Random number generation

This is beyond my retained mathematical skills, and I doubt I could have done when I was in school.

If I wanted to create the most random (i.e the lowest probability of a repeated number) generation of a set of numbers over multiple intervals, would it be equivalent to generate the number from the same range of values, or from different ones for each interval?

For example. Let's say I wanted to generate a 1,000,000 random numbers every hour for a 24 hour period, from an overall range of 0 to 999,999,999 and have the overall set over the course of a day be least likely to repeat any given number. Would it be better to generate a random number between and 000,000,000 and 099,999,999 for hour 1, then another one between 100,000,000 and 199,999,999 for hour two...etc. Or, would it be more random to generate a number from the whole range of 0 to 999,999,999 throughout the day?

Since over the course of a year, these numbers would be tied to the date, I am only concerned about not repeating a number in a given day, and cannot have sequential or predictable number patterns.

I need to get an idea of the odds of having a number repeat in any 24 hour period.

I know that random number generators are not truly random of course, but for practical purposes they do work, and especially for this purpose.

If you choose different number ranges in different time durations,
you are introducing non-randomness.

Pseudo random number generators have been designed and
statistical tests done to determine whether or not they are
susceptible to numerous recogniseable patterns.

Statistical tests can be done to compare their output distributions to
random distributions.

I would interpret your question by saying, you'd need to choose the entire range.
Two numbers repeating is also part of purely random patterns.

The randomness of a generator depends on it's design and polynomial equation,
for pseudo-random number generators generating a binary pattern,
followed by a binary to decimal converter.

The physicist follows suit, complaining he has no suitable formula.
The mathematician offers x.