## Count up with recursive prime factorization

For all your silly time-killing forum games.

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tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

691
<<<<>>><<<>>><<<>>>>
<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
good luck have fun

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

693
<<>><<>><<><>><<<<>>>>
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
good luck have fun

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

695
<<<>>><<><<<><>>>>
c<a<<aa>>>
Fp(Pd(PP))
33213114

Code: Select all

`* ****** * ****   ***    * *`

$\mathfrak{p}(\omega^{\omega^{\omega^{2}}+1}+\omega^{\omega})$
tertius et prīmus (prīmī et secundī bisprīmī)
7 by 5 with four extra dots; not happy with how the image turned out at the bottom right of the 139.
695bl.png (3.47 KiB) Viewed 4322 times

Spoiler:
A little happier with this version,
695bl2.png (3.44 KiB) Viewed 4320 times

or maybe this one.
695bl3.png (3.45 KiB) Viewed 4317 times

A version with arms
695b5al.png (1.56 KiB) Viewed 4314 times

Semiprime
Asymmetric
Not Alphabetic
square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 139

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

696
<><><><<>><<><<<>>>>
aaab<ac>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

697
<<<><>>><<<><<>>>>
<<aa>><<ab>>
d(PP)d(PD)
31133124

Code: Select all

`*** ****** **** * * *      *`

$\mathfrak{p}(\omega^{\omega^{\omega+1}}+\omega^{\omega^{2}})$
secundus bisprīmī et secundus (prīmī et secundī)

8 by 4 with one dot extra
697al.png (1.43 KiB) Viewed 4301 times

Semiprime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 41

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

698
<><<>><<<<>><<>>>>
ab<<bb>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

699
<<>><<<>><<<><>>>>
b<b<<aa>>>
Dp(Dd(PP))
22323114

Code: Select all

`* ****** * ***  * ***    * *`

$\mathfrak{p}(\omega^{\omega^{\omega^{2}}+\omega}+\omega)$
secundus et prīmus (secundī et secundī bisprīmī)
6 by 5 exactly.
699l.png (1.59 KiB) Viewed 4290 times

Semiprime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 233

----
Mistaken labyrinth notation, where I replaced a 3 with a 5, making 1165.
Spoiler:
7 by 6 with seven unused dots, not optimal - EDIT: WRONG - this is 1165.
699l.png (1.67 KiB) Viewed 4299 times

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
good luck have fun

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

701
<<><<>><<>><<><>>>
<abb<aa>>
p(PDDp(PP))
2122222113

Code: Select all

`********** * * ***  * * * *`

$\mathfrak{p}(\omega^{\omega^{2}+\omega2+1})$
prīmus (prīmī et bissecundī et prīmī bisprīmī)
5 by 5 with one extra dot.
701l.png (1.36 KiB) Viewed 4278 times

Prime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 9
Max Depth: 3

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

702
<><<>><<>><<>><<><<>>>
abbb<ab>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

703
<<><><>><<><><<>>>
<aaa><aab>
p(PPP)p(PPD)
211112211123

Code: Select all

`***** ****** * * * * *          *`

$\mathfrak{p}(\omega^{\omega+2}+\omega^{3})$
prīmus terprīmī et prīmus (bisprīmī et secundī)
5 by 4 exactly...
703al.png (1.27 KiB) Viewed 4270 times
but if I arrange it like this, you can see how similar the two factors are.
703bl.png (1.42 KiB) Viewed 4270 times

Semiprime (19 * 37)
Asymmetric
Not Alphabetic
Square-free, but recursively only tetradbiquadrate-free

Nodes: 9
Reversals: 11
Max Depth: 3
Smoothness: 37

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

704
<><><><><><><<<<>>>>
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
good luck have fun

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Count up with recursive prime factorization

706
<><<<><><<<>>>>>
a<<aac>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### Re: Count up with recursive prime factorization

707
<<><>><<><<><<>>>>
<aa><a<ab>>
spPPpPpPD1 or p(PP)p(Pp(Pp(P)))1 or spPPpPpPpPpPS1
2112212124

Code: Select all

`*** ****** * * ***      * *        *`

$\mathfrak{p}(\omega^{\omega^{\omega+1}+1}+\omega^{2})$
prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))
7 by 4 with two extra dots.
707al.png (1.45 KiB) Viewed 4265 times

Semiprime (7 * 101)
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 9
Max Depth: 4
Smoothness: 101
----
1Notes on this version of p-notation I've been developing
Spoiler:
It occurs to me that I've been using this notation for a while, and haven't really defined it anywhere (I think.). s, p, d, f, g, etc., are prefix binary functions (p*q, p*qth prime, etc.) and S, P, D, F, G, etc., are constants. (1 = "", 2 = <>, 3 = <<>>, 5 = <<<>>>, 11 = <<<<>>>>, etc..) This way, we can have a nonambiguous grammar without parentheses.

Of course, if I put parentheses afterwards, then the function just applies to the value in front, so s(Number) evaluates to Number, p(Number) evaluates to Numberth prime, etc.; also, in this case, assume sequences of terms evaluate to the product.

Without s, S, or parentheses, we can represent any prime with recursively no more than two factors. With parentheses, or with s, we can represent any number (where 1 is represented by the empty string).

tomtom2357
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
<><><<>><<<><>>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

### 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)

Code: Select all

`*******`

$\mathfrak{p}(\omega^{\omega^{\omega^{\omega^{\omega^{\omega}}}}})$
septimus
7 by 7.
709l.png (3.79 KiB) Viewed 4244 times

bad attempt of making circles
709al.png (4.51 KiB) Viewed 4241 times

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
----

solune
Posts: 121
Joined: Thu Jul 21, 2011 12:58 pm UTC

### 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

711
slurpe
<<>><<>><<><<<<>>>>>
good luck have fun

solune
Posts: 121
Joined: Thu Jul 21, 2011 12:58 pm UTC

### Re: Count up with recursive prime factorization

712 = <><><><<<<>>><<<>>>>

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