  We discuss some aspects of swampland constraints - especially the swampland
distance conjecture - in a large number of space-time dimensions $D$. We
analyze Kaluza-Klein (KK) states at large $D$ and find that some KK spectra
possess an interesting dependence on $D$. On the basis of these observations we
propose a new large dimension conjecture. We apply it to KK states of
compactifications to anti-de Sitter backgrounds where it predicts an upper
bound on the dimension of space-time as a function of its characteristic
radius. We also apply our conjecture to black hole spacetimes, whose entropies
have a $D$-dependence very similar to that of the KK spectrum.
