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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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26,001 次观看 • 2 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 • 4 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.”

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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.

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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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🚨 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

7,367,328 次观看 • 4 个月前

🐊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. 🤣🔵

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Comman Man

66,071 次观看 • 4 个月前