May I ask why?
Let's say you run your job on the hour, and you have a job running every 4h and another every 24h, without planning, because 4 divides 24, you have one in four chance of having them collide and having the 24h job running at the same time than the 4h job. If you add more 4h jobs, the probability that one of those 4h jobs collide each time with the 24h job increases.
The more jobs you have, the higher the probability that some will be divisors of others.
Using prime number for scheduling reduce the probability at a given time that those jobs collides. If you create a job every 5h and another every 23h, the 23h will collide with the 5h job every 115h. PPCM(5, 23) = 115.
Interestingly, this technique is used in nature by cicadas who developed long, prime-numbered, periodical life cycles to avoid gaining a predator that can sync up with the cicadas[0].
[0] https://www.cicadamania.com/cicadas/cicadas-and-prime-number...
If you're on a sufficiently large network, that surge can cause failures. And a fixed retry policy will just cause the same stampede to recur on the retry intervals; you want to add jitter to ensure that you spread the load out.
The more prime numbers you use, the rarer a stampede affecting a certain percent of nodes will be. To an extent that makes a bigger network safer.
Adding more nodes with the same prime numbers means the peak load scales linearly with the network size. So wouldn't that mean that a "sufficiently large" network is no worse off than a small network?
Also a backup is a bulk upload that can easily run a thousand times slower than normal and still succeed. Even if every server triggers at once, that shouldn't inherently cause failures.
15h, 2h, 9h, 20h, 7h....etc. So you won't have the backup running at the same time everyday.
Personally speaking I would prefer that the backup runs at the same time everyday but some people don't.
Depending on a more exact statement of the goal, the best constant interval to avoid repeating parts of the day on nearby dates would be to multiply a day's length by the golden ratio; this would be about every 38.833 hours.
Since the golden ratio is irrational, you'll technically never repeat the same time. But if I remember correctly, it's the best number to space out the times uniformly throughout the day and also distantly between nearby days.