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In 1963, the mathematician Stanisław Ulam noticed an unusual pattern while doodling in his notebook during a presentation. When integers are arranged in a spiral, prime numbers appear to fall along diagonal lines. At first, this is not entirely surprising, since all prime numbers except 2 are odd, and... the diagonals of such spirals alternate between odd and even numbers. What is far more striking is that primes tend to cluster along certain diagonals more than others, regardless of whether the spiral begins with 1 at the center or with any other number. Even at a much larger scale, clear diagonal lines of primes remain visible, with some lines more pronounced than others. Although there are conjectures that attempt to explain this pattern, no proof has yet been found.show more

Math Files

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25,622 次观看 • 1 个月前 •via X (Twitter)

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Prime numbers are supposed to be random. This video proves they aren't. In 1963, mathematician Stanislaw Ulam discovered an unexpected order within the "randomness" of prime numbers. While doodling during a presentation, he arranged integers in a square spiral and circled the primes. To his surprise, the primes; which were thought to be scattered without reason; clustered into distinct diagonal lines. This visual phenomenon, now called the Ulam Spiral, revealed that prime numbers follow a mysterious underlying structure often linked to quadratic polynomials, proving that even mathematical "atoms" have a hidden architecture. Credit: maths.visualization

Prime numbers are supposed to be random. This video proves they aren't. In 1963, mathematician Stanislaw Ulam discovered an unexpected order within the "randomness" of prime numbers. While doodling during a presentation, he arranged integers in a square spiral and circled the primes. To his surprise, the primes; which were thought to be scattered without reason; clustered into distinct diagonal lines. This visual phenomenon, now called the Ulam Spiral, revealed that prime numbers follow a mysterious underlying structure often linked to quadratic polynomials, proving that even mathematical "atoms" have a hidden architecture. Credit: maths.visualization

Mathematica

190,983 次观看 • 3 个月前

Matt Walsh went over black and white crime statistics and the results are actually insane “By raw numbers — that makes black males in America more dangerous than perhaps any other demographic in the the entire world, let alone in this country” - Statistically, a white person is 30 times more likely to be killed by a black person than the other way around - In 2019, there were about 560,000 violent interracial incidents between blacks and whites. 470,000 of them were black on white. That's 85%, 85%…. - 240 black people were killed by whites, 560 white people were killed by blacks - This is all in spite of the fact that white people make up 60% of the population, blacks are 13%. Just by raw numbers, not even per capita, but raw numbers, there are more black interracial killers than white. That should be impossible. There are 171 million more white people in the country, and yet there are more black interracial killers. By raw numbers, the young black males in particular are an order of magnitude more violent and more likely to commit crimes than any other group in the country. Black men are five or 6% of the population. They commit the majority of murders in the country That makes black males in America more dangerous than perhaps any other demographic inthe entire world, let alone in this country.”

Matt Walsh went over black and white crime statistics and the results are actually insane “By raw numbers — that makes black males in America more dangerous than perhaps any other demographic in the the entire world, let alone in this country” - Statistically, a white person is 30 times more likely to be killed by a black person than the other way around - In 2019, there were about 560,000 violent interracial incidents between blacks and whites. 470,000 of them were black on white. That's 85%, 85%…. - 240 black people were killed by whites, 560 white people were killed by blacks - This is all in spite of the fact that white people make up 60% of the population, blacks are 13%. Just by raw numbers, not even per capita, but raw numbers, there are more black interracial killers than white. That should be impossible. There are 171 million more white people in the country, and yet there are more black interracial killers. By raw numbers, the young black males in particular are an order of magnitude more violent and more likely to commit crimes than any other group in the country. Black men are five or 6% of the population. They commit the majority of murders in the country That makes black males in America more dangerous than perhaps any other demographic inthe entire world, let alone in this country.”

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When someone tells you that MudFlood or UndergroundTunnels are bullshit and PsyOp show them that. Moldova. During an excavation in the Ocnita district of Moldova, an extraordinary discovery was made. An arch and what appear to be "rails" under a 50ft layer of earth. A number of archaeologists were taken there and were unable to explain the discovery. More than a year has passed and no one has returned to give an explanation, as there is no record of this. PS. There are no other buildings or anything near where they are.

When someone tells you that MudFlood or UndergroundTunnels are bullshit and PsyOp show them that. Moldova. During an excavation in the Ocnita district of Moldova, an extraordinary discovery was made. An arch and what appear to be "rails" under a 50ft layer of earth. A number of archaeologists were taken there and were unable to explain the discovery. More than a year has passed and no one has returned to give an explanation, as there is no record of this. PS. There are no other buildings or anything near where they are.

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367,454 次观看 • 1 年前

The Yukon River’s fish population is in serious trouble, with thousands of pounds of halibut and king salmon lost as bycatch to bottom trawling. The numbers are concerning, and it’s clear that a solution is needed now more than ever.

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19,510 次观看 • 3 个月前

After a few days of relief from the arrival of fuel in Bamako, the fuel shortage is felt once again in the Malian capital with long lines at fuel stations this morning, this is not even talking about other cities and regions that are living in much worse conditions.

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❗️Zelenskyy: “The claim that we have more corruption than in any other European state is a lie” The risks of corruption during wartime are higher than at any other time. But Ukraine is fighting this phenomenon, the president stated in an interview with the BBC: “This is not something to boast about, of course. But the fact that we are fighting it — I believe we are doing a great job.”

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🪖MilitaryNewsUA🇺🇦

30,275 次观看 • 4 个月前

This script of Carney’s is exhausting. He is endlessly trying to look like “the smartest person in the room” with them. Even on Canada he couldn’t give a natural authentic speech to Canadians. He had to pull out the usual tired lines. And who is he kidding? There has been no other political party in the history of Canada that has divided our nation & the people more than them.

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Not a single American citizen is doing better in the Kamala Harris economy. Inflation has risen by more than 20 PERCENT since she took office! There are no limits to what Kamalanomics can touch. Listen to some of these numbers 👇 🎥: Firebrand with Matt Gaetz

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Sheen: I was watching Kash Patel—that is astonishing to me. There is no possible way that any of these people at the head of any of the agencies that we have right now would ever make it in any other administration.. And when they look at each other, they don't see anyone on the other side that is better than they are, is more heroic, has more courage. They in a real sense, I suspect they despise each other because there isn't anyone on the other side that is better than they are, and they are looking at the worst reflection of themselves

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🚨 MAMDANI: “The wealth of a median white household in the city is more than $200,000, while that of a black household is less than $20,000 … We are reckoning with the long history of racism here and starting to act upon a framework that puts equity right at the center of it.”

🚨 MAMDANI: “The wealth of a median white household in the city is more than $200,000, while that of a black household is less than $20,000 … We are reckoning with the long history of racism here and starting to act upon a framework that puts equity right at the center of it.”

Chief Nerd

7,364,447 次观看 • 3 个月前

There is no BJP in Japan There is no RSS in Japan Thousands of Japanese gathered to protest the construction of the first mosque in Fujisawa. They are okay with a Hindu temple but not Mosque The proposed mosque would be much larger than the nearby sacred Shinto shrine, an act of provocation! “We don’t want a single mosque, or Muslim cemetery here!” They calim same old pattern is starting in Japan too - build a mosque, then slowly take over the area and impose your identity. This is a pattern that is followed everywhere. Slow demographic changes are introduced.

There is no BJP in Japan There is no RSS in Japan Thousands of Japanese gathered to protest the construction of the first mosque in Fujisawa. They are okay with a Hindu temple but not Mosque The proposed mosque would be much larger than the nearby sacred Shinto shrine, an act of provocation! “We don’t want a single mosque, or Muslim cemetery here!” They calim same old pattern is starting in Japan too - build a mosque, then slowly take over the area and impose your identity. This is a pattern that is followed everywhere. Slow demographic changes are introduced.

Comman Man

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🐊The algae was never really the issue. People often say they want things fixed. Until someone fixes them. Then the argument shifts to whether they should have been touched at all. Which raises a question: Why are we sometimes more comfortable with decline than with change? 🤔 That's the underlying fight. They drained the Reflection Pool, cleaned it, and gave it a fresh look. Now the fight isn't about the water — it's about whether it should have been touched at all. And by whom. The shade of Old Glory blue. The destained stone. The change itself. Shut out the usual partisan noise for a moment. Why are we sometimes more comfortable with visible decline than with any attempt at renewal? Is this really about preserving history... Or is it resistance to change itself? The battle lines are drawn. Pick a side and weigh in on history in the making. At what point does "protecting the past" become fear of the future?👀 Think about it. The ancient battle between: preservation and renewal. Now that I think about it, that’s much more interesting mystery than the shade of blue. 🤣🔵

Tosca Austen

23,268 次观看 • 1 个月前

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Seth

48,065 次观看 • 27 天前

Any action in Venezuela will be bloody. Venezuela has more than two dozen generals and colonels imprisoned, along with another 150 officers. All of this results from failed uprising attempts and coups. Although Maduro may face immense difficulties in unifying his army to fight for him, there is certainly still a loyal faction, and this faction was predominant in other coup attempts. The situation of the army has been deteriorating, but the military also does not feel confident in the opposition that has tried several coups, all of which failed. Venezuela has become a very poor country, but in the last year, a bonus was given to military personnel and retirees in an attempt to unify the troops—an even more challenging task. For weeks, the United States has been intimidating Venezuela and bringing an arsenal to the region. However, Maduro remains in power, which leads us to believe that negotiations to open dissidence and internal uprising are failing. Perhaps they are failing at the scale the Americans need because anyone familiar with the Venezuelan scenario knows that any American military action will be supported by internal military dissent and opposition militias. Venezuela has started arming its popular militias, which, according to the government, number over 4 million(hard to believe). I doubt there are weapons for all these people, but if just 2% of that is real and armed, more than 80,000 Venezuelans are joining forces loyal to the government. It doesn’t matter how many ships the U.S. has or how many missiles they might fire. Who will be responsible for this bloodbath on the ground? The Venezuelan army has intensified training in recent weeks and will continue to do so, even though it is disorganized and poorly trained. No one benefits from a civil war in Venezuela. What would be the other card to play?

Any action in Venezuela will be bloody. Venezuela has more than two dozen generals and colonels imprisoned, along with another 150 officers. All of this results from failed uprising attempts and coups. Although Maduro may face immense difficulties in unifying his army to fight for him, there is certainly still a loyal faction, and this faction was predominant in other coup attempts. The situation of the army has been deteriorating, but the military also does not feel confident in the opposition that has tried several coups, all of which failed. Venezuela has become a very poor country, but in the last year, a bonus was given to military personnel and retirees in an attempt to unify the troops—an even more challenging task. For weeks, the United States has been intimidating Venezuela and bringing an arsenal to the region. However, Maduro remains in power, which leads us to believe that negotiations to open dissidence and internal uprising are failing. Perhaps they are failing at the scale the Americans need because anyone familiar with the Venezuelan scenario knows that any American military action will be supported by internal military dissent and opposition militias. Venezuela has started arming its popular militias, which, according to the government, number over 4 million(hard to believe). I doubt there are weapons for all these people, but if just 2% of that is real and armed, more than 80,000 Venezuelans are joining forces loyal to the government. It doesn’t matter how many ships the U.S. has or how many missiles they might fire. Who will be responsible for this bloodbath on the ground? The Venezuelan army has intensified training in recent weeks and will continue to do so, even though it is disorganized and poorly trained. No one benefits from a civil war in Venezuela. What would be the other card to play?

Patricia Marins

76,725 次观看 • 8 个月前