As at the time of answering (6 August 2016) It would be 1984. In a few days though, the answer would have been 1985.
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One billion seconds ago is roughly the equivalent of 31.7 years ago, using the US definition of one billion. One billion is one thousand millions.
1 billion minutes ago was the year 110 . 1 billion minutes later will be the year 3913 .
The answer is unknown.
That was about 114,155 years ago, or 112,142 BC
year 1991.