When watching the Numberphile video about Highly Composite Number, I spotted something that aroused some of my doubts. One of properties suggested by Ramanujan was that the highly composite number's powers of prime factors are in order of decreasing order, with the highest prime factor almost always (with exactly 2 exceptions: 4 and 36.) appearing with power of 1.
It seems to me this assertion hinges upon the next prime after the last being lower than the square of the previous one. While π(N) shows the average distance between the consecutive primes would be significantly lower than between the prime and it's square, as I understand it's more of a probabilistic thing, and while very unlikely, it's not guaranteed next prime will be found within pretty much any finite distance of the prior one. So is this property of highly composite numbers just a conjecture based on dwindling probability of such a gap between primes ever appearing, or is there some solid proof to it?