . 10/7 . 11/7 . 13/7 . 17/7 . 19/7... | ||
* The basal subgroup of '''[[ed30/7]]''' | * The basal subgroup of '''[[ed30/7]]''' - - - BSG30/7 - - - is 30/7 . 11/7 . 13/7 . 17/7 . 19/7 . 23/7... | ||
''and so on...'' | ''and so on...'' | ||
=== ed9/8, ed15/8, ed21/8, ed25/8... === | === ed9/8, ed15/8, ed21/8, ed25/8... === | ||
A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|eighth-prime subgroups]]". | ||
To find BSGn/8: | To find BSGn/8: | ||
| Line 470: | Line 456: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/8 | |||
# Add n/8 to the start of the subgroup | # Add n/8 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 475: | Line 462: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed9/8]]''' | * The basal subgroup of '''[[ed9/8]]''' - - - BSG9/8 - - - is 9/8 . 10/8 (ie 5/4) . 7/8 . 11/8 . 13/8 . 17/8... | ||
* The basal subgroup of '''[[ed15/8]]''' | * The basal subgroup of '''[[ed15/8]]''' - - - BSG15/8 - - - is 15/8 . 14/8 (ie 7/4) . 11/8 . 13/8 . 17/8 . 19/8... | ||
* The basal subgroup of '''[[ed21/8]]''' | * The basal subgroup of '''[[ed21/8]]''' - - - BSG21/8 - - - is 21/8 . 11/8 . 13/8 . 17/8 . 19/8 . 23/8.. | ||
* The basal subgroup of '''[[ed25/8]]''' | * The basal subgroup of '''[[ed25/8]]''' - - - BSG25/8 - - - is 25/8 . 14/8 (ie 7/4) . 11/8 . 13/8 . 17/8 . 19/8... | ||
* The basal subgroup of '''[[ed27/8]]''' | * The basal subgroup of '''[[ed27/8]]''' - - - BSG27/8 - - - is 27/8 . 10/8 (ie 5/4) . 7/8 . 11/8 . 13/8 . 17/8... | ||
''and so on...'' | ''and so on...'' | ||
=== ed10/9, ed14/9, ed16/9, ed20/9... === | === ed10/9, ed14/9, ed16/9, ed20/9... === | ||
A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|ninth-prime subgroups]]". | ||
To find BSGn/9: | To find BSGn/9: | ||
| Line 491: | Line 477: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/9 | |||
# Add n/9 to the start of the subgroup | # Add n/9 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 496: | Line 483: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed10/9]]''' | * The basal subgroup of '''[[ed10/9]]''' - - - BSG10/9 - - - is 10/9 . 14/9 . 11/9 . 13/9 . 17/9 . 19/9... | ||
* The basal subgroup of '''[[ed14/9]]''' | * The basal subgroup of '''[[ed14/9]]''' - - - BSG14/9 - - - is 14/9 . 11/9 . 13/9 . 17/9 . 19/9 . 23/9... | ||
* The basal subgroup of '''[[ed16/9]]''' | * The basal subgroup of '''[[ed16/9]]''' - - - BSG16/9 - - - is 16/9 . 10/9 . 7/9 . 11/9 . 13/9 . 17/9... | ||
* The basal subgroup of '''[[ed20/9]]''' | * The basal subgroup of '''[[ed20/9]]''' - - - BSG20/9 - - - is 20/9 . 14/9 . 11/9 . 13/9 . 17/9 . 19/9... | ||
* The basal subgroup of '''[[ed22/9]]''' | * The basal subgroup of '''[[ed22/9]]''' - - - BSG22/9 - - - is 22/9 . 13/9 . 17/9 . 19/9 . 23/9 . 29/9... | ||
* The basal subgroup of '''[[ed25/9]]''' | * The basal subgroup of '''[[ed25/9]]''' - - - BSG25/9 - - - is 25/9 . 14/9 . 11/9 . 13/9 . 17/9 . 19/9... | ||
* The basal subgroup of '''[[ed26/9]]''' | * The basal subgroup of '''[[ed26/9]]''' - - - BSG26/9 - - - is 26/9 . 17/9 . 19/9 . 23/9 . 29/9 . 31/9... | ||
* The basal subgroup of '''[[ed28/9]]''' | * The basal subgroup of '''[[ed28/9]]''' - - - BSG28/9 - - - is 28/9 . 11/9 . 13/9 . 17/9 . 19/9 . 23/9... | ||
''and so on...'' | ''and so on...'' | ||
=== ed21/10, ed27/10, ed33/10, ed39/10... === | === ed21/10, ed27/10, ed33/10, ed39/10... === | ||
A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|tenth-prime subgroups]]". | ||
To find BSGn/10: | To find BSGn/10: | ||
| Line 515: | Line 501: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/10 | |||
# Add n/10 to the start of the subgroup | # Add n/10 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 520: | Line 507: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed21/10]]''' | * The basal subgroup of '''[[ed21/10]]''' - - - BSG21/10 - - - is 21/10 . 11/10 . 13/10 . 17/10 . 19/10 . 23/10... | ||
* The basal subgroup of '''[[ed27/10]]''' | * The basal subgroup of '''[[ed27/10]]''' - - - BSG27/10 - - - is 27/10 . 14/10 (ie 7/5) . 11/10 . 13/10 . 17/10 . 19/10... | ||
* The basal subgroup of '''[[ed33/10]]''' | * The basal subgroup of '''[[ed33/10]]''' - - - BSG33/10 - - - is 33/10 . 13/10 . 17/10 . 19/10 . 23/10 . 29/10... | ||
* The basal subgroup of '''[[ed39/10]]''' | * The basal subgroup of '''[[ed39/10]]''' - - - BSG39/10 - - - is 39/10 . 17/10 . 19/10 . 23/10 . 29/10 . 31/10... | ||
''and so on...'' | ''and so on...'' | ||
=== ed12/11, ed14/11, ed15/11, ed16/11... === | === ed12/11, ed14/11, ed15/11, ed16/11... === | ||
A.k.a. "[[half-prime subgroup| | A.k.a. "[[half-prime subgroup|eleventh-prime subgroups]]". | ||
To find BSGn/11: | To find BSGn/11: | ||
| Line 535: | Line 521: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/11 | |||
# Add n/11 to the start of the subgroup | # Add n/11 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 540: | Line 527: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed12/11]]''' | * The basal subgroup of '''[[ed12/11]]''' - - - BSG12/11 - - - is 12/11 . 20/11 . 14/11 . 13/11 . 17/11 . 19/11... | ||
* The basal subgroup of '''[[ed14/11]]''' | * The basal subgroup of '''[[ed14/11]]''' - - - BSG14/11 - - - is 14/11 . 13/11 . 17/11 . 19/11 . 23/11 . 29/11... | ||
* The basal subgroup of '''[[ed15/11]]''' | * The basal subgroup of '''[[ed15/11]]''' - - - BSG15/11 - - - is 15/11 . 14/11 . 13/11 . 17/11 . 19/11 . 23/11... | ||
* The basal subgroup of '''[[ed16/11]]''' | * The basal subgroup of '''[[ed16/11]]''' - - - BSG16/11 - - - is 16/11 . 12/11 . 20/11 . 14/11 . 13/11 . 17/11... | ||
* The basal subgroup of '''[[ed18/11]]''' | * The basal subgroup of '''[[ed18/11]]''' - - - BSG18/11 - - - is 18/11 . 20/11 . 14/11 . 13/11 . 17/11 . 19/11... | ||
* The basal subgroup of '''[[ed20/11]]''' | * The basal subgroup of '''[[ed20/11]]''' - - - BSG20/11 - - - is 20/11 . 14/11 . 13/11 . 17/11 . 19/11 . 23/11... | ||
* The basal subgroup of '''[[ed21/11]]''' | * The basal subgroup of '''[[ed21/11]]''' - - - BSG21/11 - - - is 21/11 . 13/11 . 17/11 . 19/11 . 23/11 . 29/11... | ||
* The basal subgroup of '''[[ed24/11]]''' | * The basal subgroup of '''[[ed24/11]]''' - - - BSG24/11 - - - is 24/11 . 20/11 . 14/11 . 13/11 . 17/11 . 19/11... | ||
* The basal subgroup of '''[[ed25/11]]''' | * The basal subgroup of '''[[ed25/11]]''' - - - BSG25/11 - - - is 25/11 . 14/11 . 13/11 . 17/11 . 19/11 . 23/11... | ||
* The basal subgroup of '''[[ed26/11]]''' | * The basal subgroup of '''[[ed26/11]]''' - - - BSG26/11 - - - is 26/11 . 17/11 . 19/11 . 23/11 . 29/11 . 31/11... | ||
* The basal subgroup of '''[[ed27/11]]''' | * The basal subgroup of '''[[ed27/11]]''' - - - BSG27/11 - - - is 27/11 . 20/11 . 14/11 . 13/11 . 17/11 . 19/11... | ||
* The basal subgroup of '''[[ed28/11]]''' | * The basal subgroup of '''[[ed28/11]]''' - - - BSG28/11 - - - is 28/11 . 13/11 . 17/11 . 19/11 . 23/11 . 29/11... | ||
* The basal subgroup of '''[[ed30/11]]''' | * The basal subgroup of '''[[ed30/11]]''' - - - BSG30/11 - - - is 30/11 . 14/11 . 13/11 . 17/11 . 19/11 . 23/11... | ||
''and so on...'' | ''and so on...'' | ||
=== ed35/12, ed55/12, ed65/12, ed77/12... === | === ed35/12, ed55/12, ed65/12, ed77/12... === | ||
A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | A.k.a. "[[half-prime subgroup|twelfth-prime subgroups]]". | ||
To find BSGn/12: | To find BSGn/12: | ||
| Line 564: | Line 550: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/12 | |||
# Add n/12 to the start of the subgroup | # Add n/12 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 569: | Line 556: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed35/12]]''' | * The basal subgroup of '''[[ed35/12]]''' - - - BSG35/12 - - - is 35/12 . 22/12 (ie 11/6) . 13/12 . 17/12 . 19/12 . 23/12... | ||
* The basal subgroup of '''[[ed55/12]]''' | * The basal subgroup of '''[[ed55/12]]''' - - - BSG55/12 - - - is 55/12 . 13/12 . 17/12 . 19/12 . 23/12 . 29/12... | ||
* The basal subgroup of '''[[ed65/12]]''' | * The basal subgroup of '''[[ed65/12]]''' - - - BSG65/12 - - - is 65/12 . 17/12 . 19/12 . 23/12 . 29/12 . 31/12... | ||
* The basal subgroup of '''[[ed77/12]]''' | * The basal subgroup of '''[[ed77/12]]''' - - - BSG77/12 - - - is 77/12 . 13/12 . 17/12 . 19/12 . 23/12 . 29/12... | ||
''and so on...'' | ''and so on...'' | ||
| Line 581: | Line 568: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/13 | |||
# Add n/13 to the start of the subgroup | # Add n/13 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 586: | Line 574: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed14/13]]''' | * The basal subgroup of '''[[ed14/13]]''' - - - BSG14/13 - - - is 14/13 . 22/13 . 17/13 . 19/13 . 23/13 . 29/13... | ||
* The basal subgroup of '''[[ed15/13]]''' | * The basal subgroup of '''[[ed15/13]]''' - - - BSG15/13 - - - is 15/13 . 14/13 . 22/13 . 13/13 . 17/13 . 19/13... | ||
* The basal subgroup of '''[[ed16/13]]''' | * The basal subgroup of '''[[ed16/13]]''' - - - BSG16/13 - - - is 16/13 . 24/13 . 20/13 . 14/13 . 22/13 . 17/13... | ||
* The basal subgroup of '''[[ed18/13]]''' | * The basal subgroup of '''[[ed18/13]]''' - - - BSG18/13 - - - is 18/13 . 20/13 . 14/13 . 22/13 . 17/13 . 19/13... | ||
* The basal subgroup of '''[[ed20/13]]''' | * The basal subgroup of '''[[ed20/13]]''' - - - BSG20/13 - - - is 20/13 . 14/13 . 22/13 . 17/13 . 19/13 . 23/13... | ||
* The basal subgroup of '''[[ed21/13]]''' | * The basal subgroup of '''[[ed21/13]]''' - - - BSG21/13 - - - is 21/13 . 22/13 . 17/13 . 19/13 . 23/13 . 29/13... | ||
* The basal subgroup of '''[[ed22/13]]''' | * The basal subgroup of '''[[ed22/13]]''' - - - BSG22/13 - - - is 22/13 . 17/13 . 19/13 . 23/13 . 29/13 . 31/13... | ||
* The basal subgroup of '''[[ed24/13]]''' | * The basal subgroup of '''[[ed24/13]]''' - - - BSG24/13 - - - is 24/13 . 20/13 . 14/13 . 22/13 . 17/13 . 19/13... | ||
* The basal subgroup of '''[[ed25/13]]''' | * The basal subgroup of '''[[ed25/13]]''' - - - BSG25/13 - - - is 25/13 . 14/13 . 22/13 . 17/13 . 19/13 . 23/13... | ||
* The basal subgroup of '''[[ed27/13]]''' | * The basal subgroup of '''[[ed27/13]]''' - - - BSG27/13 - - - is 27/13 . 20/13 . 14/13 . 22/13 . 17/13 . 19/13... | ||
* The basal subgroup of '''[[ed28/13]]''' | * The basal subgroup of '''[[ed28/13]]''' - - - BSG28/13 - - - is 28/13 . 22/13 . 17/13 . 19/13 . 23/13 . 29/13... | ||
* The basal subgroup of '''[[ed30/13]]''' | * The basal subgroup of '''[[ed30/13]]''' - - - BSG30/13 - - - is 30/13 . 14/13 . 22/13 . 17/13 . 19/13 . 23/13... | ||
''and so on...'' | ''and so on...'' | ||
| Line 606: | Line 594: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/14 | |||
# Add n/14 to the start of the subgroup | # Add n/14 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 611: | Line 600: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed15/14]]''' | * The basal subgroup of '''[[ed15/14]]''' - - - BSG15/14 - - - is 15/14 . 22/14 (ie 11/7) . 26/14 (ie 13/7) . 17/14 . 19/14 . 23/14... | ||
* The basal subgroup of '''[[ed25/14]]''' | * The basal subgroup of '''[[ed25/14]]''' - - - BSG25/14 - - - is 25/14 . 11/14 . 26/14 (ie 13/7) . 17/14 . 19/14 . 23/14... | ||
* The basal subgroup of '''[[ed27/14]]''' | * The basal subgroup of '''[[ed27/14]]''' - - - BSG27/14 - - - is 27/14 . 20/14 (ie 10/7) . 11/14 . 13/14 . 17/14 . 19/14... | ||
* The basal subgroup of '''[[ed33/14]]''' | * The basal subgroup of '''[[ed33/14]]''' - - - BSG33/14 - - - is 33/14 . 26/14 (ie 13/7) . 17/14 . 19/14 . 23/14 . 29/14... | ||
''and so on...'' | ''and so on...'' | ||
| Line 623: | Line 612: | ||
# Remove all instances of m/1 where m is a prime factor of n | # Remove all instances of m/1 where m is a prime factor of n | ||
# Remove all instances of m/1 where m is less than n's largest prime factor | # Remove all instances of m/1 where m is less than n's largest prime factor | ||
# Replace all instances of m/1 with m/15 | |||
# Add n/15 to the start of the subgroup | # Add n/15 to the start of the subgroup | ||
# In all instances a/b where a<b, double a | # In all instances a/b where a<b, double a | ||
| Line 628: | Line 618: | ||
'''List:''' | '''List:''' | ||
* The basal subgroup of '''[[ed16/15]]''' | * The basal subgroup of '''[[ed16/15]]''' - - - BSG16/15 - - - is 16/15 . 28/15 . 22/15 . 26/15... | ||
* The basal subgroup of '''[[ed22/15]]''' | * The basal subgroup of '''[[ed22/15]]''' - - - BSG22/15 - - - is 22/15 . 26/15 . 17/15 . 19/15 . 23/15 . 29/15... | ||
* The basal subgroup of '''[[ed26/15]]''' | * The basal subgroup of '''[[ed26/15]]''' - - - BSG26/15 - - - is 26/15 . 17/15 . 19/15 . 23/15 . 29/15 . 31/15... | ||
* The basal subgroup of '''[[ed28/15]]''' | * The basal subgroup of '''[[ed28/15]]''' - - - BSG28/15 - - - is 28/15 . 22/15 . 26/15 . 17/15 . 19/15 . 23/15... | ||
''and so on...'' | ''and so on...'' | ||