Are numbers generated by True (hardware) Random Number Generators (TRNGs) more uniform than numbers from a Pseudo Random Number Generator (PRNG)? I understand that there are not much (analytical/numerical) information of TRNGs compared with PRNGs. What are the main users of TRNGs other than in gaming and cryptography?

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    $\begingroup$ Uniformity is unrelated to randomness. A TRNG could create an exponentially distributed variable. $\endgroup$ – Hugh Mar 13 '17 at 0:58
  • $\begingroup$ This provider of a TRNG gives some explanation of its uses random.org $\endgroup$ – Hugh Mar 13 '17 at 0:59
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    $\begingroup$ Uniformity is usually not an issue. In fact, most (if not all) PRNGs are constructed to be perfectly uniform over sufficiently long sequences (their periods). The concerns about PRNGs are associated with lack of independence. $\endgroup$ – whuber Mar 14 '17 at 19:38
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    $\begingroup$ I don't see why this would be considered off topic here. Understanding randomness, independence, and uniformity are clearly within our mandate. We have a [random-generation] tag, & questions about the generation of random &/or pseudo-random variates have traditionally been considered on topic here. I'm voting to leave open. $\endgroup$ – gung Mar 19 '17 at 14:19
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    $\begingroup$ @whuber, why not develop that into an answer? (This field is a bit esoteric & outside my expertise, but, w/ deference, I do wonder if it is a completely correct answer, however. My reasoning is that it seems to me a distribution cannot be perfectly uniform if there are gaps in the number line, as the probability of drawing a realization would be 0 w/i those gaps. Moreover, if a PRNG's period is finite, it seems to me there must be gaps, although they may be inconsequentially small. I am not sure if that would be equally true of a TRNG, & thus wonder if TRNGs could be considered more uniform.) $\endgroup$ – gung Mar 19 '17 at 14:27

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