DES MOINES, Iowa >> The Mega Millions jackpot inched toward a U.S. lottery record today as it soared to $586 million amid a frenzy of ticket purchases, raising the possibility that the prize could pass the once-unthinkable $1 billion mark by Christmas Eve should nobody win before then.

Paula Otto, executive director of the Virginia Lottery and lead director for Mega Millions, said ticket sales are ahead of projections for Tuesday’s drawing, increasing the likelihood it could shatter the current record of $656 million, set in a March 2012 Mega Millions drawing.

That was enough for Drew Gentsch to buy one ticket Monday morning. The attorney from Des Moines never plays, but the ballooning 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."

The large Mega Millions prize is the product of a major game revamp in October that dramatically lowered the odds of winning the jackpot. If a winner isn’t selected Tuesday night and it rolls over past the next drawing scheduled Friday night, Otto predicts the jackpot will reach $1 billion — an unheard of amount for Mega Millions or Powerball, the nation’s two main lottery games.

"We had predicted last week that if we are still on the same roll on Christmas Eve, we’ll definitely be over a billion," she said.

Scott Norris, a mathematician from Southern Methodist University, said he estimates around 700 million more tickets must be sold without producing a winner for the jackpot to reach $1 billion on this run. He puts the odds of that around 6 percent.

Norris emphasized his calculation does not take into account the extra $1 that players can throw in for the Megaplier option, which allows them to increase their non-jackpot prize by up to five times.

John Hagerty, a spokesman for the Virginia Lottery, said officials can’t confirm Norris’ calculation. He said there’s no clear number for sales if the jackpot rolls past Tuesday, so they can’t accurately calculate what percentage of the possible combinations will be covered.

The current jackpot, which is the fourth largest in U.S. history and closely trails the $587.5 million and $590.5 million set by Powerball, has had heavy sales over the last several days. Otto noted that the higher the jackpot, the higher the sales. For example, when the jackpot was $99 million on Nov. 5, lottery officials sold just over $20 million worth of tickets. For Friday’s then-$425 million jackpot, $168 million worth of tickets were sold.

Otto said it’s likely the jackpot will be increased again after lottery officials meet Tuesday morning to discuss sales. Between 65 and 70 percent of the roughly 259 million possible number combinations will be in play when the numbers are drawn, Otto estimated.

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

Some players were taken aback by the growing jackpot and the possibility that it could keep getting bigger if it rolls for a 22nd consecutive time.

Natali Justiniano Pahl, 47, bought five tickets Monday morning from a convenience store in downtown. 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."

Otto said officials have never had such a huge jackpot around this time of year, and it’s unclear how holiday shoppers are driving sales.

"To have that kind of money on the line the week before Christmas, we’ve never had that happen before," she said, "What fun."

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Associated Press writers David Pitt in Des Moines and John Mone in Dallas contributed to this report.