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Jun 23, 2015 · SSCG (Simple Subcubic Graph) numbers grow more rapidly: SSCG(0) = 2, SSCG(1) = 5, SSCG(2) = 3*2^(3*2^95 ...

Oct 28, 2017 · Contrary to r.e.s.'s answer, the restriction to subcubic graphs is not necessary. See here, for example.. It is not hard to prove this:

Apr 5, 2023 · From what I have gathered online about these numbers, they say that Loader's Number is larger than TREE(3) or SSCG(3) or similar. The reasoning I have seen goes is that Loader's Number is the largest computable number and TREE(3) and SSCG(3) are ostensibly computable numbers. But how do we know that:

I'll try to answer. It's a rather difficult question since (1) answering why something in mathematics is the way it is is troublesome; and (2) this subject has technical details that make it difficult to give a "beginner's explanation".

Aug 13, 2016 · $\begingroup$ Suppose you took your example number manipulated it as follows: $$2091580284\dots384901284021=2091580284\dots384901284020+1$$ $$=2(1045290142\dots192450642010)+1$$ $$=4(522645071\dots096225321005)+1$$ $$=20(1045290014\dots019245064201)+1$$ And so one, we factor.

$\begingroup$ Yes, I read that question and its answers, and followed the link to Prof. Friedman's post. He mentions a theorem relating SCG(13) to the halting-time of a Turning machine.

Oct 19, 2023 · $\begingroup$ Thanks for the link Benjamin! On the one hand, it appears that this is a very difficult question, yet on the other hand, Friedman writes, "Also, numbers derived from Goodstein sequences or Paris/Harrington Ramsey theory, although bigger than n(4), are also completely UNNOTICEABLE in comparison to TREE[3]."

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May 21, 2017 · No, Rayo's Number is just too big, imagine a Googol symbols in the first order set theory, you cannot express it, why? because even writing down a symbol per Planck time (5.39 x 10^-44 seconds) it would still take about 10^48 years, and another problem is the space, the number of particles in the observable is about 10^80, a Googol is 10^100,and bigger than any …