At $540m and counting, Mega Millions is the ‘big one’

“Oh my God!’’ a customer exclaimed, carefully tucking a batch of tickets into a purse pocket. “It just went up again! $540 million!’’

As if hearing her call, a new rush of people arrived at the Dorchester convenience store, eyes widening at the staggering sum. With half a billion dollars up for grabs in the national contest, they weren’t there to buy milk and bread.

“It’s crazy,’’ El-Shurafa said. “People aren’t even playing the other games. Faces I’ve never seen, and they don’t even know what the game is called. They just say they want a ticket for the big one.’’

Massachusetts has always loved its lottery, but the frenzy leading up to Friday night’s Mega Millions drawing has reached new heights.

Since Tuesday, when the latest drawing again produced no grand prize winner, players have spent $3.6 million on $1 tickets. On Friday alone, lottery officials say sales could easily top $10 million.

To put that in perspective, the state’s population is 6.5 million.

“This is uncharted territory,’’ said Beth Bresnahan, spokeswoman for the Massachusetts State Lottery. “Each time the jackpot jumps, more and more people get involved. We’re at the point where people who would never play the lottery are buying tickets, simply because it’s such an amazing amount.’’

The largest prize yet awarded to a Massachusetts player was $294 million, a Mega Millions jackpot won in 2004 by a Lowell woman.

While smaller prizes still yield more money than most people dream of, ticket sales surge when jackpots reach the stratosphere.

Somewhere around that threshold, media attention and word of mouth attract casual players and cause regulars to buy that many more.

“It draws people out of the woodwork,’’ Bresnahan said.

Eileen Healy, for instance, bought one ticket for Tuesday’s drawing. This time, she outside the Tedeschi, she grabbed three.

“I don’t usually gamble, except when it gets really big,’’ she said. “Just like everybody else.’’

Maria Gonzales, 51, said she plays the lottery every day, sometimes spending $100 a week. But for the big-ticket draw, she has boosted her investment - against her better judgment.

“Too much,’’ she said, shaking her head at a roll of tickets. “I’m a crazy player.’’

She wasn’t alone, convenience store clerks said.

“Everybody is crazy about it right now,’’ said Raj Patel, a clerk at Daily Mart in Medford. “Usually it is busy, but right now it is Mega Millions.’’

At the Tedeschi, signs for Mega Millions were plentiful, even on top of the ATM. And nearly everyone who stopped in snagged a ticket or 10, from police officers and mail carriers to mothers with toddlers.

No one really expected to win. But they weren’t about to give up the chance to try.

“Why not?’’ asked Chuck Hulme, 52. “Take a shot.’’

Hulme hadn’t given much thought to what he would do with so much money, but quipped that others would be happy to take some off his hands.

“Twelve brothers and sisters, knocking on the door,’’ he said.

The current jackpot far surpasses the previous Mega Millions high of $390 million, and as players in 42 states stake their claim before Friday’s drawing, it could climb further still.

“There is a strong possibility that it will increase before the drawing tomorrow,’’ said Paul Sternburg, who directs the Massachusetts Lottery Commission. “Each day, sales increase exponentially.’’

The odds, of course, are long - approximately 1 in 176 million. To win the jackpot, a player must match all six numbers drawn. Smaller prizes are available.

But those with a dollar and a dream were dreaming of the jackpot, even if they couldn’t really wrap their mind around its scale.

“I’d buy a second house,’’ said Lorraine Nania, a 79-year-old from Dorchester. “And get someone to clean it. So I could just sit back. Maybe play some more bingo.’’

Ed Kelly, 87, was among the few who didn’t buy a ticket Thursday. He prefers Keno. The game unfolds slowly and lends itself to a beer and a chat, he said. If the chat is boring, at least the numbers can entertain you.

“That’s my game,’’ he said. “It’s been good to me.’’

Peter Schworm can be reached at schworm@globe.com. Follow him on Twitter @GlobePete. Colin A. Young can be reached at colin.young@globe.com