## Count up with recursive prime factorization

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

### Re: Count up with recursive prime factorization

611
<<><<>>><<<>><<<>>>>
<ab><bc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

612
<><><<>><<>><<<><>>>
ab<<aa>>ba
$\mathfrak{p}(\omega^{\omega^2}+\omega2+2)$

@faubi: That looks fine.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

613
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113

Code: Select all

`************ * * * ***        * *`
$\mathfrak{p}(\omega^{\omega^{2}+4})$

Prime: Yes
Symmetrical: Yes
Alphabetical: No

Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

614
<><<<>><<>><<><>>>
a<bb<aa>>
$\mathfrak{p}(\omega^{\omega^2+\omega2}+1)$

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

615
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124

Code: Select all

`* * **** * ***  * * *      *`
$\mathfrak{p}(\omega^{\omega^{\omega+1}}+\omega^{\omega}+\omega)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

616
<><><><<><>><<<<>>>>
aaa<aa>d
$\mathfrak{p}(\omega^{\omega^\omega}+\omega^2+3)$

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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

### Re: Count up with recursive prime factorization

617
<<<><<>><<<>>>>>
<<abc>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

618
<><<>><<<>><<>><<>>>
ab<bbb>
$\mathfrak{p}(\omega^{\omega3}+\omega+1)$

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

619
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113

Code: Select all

`********** * *****  * * * *`
$\mathfrak{p}(\omega^{\omega^{3}+\omega+1})$

Prime: Yes
Symmetrical: No
Alphabetical: No

Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4

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

### Re: Count up with recursive prime factorization

620
<><><<<>>><<<<<>>>>>
aace
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

621
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223

Code: Select all

`* * * **** * * * *      * *`
$\mathfrak{p}(\omega^{\omega2}+\omega3)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2

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

### Re: Count up with recursive prime factorization

<><<><><><><><>>
a<aaaaaa>
P(w6+1)
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

623
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123

Code: Select all

`*** ******** * * * * *          *`
$\mathfrak{p}(\omega^{\omega+3}+\omega^{2})$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

624
<><><><><<>><<><<>>>
aaaab<ab>
$\mathfrak{p}(\omega^{\omega+1}+\omega+4)$

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

625
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333

Code: Select all

`* * * ** * * ** * * *`
$\mathfrak{p}(\omega^{\omega}4)$

Prime: No
Symmetrical: Yes
Alphabetical: Yes

Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0

Another integer power.

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: Count up with recursive prime factorization

626
<><<><><><<><<>>>>
a<c<ab>>
$\mathfrak{p}(\omega^{\omega^{\omega+1}+\omega^{\omega}}+1)$

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

627
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112

Code: Select all

`* * ****** * * * *  *        *      `
$\mathfrak{p}(\omega^{3}+\omega^{\omega^{\omega}}+\omega)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2

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

### Re: Count up with recursive prime factorization

The number is 628.

Here's a new notation!
103242301
423230101

In the more standard bracket-notation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Half-length: 7
Reversals: 9
Depth: 4
$\mathfrak{p}\left(\omega^{\omega^{\omega+2}} + 2\right)$
in pink ordinals (fora, echo), whatever they are.

628l.png (421 Bytes) Viewed 2083 times

(note: boundary notation, not level-set. The boundary between blobs represents the rooted tree formation thing.)

Minimal square is 11*11 or 9*9, depending on counting method.
Minimal area is 9*13 or 7*11. First number is twice depth ± 1. Obvious proof. Twice depth ± 1 is the smallest number.

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

629
<<<><>>><<><><<>>>
65.9% efficiency
good luck have fun

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

630
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112

Code: Select all

`* * * * ***  * * * * *      *    `
$\mathfrak{p}(\omega^{2}+\omega^{\omega}+\omega2+1)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

631
<<<<>>><<<>><<>>>>
65.92% efficiency
good luck have fun

ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

### Re: Count up with recursive prime factorization

632
Last edited by ygh on Sat Jul 30, 2016 3:15 am UTC, edited 1 time in total.
I don't know what I'm doing.

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

633
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235

Code: Select all

`* **** ***  * *  * *    *`
$\mathfrak{p}(\omega^{\omega^{\omega^{\omega}+\omega}}+\omega)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

634
<><<><<>><<<<>>>>>
65.95% efficiency
good luck have fun

ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

### Re: Count up with recursive prime factorization

635
cf
I don't know what I'm doing.

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

636
<><><<>><<><><><>>
65.96% efficiency
good luck have fun

ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

### Re: Count up with recursive prime factorization

637-
<aa><aa><ab>
I don't know what I'm doing.

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

638
<><<<<>>>><<><<<>>>>
64.35% efficiency
good luck have fun

ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

### Re: Count up with recursive prime factorization

639

<<>><<><><<<>>>><<>>
I don't know what I'm doing.

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

640
<><><><><><><><<<>>>
64.36% efficiency.
good luck have fun

ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

### Re: Count up with recursive prime factorization

641
<aa<ac>>
I don't know what I'm doing.

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

642
<><<>><<><><<><>>>
66.01% efficiency
good luck have fun

Sabrar
Posts: 42
Joined: Tue Nov 03, 2015 6:29 pm UTC

### Re: Count up with recursive prime factorization

643
<<<>><<>><<><<>>>>

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

### Re: Count up with recursive prime factorization

AarexTiaokhiao wrote:
<<><>>
<<<>><<>>>

161

Times four makes my number, 644. Thus, we have

<><><<><>><<<>><<>>>

Code: Select all

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

I like this notation; it's easy to read.

That's four factors.

You can count the nodes at each level;
4, 4, 2, 0, 0...
This gives max depth and factors automatically.
The length is twice the sum: 10 ↦ 20.
Since the depth is less than five, you can use bbcode for the ordinal number;
ωω2 + ω2 + 2

I'm wondering, how many people are using a program, and how many are doing this manually?

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

645
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113

Code: Select all

`* * ****** * * ***  *   * *`
$\mathfrak{p}(\omega^{\omega^{2}+1}+\omega^{\omega}+\omega)$

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 9
Max Depth: 3
Factors: 3
Smoothness: 43
Necessary Brackets: 4

I've been using a program for a while now. Here's the current version

Sabrar
Posts: 42
Joined: Tue Nov 03, 2015 6:29 pm UTC

### Re: Count up with recursive prime factorization

646
<><<<><>>><<><><>>

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

647
<<><<<<><>>>>>
69.94% efficiency
good luck have fun

Sabrar
Posts: 42
Joined: Tue Nov 03, 2015 6:29 pm UTC

### Re: Count up with recursive prime factorization

648
<><><><<>><<>><<>><<>>

phillip1882
Posts: 117
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

649
<<<<>>>><<<<><>>>>
66.07% efficiency
good luck have fun

Sabrar
Posts: 42
Joined: Tue Nov 03, 2015 6:29 pm UTC

### Re: Count up with recursive prime factorization

650
<><<<>>><<<>>><<><<>>>