Privalova's husband and coach Vladimir Parashchyuk called her comeback a test of human potential.
"Being the mother of three, I don't think it has been done before, at least in athletics," he said.
Fanny Blankers-Koen, a 30-year-old mother of two, won four gold medals, in the 100, 200, 80 metres hurdles and the 4x100 relay, at the 1948 London Olympics.
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Being the world record holder in the high and long jump, the Dutchwoman could have won six but the Olympic rules at the time allowed women to compete in only four events.
"I don't think it's a fair comparison," Parashchyuk said.
"It was a long time ago. The competition is a lot tougher now, especially among women. For Irina, just making the Russian Olympic team would be like winning a medal."