Count up with recursive prime factorization
Moderators: jestingrabbit, Moderators General, Prelates

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
691
<<<<>>><<<>>><<<>>>>
<ccc>
<<<<>>><<<>>><<<>>>>
<ccc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
692
<><><<><><><<<>>>>
72.66% efficiency
<><><<><><><<<>>>>
72.66% efficiency
good luck have fun

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
693
<<>><<>><<><>><<<<>>>>
bb<aa>d
<<>><<>><<><>><<<<>>>>
bb<aa>d
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
694
<><<<>><<<>><<>>>>
72.69% efficiency
<><<<>><<<>><<>>>>
72.69% efficiency
good luck have fun
Re: Count up with recursive prime factorization
695
<<<>>><<><<<><>>>>
c<a<<aa>>>
Fp(Pd(PP))
33213114
tertius et prīmus (prīmī et secundī bisprīmī)
Semiprime
Asymmetric
Not Alphabetic
squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 139
<<<>>><<><<<><>>>>
c<a<<aa>>>
Fp(Pd(PP))
33213114
Code: Select all
* *****
* * ***
* ***
* *
tertius et prīmus (prīmī et secundī bisprīmī)
Spoiler:
Semiprime
Asymmetric
Not Alphabetic
squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 139

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
696
<><><><<>><<><<<>>>>
aaab<ac>
<><><><<>><<><<<>>>>
aaab<ac>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
697
<<<><>>><<<><<>>>>
<<aa>><<ab>>
d(PP)d(PD)
31133124
secundus bisprīmī et secundus (prīmī et secundī)
Semiprime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 41
<<<><>>><<<><<>>>>
<<aa>><<ab>>
d(PP)d(PD)
31133124
Code: Select all
*** ***
*** ***
* * * *
*
secundus bisprīmī et secundus (prīmī et secundī)
Semiprime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 41

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
698
<><<>><<<<>><<>>>>
ab<<bb>>
<><<>><<<<>><<>>>>
ab<<bb>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
699
<<>><<<>><<<><>>>>
b<b<<aa>>>
Dp(Dd(PP))
22323114
secundus et prīmus (secundī et secundī bisprīmī)
Semiprime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 233

Mistaken labyrinth notation, where I replaced a 3 with a 5, making 1165.
<<>><<<>><<<><>>>>
b<b<<aa>>>
Dp(Dd(PP))
22323114
Code: Select all
* *****
* * ***
* ***
* *
secundus et prīmus (secundī et secundī bisprīmī)
Semiprime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 233

Mistaken labyrinth notation, where I replaced a 3 with a 5, making 1165.
Spoiler:
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
700
<><><<<>>><<<>>><<><>>
59.56% efficiency
<><><<<>>><<<>>><<><>>
59.56% efficiency
good luck have fun
Re: Count up with recursive prime factorization
701
<<><<>><<>><<><>>>
<abb<aa>>
p(PDDp(PP))
2122222113
prīmus (prīmī et bissecundī et prīmī bisprīmī)
Prime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 9
Max Depth: 3
<<><<>><<>><<><>>>
<abb<aa>>
p(PDDp(PP))
2122222113
Code: Select all
*********
* * * ***
* * * *
prīmus (prīmī et bissecundī et prīmī bisprīmī)
Prime
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 9
Max Depth: 3

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
702
<><<>><<>><<>><<><<>>>
abbb<ab>
<><<>><<>><<>><<><<>>>
abbb<ab>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
703
<<><><>><<><><<>>>
<aaa><aab>
p(PPP)p(PPD)
211112211123
prīmus terprīmī et prīmus (bisprīmī et secundī)
Semiprime (19 * 37)
Asymmetric
Not Alphabetic
Squarefree, but recursively onlytetradbiquadratefree
Nodes: 9
Reversals: 11
Max Depth: 3
Smoothness: 37
<<><><>><<><><<>>>
<aaa><aab>
p(PPP)p(PPD)
211112211123
Code: Select all
***** *****
* * * * * *
*
prīmus terprīmī et prīmus (bisprīmī et secundī)
Semiprime (19 * 37)
Asymmetric
Not Alphabetic
Squarefree, but recursively only
Nodes: 9
Reversals: 11
Max Depth: 3
Smoothness: 37

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
704
<><><><><><><<<<>>>>
aaaaaad
<><><><><><><<<<>>>>
aaaaaad
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
705
<<>><<<>>><<<>><<<>>>>
59.62% efficiency
<<>><<<>>><<<>><<<>>>>
59.62% efficiency
good luck have fun

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
706
<><<<><><<<>>>>>
a<<aac>>
<><<<><><<<>>>>>
a<<aac>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
707
<<><>><<><<><<>>>>
<aa><a<ab>>
spPPpPpPD^{1} or p(PP)p(Pp(Pp(P)))^{1} or spPPpPpPpPpPS^{1}
2112212124
prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))
Semiprime (7 * 101)
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 9
Max Depth: 4
Smoothness: 101

^{1}Notes on this version of pnotation I've been developing
<<><>><<><<><<>>>>
<aa><a<ab>>
spPPpPpPD^{1} or p(PP)p(Pp(Pp(P)))^{1} or spPPpPpPpPpPS^{1}
2112212124
Code: Select all
*** *****
* * * ***
* *
*
prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))
Semiprime (7 * 101)
Asymmetric
Not Alphabetic
Squarefree, but recursively only cubefree
Nodes: 9
Reversals: 9
Max Depth: 4
Smoothness: 101

^{1}Notes on this version of pnotation I've been developing
Spoiler:

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
*sigh* We all want to have 709 don't we?
708
<><><<>><<<><>>>
708
<><><<>><<<><>>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
I just realized that 709 is a special number. That explains why the activity suddenly dropped.

709
<<<<<<<>>>>>>>
g (alphabet)
J (SPDFGHIJ/orbitals)
77 (7 up, then 7 down)
septimus
Recursively prime/alphabetic atom. This sequence goes 1,2,3,5,11,31,127,709. The next one is 5381. According to OEIS, this is A007097.
Nodes: 7
Reversals: 1
Max Depth: 7


709
<<<<<<<>>>>>>>
g (alphabet)
J (SPDFGHIJ/orbitals)
77 (7 up, then 7 down)
Code: Select all
*
*
*
*
*
*
*
septimus
Recursively prime/alphabetic atom. This sequence goes 1,2,3,5,11,31,127,709. The next one is 5381. According to OEIS, this is A007097.
Nodes: 7
Reversals: 1
Max Depth: 7

Re: Count up with recursive prime factorization
710 = <><<>><<>^{<>}<<>>>
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
712 = <><><><<<<>>><<<>>>>
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