@basedlarp32: Son what is this 😭😭😭 #starmer #acceleration #dwbi #larp Graham’s number is an extremely, absurdly large number from a branch of mathematics called Combinatorics. It came up in a problem about high-dimensional geometry and colorings. Here’s the idea: * Normal huge numbers: * A million = 10^6 * A googol = 10^{100} * A googolplex = 10^{(10^{100})} Those are already enormous. Graham’s number is built using Knuth’s up-arrow notation, which grows way faster: * 3 \uparrow\uparrow\uparrow\uparrow 3 is unimaginably bigger than a googolplex. * Graham’s number starts with: g_1 = 3 \uparrow\uparrow\uparrow\uparrow 3 Then each next step uses the previous one as the number of arrows: g_2 = 3 \uparrow^{g_1} 3 and this repeats 64 times. The final g_{64} is Graham’s number. Why it’s wild: * It’s so huge that the observable universe couldn’t store all its digits. * You could never write it out fully. * Even the number of digits in Graham’s number is incomprehensibly massive. But here’s the surprising part: We know its last digits. It ends in: …7262464195387 That’s because mathematicians can use modular arithmetic to compute the end without knowing the whole thing. A funny perspective: Even though Graham’s number is gigantic, there are still much larger numbers in math, like those from Busy Beaver function or large countable ordinals. So Graham’s number is famous not because it’s “the biggest,” but because it’s one of the largest numbers ever used in a serious proof.
