A positive integer $n$ is extremely abundant if either $n=10080$, or $n>10080$ and


$$σ(n)/(n×log(log (n)))>σ(m)/(m×log(log (m)))$$


for all $10080≤m<n$. Here $σ(n)$ is the sum-of-divisors function and $log$ is the natural logarithm.


My **question** is: About any known result relating prime numbers with extremely abundant numbers.



Results relating prime numbers with extremely abundant numbers
[This paper](https://cs.uwaterloo.ca/journals/JIS/VOL17/Nazar/nazar4.pdf) lists several statements relating extremely abundant numbers and prime numbers, for example:


* There is an infinite number of primes which cannot be the largest
prime factor of any extremely abundant number.
* The largest prime factor $p(n)$ of any extremely abundant number $n$
satisfies $p(n)<\log n$.
* If $m\leq n$ then $p(m)\leq p(n)$.


