While the total period of MT19937 is $2^{19937}-1$ by design, is the period of the sequence of any of the individual bits from the output less than this? I'll admit I'm far too unfamiliar with group theory to understand Matsumoto and Nishimura's original proof for the period of the untruncated output, so I apologize if the answer follows trivially from it.

  • $\begingroup$ Each single one and zero bit repeats with about 50% chance directly. I think you need to clarify your question. $\endgroup$ – Maarten Bodewes Dec 7 '18 at 5:07
  • $\begingroup$ @MaartenBodewes Fair point, edited. $\endgroup$ – concat Dec 7 '18 at 5:20
  • $\begingroup$ are you talking about a part of the sequence or a sub-sequence $\endgroup$ – kelalaka Dec 7 '18 at 8:50
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    $\begingroup$ I'm voting to close this question as off-topic because it's about a non-cryptographic random generator. It would be on-topic on Computer Science. $\endgroup$ – Gilles 'SO- stop being evil' Dec 7 '18 at 9:51
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    $\begingroup$ i think this is a fine question. $\endgroup$ – b degnan Dec 7 '18 at 13:59