Revelation 20:2 - 7
ESV - 2 And he seized the dragon, that ancient serpent, who is the devil and Satan, and bound him for a thousand years. 3 And threw him into the pit, and shut it and sealed it over him, so that he might not deceive the nations any longer, until the thousand years were ended. After that he must be released for a little while.
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I make no claim to be an "end-times" expert, but as I understand prophecies of the millennium (such as the passage cited in the question), it will involve the visible (that is, not concealed or secret) reign of the returned Christ on earth, during which Satan will be confined. Given that description, I would say that, regardless of whatever stage of the close of the present age we may be in judging from other given signs of its occurrence, we are not currently in the millennial kingdom, since Christ has not yet returned, and Satan is still very much active.
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