Aug 11, 2017 · $\begingroup$ To see the computational effort for this last case, this is the partial 2015 blog posting of the above results: Sep 2015 Default New confirmed pi(10^27), pi(10^28) prime counting function records I am happy to announce that David Baugh and I have computed the number of primes below 10^27, the result is: pi(10^27) = …

On the other hand assuming typos is a last resort when parsing a proof. It is good to see the overall strategy of the proof before working through it and (2) makes no sense to me. There is a brief account of the proof in the Wiki page (bottom) on Skewes' number but I think it casts no light on this question.

Jul 23, 2010 · The first example which came to my mind is the Skewes' number, that is the smallest natural number n for which π(n) > li(n). Wikipedia states that now the limit is near e 727.952, but the first estimation was much higher.

Apr 17, 2017 · The Skewes number (or first Skewes number) is the number Sk_1 above which pi(n) is less than li(n) must fail (assuming that the Riemann hypothesis is true), where pi(n) is the prime counting function and li(n) is the logarithmic integral

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sadly, but according to my evaluation the number of ways of selecting half the universal atom tours is larger than Skewes' number. It is at least in the same ballpark (I think), which suggests Skewes' number is within reach of intuition (or at least, the stretched form of intuition I speak of in the OP). $\endgroup$ –

Jan 7, 2016 · It is difficult to describe the magnitude of Graham's number. With power towers , it is hopeless to describe it because the height of the power tower would have a comparable magnitude. Already a number like $3 \uparrow^{10} 3$ is much larger than the given number constructed by Skewes number.

Apr 9, 2019 · $\begingroup$ So g₁ lies in between Moser's number and Skewes' number and we may write : Skewes' number ≪ g₁ < Moser's number. $\endgroup$ – Beedassy Lekraj Commented Apr 11, 2019 at 18:24

Dec 3, 2018 · So for an x just beyond Skewes number the graph changes sign (if I have calculated correctly) near 3.8 and the first point at k=1 is now negative, and it is tempting to speculate (and well beyond the scope of the question but included for context) that the entire set of points changes sign.

Aug 10, 2018 · There are quite a few famous gigantic numbers used in useful mathematical proofs, like Skewes's number, Graham's number, and the number $2 \uparrow \uparrow 10^{10^6}$ from Coward and Lackenby's 2011 result on determining the ambient isotropy of links. However, these numbers are all upper (or lower) bounds, which I think is not quite as ...