Skewes' Massive Number - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as an accessible background on Skewes' number and on patterns that hold for huge ranges before failing.
Recommended by 1 people across 1 different months, 2018 to 2020.
What it is
A Numberphile video in which Dr James Grime explains Skewes' Number, a huge bound tied to the prime counting function and the claim that li(x) always exceeds pi(x). He describes how the pattern holds for enormous values and then flips. Filmed by Brady Haran.
What people said
Recommends Mr Pie · 2018-01 · Mathematics Stack Exchange · on “A formula for $\pi(x)$”
It is trivial that there are smaller terms that we do not know, for otherwise the equation would be expressed differently with the actual smaller terms *included*. Here is a video that provides a background on this sort of equation $\longrightarrow$ [this video]
Cites Brian · 2019-01 · Mathematics Stack Exchange · on “Examples of patterns that eventually fail”
Quoting James Grime on Numberphile: "So this is a pattern that holds ... into huge sizes of googols of googols of googols, and it appears that this inequality holds and then it flips." ( [this video] )
Cites mathematics2x2life · 2020-05 · Mathematics Stack Exchange · on “Should I waste my time with wolfram alpha to solve such problem like $x^3+y^3+z^3=390$?”
How do you know solutions exist? This should always be the first step. You will never disprove that there are no solutions (in this case) by trying 'lots' of numbers. [I hear the words of John Conway talking about 'proving Fermat's Last Theorem by inspection' when asked by a reporter echo in my ears.] Even if you know they exist, unless you have bounds on the solutions or another some other better method, they are not likely to be 'easily' (if at all) found by computational 'guess 'n check'. Even if this is the way to go, WolframAlpha will NEVER be the way to do this. It will time you out after less than 30 seconds of computation. So you better hope that whatever you are trying is done by th