Here is an argument I made that it is NP-complete to determine if a number n is the product of two numbers that differ by less than the fourth root of n:
5.5 bits is also the average information content of a single run of the GHZ experiment. In this setup three parties independently choose a binary detector setting and each observe a binary outcome. The first two parties observe an independent random bit regardless of their settings. If an odd number of the parties have their setting "on", then the third party also observes an independently random bit (6 bits total to record, 3 for the settings and 3 for the observations). But if an even number of of the three settings are "on", then the third party's observation is completely determined by the other 5 bits. When the settings are chosen randomly these two possibilities are equally likely so on average it takes 5.5 bits to record the results of the experiment.
Check out my new generative world map! It uses an iterated resolution-doubling conditional GAN currently trained on Van Gogh's collective works. Each zoom level takes 5-10 seconds to generate if not already cached so please be patient. You can go all the way to zoom level 2^30 making total number of pixels equal to about 1/8 of Avogadro's number.
But I might be over median!