DES MOINES, Iowa —

Paula Otto, executive director of the Virginia Lottery and Mega Millions’ lead director, said ticket sales are ahead of projections for Tuesday’s drawing, increasing the likelihood that the record could fall by then. If the prize goes unclaimed for a 22nd consecutive drawing, the next one likely would shatter the record, set in March 2012, she said.

“I think we’ll be very close to the record, and maybe even surpass it,” Otto said, adding that sales are difficult to predict.

That was enough for Drew Gentsch to play one ticket Monday morning. The attorney from Des Moines never plays, but the jackpot was too good to pass up.

“I think it’s ridiculous but you have to dream big,” he said. “The odds of winning are so low, there’s no real reason to play. But it’s fun to do so once in a while.”

Between 65 and 75 percent of the roughly 259 million possible number combinations will be in play when the numbers are drawn, Otto estimated. She said the jackpot may be increased one more time on Tuesday morning in advance of the evening drawing.

“Lotto players are procrastinators. They tend to buy on the day of the draw,” she said.

No ticket matched the six numbers needed to win Friday’s $425 million prize. The jackpot was raised Saturday to $550 million before Monday’s jump to $586 million. It is currently the fourth-largest jackpot in U.S. history.

Some players were taken aback by the growing jackpot and the possibility that it could keep getting bigger.

Natali Justiniano Pahl, 47, bought five tickets from a convenience store in downtown Des Moines. She said the growing jackpot made her excited, albeit somewhat weary.

“It gets the excitement up, but there’s a point when it’s too much,” said Justiniano Pahl, who works in human resources. “$5 million would be good; $550 million would be good. Either one would change your life.”