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  • Christmas Eve’s Powerball jackpot worth an estimated $1.8B, 4th-largest in history

    Christmas Eve’s Powerball jackpot worth an estimated $1.8B, 4th-largest in history

    BUYING A TICKET AND A DREAM. >> POWERBALL AT 1.6 BILLION. TONIGHT, PEOPLE IN MILWAUKEE ARE TESTING THEIR LUCK. IT IS A GAME OF CHANCE. THAT IGNITES FANTASY. >> FEELING LUCKY TONIGHT. >> SO PEOPLE IN LINE AT THIS EAST SIDE CORNER STORE DAYDREAMING. >> IF I WON THE POWERBALL TONIGHT, I’D TAKE ALL OF US TO A HOTEL. >> OKAY? >> BECAUSE I’D LIKE TO WAKE UP IN A NICE HOTEL. >> OR ACTUALLY DREAMING. >> I WOKE UP WITH A DREAM, TOO. SO IT’S. IT’S IN MY CULTURE. IF YOU IF POOPED ON THAT, IT’S A GOOD DREAM. SO, HEY, WE’LL TEST IT OUT. >> ABOUT WHAT THEY WOULD DO FIRST. WITH $1.6 BILLION. >> SO FIRST, MY PARENTS WILL RETIRE. >> THE FIFTH LARGEST JACKPOT IN U.S. HISTORY. DREAMS STARTING OFF WITH FAMILY PLANNING. >> I WILL COME TOGETHER WITH THE KIDS, AND WE’LL GAME PLAN FROM THERE. >> AND ENDING WITH HORSE FARMS. >> LIZ AND I ARE GOING TO BUY A HORSE FARM TOGETHER. OKAY. NO, WE’RE NOT. >> LIZ QUICKLY OBJECTED. OR NOT? WISCONSIN HAD WINNERS BEFORE. >> I PRETTY MUCH FELT LUCKY. >> A $768 MILLION WINNER FROM NEW BERLIN IN 2019. THREE YEARS LATER, SOMEONE NEAR GREEN BAY HIT THE JACKPOT AND WON 316 MILLION. THIS TIME, EACH TICKET HOLDER CONVINCED. IF YOU HAVE A VISION FOR IT, YOU JUST MIGHT WIN THE PRIZE. >> THAT COULD BE THE SECRET. >> GOOD LUCK. >> THANK YOU. AN

    Christmas Eve’s Powerball jackpot worth an estimated $1.8B, 4th-largest in history

    Updated: 11:07 PM EST Dec 24, 2025

    Editorial Standards ⓘ

    The Powerball jackpot snowballed to an estimated $1.8 billion for Wednesday night’s drawing after no ticket won the grand prize for Monday’s drawing.The numbers below were pulled for the Dec. 24, 2025, drawing.The winning numbers were: 04-25-31-52-59 Powerball: 19Power Play 2XThe jackpot for the Christmas Eve drawing is the fourth-largest in Powerball history, with a cash value of $781.3 million, the Powerball lottery announced earlier.

    The Powerball jackpot snowballed to an estimated $1.8 billion for Wednesday night’s drawing after no ticket won the grand prize for Monday’s drawing.

    The numbers below were pulled for the Dec. 24, 2025, drawing.

    The winning numbers were:

    04-25-31-52-59

    Powerball: 19

    Power Play 2X

    The jackpot for the Christmas Eve drawing is the fourth-largest in Powerball history, with a cash value of $781.3 million, the Powerball lottery announced earlier.

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  • The Quest to Find the Longest-Running Simple Computer Program

    But just how much harder? In 1962, the mathematician Tibor Radó invented a new way to explore this question through what he called the busy beaver game. To play, start by choosing a specific number of rules—call that number n. Your goal is to find the n-rule Turing machine that runs the longest before eventually halting. This machine is called the busy beaver, and the corresponding busy beaver number, BB(n), is the number of steps that it takes.

    In principle, if you want to find the busy beaver for any given n, you just need to do a few things. First, list out all the possible n-rule Turing machines. Next, use a computer program to simulate running each machine. Look for telltale signs that machines will never halt—for example, many machines will fall into infinite repeating loops. Discard all these non-halting machines. Finally, record how many steps every other machine took before halting. The one with the longest runtime is your busy beaver.

    In practice, this gets tricky. For starters, the number of possible machines grows rapidly with each new rule. Analyzing them all individually would be hopeless, so you’ll need to write a custom computer program to classify and discard machines. Some machines are easy to classify: They either halt quickly or fall into easily identifiable infinite loops. But others run for a long time without displaying any obvious pattern. For these machines, the halting problem deserves its fearsome reputation.

    The more rules you add, the more computing power you need. But brute force isn’t enough. Some machines run for so long before halting that simulating them step by step is impossible. You need clever mathematical tricks to measure their runtimes.

    “Technology improvements definitely help,” said Shawn Ligocki, a software engineer and longtime busy beaver hunter. “But they only help so far.”

    End of an Era

    Busy beaver hunters started chipping away at the BB(6) problem in earnest in the 1990s and 2000s, during an impasse in the BB(5) hunt. Among them were Shawn Ligocki and his father, Terry, an applied mathematician who ran their search program in the off hours on powerful computers at Lawrence Berkeley National Laboratory. In 2007, they found a six-rule Turing machine that broke the record for the longest runtime: The number of steps it took before halting had nearly 3,000 digits. That’s a colossal number by any ordinary measure. But it’s not too big to write down. In 12-point font, those 3,000 digits will just about cover a single sheet of paper.

    In 2022, Shawn Ligocki discovered a six-rule Turing machine whose runtime has more digits than the number of atoms in the universe.

    Photograph: Kira Treibergs

    Three years later, a Slovakian undergraduate computer science student named Pavel Kropitz decided to tackle the BB(6) hunt as a senior thesis project. He wrote his own search program and set it up to run in the background on a network of 30 computers in a university lab. After a month he found a machine that ran far longer than the one discovered by the Ligockis—a new “champion,” in the lingo of busy beaver hunters.

    “I was lucky, because people in the lab were already complaining about my CPU usage and I had to scale back a bit,” Kropitz wrote in a direct message exchange on the Busy Beaver Challenge Discord server. After another month of searching, he broke his own record with a machine whose runtime had over 30,000 digits—enough to fill about 10 pages.

    Ben Brubaker

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  • ‘Groups’ Underpin Modern Math. Here’s How They Work

    ‘Groups’ Underpin Modern Math. Here’s How They Work

    Figuring out what subgroups a group contains is one way to understand its structure. For example, the subgroups of Z6 are {0}, {0, 2, 4} and {0, 3}—the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D6, rotations form a subgroup, but reflections don’t. That’s because two reflections performed in sequence produce a rotation, not a reflection, just as adding two odd numbers results in an even one.

    Certain types of subgroups called “normal” subgroups are especially helpful to mathematicians. In a commutative group, all subgroups are normal, but this isn’t always true more generally. These subgroups retain some of the most useful properties of commutativity, without forcing the entire group to be commutative. If a list of normal subgroups can be identified, groups can be broken up into components much the way integers can be broken up into products of primes. Groups that have no normal subgroups are called simple groups and cannot be broken down any further, just as prime numbers can’t be factored. The group Zn is simple only when n is prime—the multiples of 2 and 3, for instance, form normal subgroups in Z6.

    However, simple groups are not always so simple. “It’s the biggest misnomer in mathematics,” Hart said. In 1892, the mathematician Otto Hölder proposed that researchers assemble a complete list of all possible finite simple groups. (Infinite groups such as the integers form their own field of study.)

    It turns out that almost all finite simple groups either look like Zn (for prime values of n) or fall into one of two other families. And there are 26 exceptions, called sporadic groups. Pinning them down, and showing that there are no other possibilities, took over a century.

    The largest sporadic group, aptly called the monster group, was discovered in 1973. It has more than 8 × 1054 elements and represents geometric rotations in a space with nearly 200,000 dimensions. “It’s just crazy that this thing could be found by humans,” Hart said.

    By the 1980s, the bulk of the work Hölder had called for appeared to have been completed, but it was tough to show that there were no more sporadic groups lingering out there. The classification was further delayed when, in 1989, the community found gaps in one 800-page proof from the early 1980s. A new proof was finally published in 2004, finishing off the classification.

    Many structures in modern math—rings, fields, and vector spaces, for example—are created when more structure is added to groups. In rings, you can multiply as well as add and subtract; in fields, you can also divide. But underneath all of these more intricate structures is that same original group idea, with its four axioms. “The richness that’s possible within this structure, with these four rules, is mind-blowing,” Hart said.

    Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

    Leila Sloman

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  • ‘Gem’ of a Proof Breaks 80-Year-Old Record, Offers New Insights Into Prime Numbers

    ‘Gem’ of a Proof Breaks 80-Year-Old Record, Offers New Insights Into Prime Numbers

    The original version of this story appeared in Quanta Magazine.

    Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a $1 million reward from the Clay Mathematics Institute. Its proof would give mathematicians much deeper certainty about how prime numbers are distributed, while also implying a host of other consequences—making it arguably the most important open question in math.

    Mathematicians have no idea how to prove the Riemann hypothesis. But they can still get useful results just by showing that the number of possible exceptions to it is limited. “In many cases, that can be as good as the Riemann hypothesis itself,” said James Maynard of the University of Oxford. “We can get similar results about prime numbers from this.”

    In a breakthrough result posted online in May, Maynard and Larry Guth of the Massachusetts Institute of Technology established a new cap on the number of exceptions of a particular type, finally beating a record that had been set more than 80 years earlier. “It’s a sensational result,” said Henryk Iwaniec of Rutgers University. “It’s very, very, very hard. But it’s a gem.”

    The new proof automatically leads to better approximations of how many primes exist in short intervals on the number line, and stands to offer many other insights into how primes behave.

    A Careful Sidestep

    The Riemann hypothesis is a statement about a central formula in number theory called the Riemann zeta function. The zeta (ζ) function is a generalization of a straightforward sum:

    1 + 1/2 + 1/3 + 1/4 + 1/5 + ⋯.

    This series will become arbitrarily large as more and more terms are added to it—mathematicians say that it diverges. But if instead you were to sum up

    1 + 1/22 + 1/32 + 1/42 + 1/52 + ⋯ = 1 + 1/4 + 1/9+ 1/16 + 1/25 +⋯

    you would get π2/6, or about 1.64. Riemann’s surprisingly powerful idea was to turn a series like this into a function, like so:

    ζ(s) = 1 + 1/2s + 1/3s + 1/4s + 1/5s + ⋯.

    So ζ(1) is infinite, but ζ(2) = π2/6.

    Things get really interesting when you let s be a complex number, which has two parts: a “real” part, which is an everyday number, and an “imaginary” part, which is an everyday number multiplied by the square root of −1 (or i, as mathematicians write it). Complex numbers can be plotted on a plane, with the real part on the x-axis and the imaginary part on the y-axis. Here, for example, is 3 + 4i.

    Graph: Mark Belan for Quanta Magazine

    Jordana Cepelewicz

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  • Portland’s Unemployment Rate Essentially Unchanged In June – KXL

    Portland’s Unemployment Rate Essentially Unchanged In June – KXL

    PORTLAND, Ore. – The unemployment rate in the Portland metro area was 4.0 percent in June.

    That’s essentially unchanged from 4.1 percent in May.

    But, it’s higher than it was a year ago, when it was 3.4 percent.

    The area held steady with over 1.2 million non-farm jobs last month.

    More about:

    Grant McHill

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  • Lottery player buys 40 Pick 4 tickets with 4-digit combination of 4444. Yes, it worked

    Lottery player buys 40 Pick 4 tickets with 4-digit combination of 4444. Yes, it worked

    A Virginia man won $200,000 in the lottery with an unusual approach involving the number 4, officials say.

    A Virginia man won $200,000 in the lottery with an unusual approach involving the number 4, officials say.

    DBPD photo

    A man in Virginia with a complicated name came up with a surprisingly simple approach to winning six figures in the Virginia Lottery.

    Wassihun Woldeamanuel didn’t divulge how he got the idea, but he almost didn’t have to reveal it.

    “The Arlington man bought 40 plays … each with the same four-digit combination: 4-4-4-4,” the Virginia Lottery said in an April 2 news release.

    Wassihun Woldeamanuel didn’t divulge how he came up with the idea, but he almost didn’t have to.
    Wassihun Woldeamanuel didn’t divulge how he came up with the idea, but he almost didn’t have to. Virginia Lottery

    “The prize for matching all four winning numbers in the Pick 4 game is $5,000. Since he had 40 plays with the winning combination, he won a total of $200,000.”

    Odds of hitting all four numbers in order are 1 in 10,000, but Woldeamanuel is in a different category after winning 40 times.

    When lottery officials asked about his approach, Woldeamanuel said he “knew four is coming.”

    A review of winning Pick 4 numbers dating to January 2022 suggests no previous players were inclined to gamble on just one number.

    Another thing that stuck out about his win is a decision not to buy all the tickets in one place. He bought 30 at a grocery store in Arlington and 10 at a store in Alexandria, about 8 miles away, officials said.

    Woldeamanuel didn’t say how he intends to spend his winnings from the Feb. 20 drawing.

    Pick 4 is a game that lets players choose any four-digit numbers from 0000 through 9999.

    Many people can gamble or play games of chance without harm. However, for some, gambling is an addiction that can ruin lives and families.

    If you or a loved one shows signs of gambling addiction, you can seek help by calling the national gambling hotline at 1-800-522-4700 or visiting the National Council on Problem Gambling website.

    Mark Price is a National Reporter for McClatchy News. He joined the network of newspapers in 1991 at The Charlotte Observer, covering beats including schools, crime, immigration, LGBTQ issues, homelessness and nonprofits. He graduated from the University of Memphis with majors in journalism and art history, and a minor in geology.

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  • Mega Millions jackpot climbs to estimated $875 million after no big winners Friday night

    Mega Millions jackpot climbs to estimated $875 million after no big winners Friday night

    The Mega Millions jackpot has once again increased after no tickets matched all six numbers drawn in Friday night’s drawing.Friday night’s winning numbers are:13, 25, 50, 51, 66 and Mega Ball 6The jackpot for Friday’s drawing rose to $815 million this week after there were no jackpot winners in Tuesday’s drawing. Now, it climbs even higher to an estimated $875 million ($413.5 million cash) for the next drawing, which is set for Tuesday, March 19.If a ticket matches all six numbers in the Tuesday night drawing, it would be the sixth-largest jackpot in the 22-year history of the game. While there were no grand prize winners in Friday night’s drawing, one ticket sold in New York matched all five white balls and wins $1 million.According to Mega Millions officials, only five jackpots exceeding $1 billion have been higher.Officials said the jackpot has been growing since it was last won with two tickets in California on Dec. 8.In its history, the Mega Millions has awarded five jackpots exceeding $1 billion in five different states — Florida, South Carolina, Maine, Illinois and Michigan.Tickets are sold in 45 states, Washington, D.C., and the U.S. Virgin Islands. Tickets are $2 each and in most jurisdictions, players can add the Megaplier for an additional $1 to multiply their non-jackpot prizes.The overall odds of winning any Mega Millions prize are 1 in 24, while the odds of winning the jackpot are 1 in 302,575,350.

    The Mega Millions jackpot has once again increased after no tickets matched all six numbers drawn in Friday night’s drawing.

    Friday night’s winning numbers are:

    13, 25, 50, 51, 66 and Mega Ball 6

    The jackpot for Friday’s drawing rose to $815 million this week after there were no jackpot winners in Tuesday’s drawing. Now, it climbs even higher to an estimated $875 million ($413.5 million cash) for the next drawing, which is set for Tuesday, March 19.

    If a ticket matches all six numbers in the Tuesday night drawing, it would be the sixth-largest jackpot in the 22-year history of the game.

    While there were no grand prize winners in Friday night’s drawing, one ticket sold in New York matched all five white balls and wins $1 million.

    According to Mega Millions officials, only five jackpots exceeding $1 billion have been higher.

    Officials said the jackpot has been growing since it was last won with two tickets in California on Dec. 8.

    In its history, the Mega Millions has awarded five jackpots exceeding $1 billion in five different states — Florida, South Carolina, Maine, Illinois and Michigan.

    Tickets are sold in 45 states, Washington, D.C., and the U.S. Virgin Islands. Tickets are $2 each and in most jurisdictions, players can add the Megaplier for an additional $1 to multiply their non-jackpot prizes.

    The overall odds of winning any Mega Millions prize are 1 in 24, while the odds of winning the jackpot are 1 in 302,575,350.

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  • According to CNN, Trump Has 'Strongest' Poll Numbers In The 'History' Of The Iowa Caucus

    According to CNN, Trump Has 'Strongest' Poll Numbers In The 'History' Of The Iowa Caucus

    Politics

    Gage Skidmore, CC BY-SA 3.0

    With only about ten days to go, we will soon be seeing the first presidential contest of 2024 with the Iowa caucus.

    And according to CNN – yes, CNN – Donald Trump is absolutely killing it.

    The Daily Caller reported, “CNN Data Reporter: Trump Has CNN’s senior data reporter Harry Enten said Thursday that former President Donald Trump has the ‘strongest’ poll numbers in the ‘history’ of the Iowa caucus.”

    The numbers have to be discouraging for the campaigns of challengers Nikki Haley and Ron DeSantis, who are both counting on a strong showing in early states.

    RELATED: NSC Spokesman John Kirby Snaps At Reporter Who Suggested US Has Escalated Tensions In The Middle East

    ‘Just How Large Trump’s Lead Is’

    The story noted, “Trump is currently leading the Republican candidates in both New Hampshire and Iowa at 46% and 51% respectively, according to RealClearPolitics. Former South Carolina Gov. Nikki Haley is trailing Trump by 24.8% and 16% in both states respectively.”

    Harry Enten was emphatic about how strong Trump’s numbers were in Iowa:

    “It’s an enormous lead!” Enten exclaimed. “I’m gonna show the trend line for the Des Moines Register poll which is the premier poll in that state.  And what you essentially see here is Donald Trump has only gotten stronger. He was at 43% in October. Look where he is now. More than a majority, more than 50%, a majority at 51%. And you see Ron DeSantis within the margin of error where he was in October. Look at Nikki Haley, she’s stable. This is an over 30-point advantage with Trump getting a majority of the vote. And I want to put this in a historic context for you. Just how large Trump’s lead is. These are folks who polled at 45% or greater in Iowa at this point. All before Trump won the caucuses.  Mondale in ’84, Bush in 2000, Gore in 2000, Hillary Clinton in 2016, and now we see Trump in 2024.

    I would note, in fact, Trump is the only one to actually be at greater than 50% of the vote. The rest of these folks were at 50% of the vote or lower.”

    RELATED: Associated Press Quietly Edits Article After Suggesting ‘Scalping’ Was Introduced To Native Americans By White Colonists

    Strongest in Iowa Caucus History

    Mattingly followed up, “History?”

    “History,” Enten replied.

    Iowa is not necessarily indicative of how all the upcoming primaries and caucuses will go in the various states.

    In 2016, Ted Cruz won Iowa and went down in flames to Donald Trump. In 2012, Rick Santorum won Iowa, only to be blown out of the water by Mitt Romney.

    In 2008, eventual winner John McCain took last place in Iowa.

    But if Donald Trump is currently outpacing every other candidate in the history of such an event, it’s worth paying attention to.

    2024 has only just begun.

    Nikki Haley Moves Past Ron DeSantis In National Polling 12 Days Before First Primary Voting

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    John Hanson

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  • Ghost towers get lease of life, Auckland CBD office vacancies plummet – Medical Marijuana Program Connection

    Ghost towers get lease of life, Auckland CBD office vacancies plummet – Medical Marijuana Program Connection

    The PwC Tower (left) has a zero vacancy factor. Photo / Michael Craig

    Don’t call them ghost towers any longer because the chief of a billionaire landlord and a research boss have cited rising numbers of workers back in Auckland’s heart.

    On Monday, Precinct Properties chief executive Scott

    Original Author Link click here to read complete story..

    MMP News Author

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