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  • PsiCubed2

    Seeing as how many people are having difficulties keeping track of the various googological realms, I've decided to to create my own googological ruler which aims to be as straightforward and as easy to use as possible.

    I call my googological levels "Psi Levels", and they are simply integers between 0 to around 100. The proposed numbers are the bottom boundary of each level.

    Please tell me if you find this useful. Feedback and suggestions are welcome.



    Proposed Psi Level Arrows/BEAF Equivalent Ordinal Letter Notation Wiki Class Name
    0 0
    Class 0
    1 10
    E1 Class 1
    2 10↑10 1 E10 Class 2
    3 10↑↑3
    F3 Class 3
    4 10↑↑4
    F4 Class 4
    5 10↑↑5
    F5 Class 5
    6 10↑↑10 2 F10 = G2 Tetration Level
    7 10↑↑↑3
    G3 Up-arrow Notation Level
    8 10↑↑↑10
    G10

    9 10↑↑↑↑10 4 H10 = J4

    10…












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  • PsiCubed2

    Which number is bigger:

    (1) L = Loader's number

    (2) X = The largest possible output of a TM with 10100 states whose halting is provable by 2nd order Arithemetic?

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  • PsiCubed2

    n Ξ(n) (expand prefixes only) Ξ(n) (expand anywhere)
    1 1 1
    2 2 2
    3 3 3
    4 4 4
    5 6 6
    6 17 17
    7 51

    8 ≥137 ≥80
    9 ≥519

    10 ≥21768

    11 ≥43539

    12 ≥87081 ≥196606 Read more >
  • PsiCubed2

    Counting with Ordinals

    November 30, 2017 by PsiCubed2






    Ordinal Array Visualization Box Visualiation Letter Equivlaent
    1 1 ● E10 = F2
    2 2 ●● F10 = G2
    3 3 ●●● G10 = H2
    4 4 ●●●● H10 = J4
    5 5 ●●●●● J5
    6 6 ●●●●●● J6
    7 7 ●●●●●●● J7
    ω (1,0) [●] J10 = K2
    ω+1 (1,1) [●]● K10 = L2
    ω+2 (1,2) [●]●● L10 = M2
    ω+3 (1,3) [●]●●● M3
    ω+4 (1,4) [●]●●●● M4
    ω+5 (1,5) [●]●●●●● M5
    ω×2 (2,0) [●][●] M10 = N2
    ω×2+1 (2,1) [●][●]● N2.1
    ω×2+2 (2,2) [●][●]●● N2.2
    ω×2+3 (2,3) [●][●]●●● N2.3
    ω×3 (3,0) [●][●][●] N3
    ω×3+1 (3,1) [●][●][●]● N3.1
    ω×4 (4,0) [●][●][●][●] N4
    ω×5 (5,0) [●][●][●][●][●] N5
    ω2 (1,0,0) [●●] N10 = 1P2
    ω2+1 (1,0,1) [●●]● P2-101
    ω2+2 (1,0,2) [●●]●● P2-102
    ω2+3 (1,0,3) [●●]●●● P2-103
    ω2+4 (1,0,4) [●●]●●●● P2-104
    ω2+ω (1,1,0) [●●][●] P2-11
    ω2+ω+1 (1,1,1) [●●][●]●

    P2-111


    ω2+ω+2 (1,1,2) [●●][●]●● P2-112
    ω2+ω×2 (1,2,0) [●●][●][●] P2-12
    ω2+ω×2+1 (…




































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  • PsiCubed2

    Since some people here have strong backgrounds in number theory, I figured I'll ask this here:

    Suppose I have a semprime N that factors into two distinct primes of a similar size p and q.

    We all know that if N is large enough, it would impractical to factor it (that's how RSA works). But is there a practical way to derive some information on the digits of p and q?


    If anyone is interested why I'm asking, here's the deal:

    I'm mastering an rpg game and I want to give my players a secret document that has the following properties:

    (1) They get an actual encrypted document (a string of numbers on a piece of paper) at a certain point in time, which wel'll call "Time A".

    (2) They are supposed to find "the key" at a later point in time, which we'll call "Ti…


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