This is an interesting question with not so obvious answers. In addition to the helpful observations already made, there is a bit more to add.

A good RG discussion to check concerning this question (and the implementation of a so-called true random number generator) is

https://www.researchgate.net/post/What_approach_would_you_take_to_implement_a_true_random_number_generator

See, for example, the observation by @ Mario Stipčević using a photon counter. See, also, Mario Stipčević

Another important RG discussion on randomness is ongoing at

https://www.researchgate.net/post/Are_there_any_random_phenomena_the_randomness_of_which_is_based_upon_their_causeless_nature2

See, also:

https://www.researchgate.net/post/Is_there_a_test_to_determine_how_random_a_number_sequence_is

This is an interesting question with not so obvious answers. In addition to the helpful observations already made, there is a bit more to add.

A good RG discussion to check concerning this question (and the implementation of a so-called true random number generator) is

https://www.researchgate.net/post/What_approach_would_you_take_to_implement_a_true_random_number_generator

See, for example, the observation by @ Mario Stipčević using a photon counter. See, also, Mario Stipčević

Another important RG discussion on randomness is ongoing at

https://www.researchgate.net/post/Are_there_any_random_phenomena_the_randomness_of_which_is_based_upon_their_causeless_nature2

See, also:

https://www.researchgate.net/post/Is_there_a_test_to_determine_how_random_a_number_sequence_is

Good resources and informative links. Indeed, a lot of evidence abounds that there exists true randomness.

Within electronic, digital computational environments, there is no such thing as a random number. The best one can do is to distribute probability of occurrence across a set of options, and the number of those options is related to the number of bits that are taken to represent any one such option. Hence, the proper understanding of randomness within computational environments is in terms of disorder; this is the best you can do, to obtain maximal disorder; and thus, predictability in a maximal sense.

I follow the link above by Dr. James F Peters

A few months ago I drafted a paper 'Probability and Duplication Theory' which is on this site. My answer to your question is that absolutely perfect randomness is impossible and what I define as a singulairity state. However as with all other singulaity states, as close approaches are made to them, the rules of nature as they are currently familiar to us, or were, start to vary (for instance light speed , absolute zero of temperature et al.)

I use this conjecture to explain my first interest which is the operation of memory which I see as the transfer of similar structures formed in the brain by interference patterns generated by flow of electrochemcial currents between neurons. I speculate these produce holographic images which are capable of resonance through time using a rationale of quantum entanglement.

It is now known that successful experiments to produce entanglement rely upon both the receiving and transmitting ends of the process to operate as perfectly randomly as possible. This is very similar to the assumptions I use for my proposals to explain the modus operandi behind memory, and a few other allied phenomena, one of which I recently realised was possibly the law probability for which there has to be an explanation for its existence, and a simple one at that, which currently has not been divined, and ditto light speed and why it is that one particular figure.

This and a few other papers can be found on this web site under my name, although there is an improved and synopsis version of Duplication theory nearing completion , and much shorter than the original 26 pages: so many academci papers are far too long. There is also a website (www.mindandmemory.net) but this needs seerious updating and improvement.

I am still with Einstein about the "hidden-variables" that follows in this excerpt:

Article Particles and Paradoxes: The Limits of Quantum Logic.

(http://assets.cambridge.org/97805213/36918/excerpt/9780521336918_excerpt.pdf)

and an article i wrote about how frequency of variables in physical aspects should be tracked and understood to reach a proper mechanics of events:

Article Trend of Random Events in Organizing When Influenced by a No...