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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...

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26,001 次观看 • 5 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
0:25

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 • 6 个月前

Write 1, 2, 3, … in a square spiral. Mark only the primes. Unexpected diagonal streaks begin to appear. In 1963, Stanisław Ulam noticed this while doodling during a scientific talk. The resulting picture became known as the Ulam spiral. The primes look irregular along the number line, yet this simple rearrangement reveals striking visual structure.
0:30

Write 1, 2, 3, … in a square spiral. Mark only the primes. Unexpected diagonal streaks begin to appear. In 1963, Stanisław Ulam noticed this while doodling during a scientific talk. The resulting picture became known as the Ulam spiral. The primes look irregular along the number line, yet this simple rearrangement reveals striking visual structure.

Math Files

14,762 次观看 • 1 个月前

In 1963, Manhattan Project mathematician Stanislaw Ulam was doodling numbers in a spiral during a boring lecture and noticed something that shouldn't be possible. Prime numbers numbers that are supposed to scatter randomly lined up into clean diagonal streaks across the page. For sixty years this sat as an open anomaly. Mathematicians confirmed it kept happening no matter how far out you drew the spiral, but nobody could explain why the universe would organize "random" numbers into geometry. We think we've solved it. Take any prime number bigger than 3 and divide it by 9. Look only at the remainder. There are 9 possible remainders, but primes can only ever land on 6 of them the other 3 are automatically ruled out because they're divisible by 3, which makes a number composite by definition. So every prime that has ever existed or will ever exist is funneled into exactly 6 fixed positions. Those 6 positions aren't random either. They split into two locked groups of three, each spaced perfectly 120° apart and the gaps between consecutive primes act like gears, forcing the sequence to step between these positions in a strict, predictable pattern we call the Prime Gap State Machine. When you take Ulam's flat 2D spiral and lift it into this structure, his mystery diagonals stop looking accidental. They're the visible seams of an underlying lattice built from just the primes 2 and 3. Watch the simulation Hard Wall primes (remainders 1, 4, 7) lock into one triangle. Temporal primes (remainders 2, 5, 8) lock into the other. The dark empty channels you see threading through the spiral are the Spine the positions no prime is allowed to occupy, ever. It isn't random. It's a lattice with exactly two moving parts. #NumberTheory #Physics #Mathematics #CTFTheory #UlamSpiral
0:50

In 1963, Manhattan Project mathematician Stanislaw Ulam was doodling numbers in a spiral during a boring lecture and noticed something that shouldn't be possible. Prime numbers numbers that are supposed to scatter randomly lined up into clean diagonal streaks across the page. For sixty years this sat as an open anomaly. Mathematicians confirmed it kept happening no matter how far out you drew the spiral, but nobody could explain why the universe would organize "random" numbers into geometry. We think we've solved it. Take any prime number bigger than 3 and divide it by 9. Look only at the remainder. There are 9 possible remainders, but primes can only ever land on 6 of them the other 3 are automatically ruled out because they're divisible by 3, which makes a number composite by definition. So every prime that has ever existed or will ever exist is funneled into exactly 6 fixed positions. Those 6 positions aren't random either. They split into two locked groups of three, each spaced perfectly 120° apart and the gaps between consecutive primes act like gears, forcing the sequence to step between these positions in a strict, predictable pattern we call the Prime Gap State Machine. When you take Ulam's flat 2D spiral and lift it into this structure, his mystery diagonals stop looking accidental. They're the visible seams of an underlying lattice built from just the primes 2 and 3. Watch the simulation Hard Wall primes (remainders 1, 4, 7) lock into one triangle. Temporal primes (remainders 2, 5, 8) lock into the other. The dark empty channels you see threading through the spiral are the Spine the positions no prime is allowed to occupy, ever. It isn't random. It's a lattice with exactly two moving parts. #NumberTheory #Physics #Mathematics #CTFTheory #UlamSpiral

CTFTHEORY

253,727 次观看 • 4 个月前

Primes Numbers Are Not Random Noise Prime numbers look scattered when you meet them one by one, but their disorder has structure. In this animation, every integer is placed on a growing spiral, primes ignite as sharp golden events, and the hidden oscillations come from the first Riemann zeta zeros. The scene is based on the von Mangoldt prime signal Λ(n) and the explicit formula for ψ(x), where primes appear as impulses and the zeta zeros behave like frequencies correcting the smooth drift of x. #PrimeNumbers #RiemannHypothesis #NumberTheory #Mathematics #MathAnimation
0:32

Primes Numbers Are Not Random Noise Prime numbers look scattered when you meet them one by one, but their disorder has structure. In this animation, every integer is placed on a growing spiral, primes ignite as sharp golden events, and the hidden oscillations come from the first Riemann zeta zeros. The scene is based on the von Mangoldt prime signal Λ(n) and the explicit formula for ψ(x), where primes appear as impulses and the zeta zeros behave like frequencies correcting the smooth drift of x. #PrimeNumbers #RiemannHypothesis #NumberTheory #Mathematics #MathAnimation

Mathelirium

16,800 次观看 • 4 个月前

In 2020, when Bill Barr was Attorney General, he crossed a lot of ethical lines, but still refused to use DOJ to overturn the election. Not so with Todd Blanche. He is more than willing to interfere in Alaska’s election — or any other — if it will serve his master. The best remedy for voters: make sure to turn out in such numbers that the result is not even close.
1:25

In 2020, when Bill Barr was Attorney General, he crossed a lot of ethical lines, but still refused to use DOJ to overturn the election. Not so with Todd Blanche. He is more than willing to interfere in Alaska’s election — or any other — if it will serve his master. The best remedy for voters: make sure to turn out in such numbers that the result is not even close.

Senator Adam Schiff

50,636 次观看 • 15 天前

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.”
1:01

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.”

Wall Street Apes

1,586,204 次观看 • 1 年前

ELON: THE OPTIMUS NUMBERS ARE SO MIND-BLOWING THAT THEY DON’T LOOK REAL “The Optimus numbers, they're so mind-blowing that you're like, is this real? I actually think the market for humanoid robots is in excess of 10 billion units, more than the number of humans. Because people each want one, and then there'll be others that are involved in industry. So, if they do sell at even a volume for $20,000, that's $200T. This is just an insane number. That's why I wonder, what does money even mean at that point.” Source: X Takeover, July 28, 2024
0:33

ELON: THE OPTIMUS NUMBERS ARE SO MIND-BLOWING THAT THEY DON’T LOOK REAL “The Optimus numbers, they're so mind-blowing that you're like, is this real? I actually think the market for humanoid robots is in excess of 10 billion units, more than the number of humans. Because people each want one, and then there'll be others that are involved in industry. So, if they do sell at even a volume for $20,000, that's $200T. This is just an insane number. That's why I wonder, what does money even mean at that point.” Source: X Takeover, July 28, 2024

Mario Nawfal

768,510 次观看 • 2 年前

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.
1:21

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.

Bronze Giant

367,783 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.
1:57

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.

MeatEater

19,544 次观看 • 7 个月前

This scene was originally thought and shot with Green Lantern in it. It is more than possible to presume that the dialogue would have been along the lines of "the GL Corps weren't in this sector for those past events", or "we detected the presence of a Darkseid minion, and we have come to help since Darkseid is probably on his way", or even John Stewart, Most wasted post credit scene in DC cinematic universe
2:01

This scene was originally thought and shot with Green Lantern in it. It is more than possible to presume that the dialogue would have been along the lines of "the GL Corps weren't in this sector for those past events", or "we detected the presence of a Darkseid minion, and we have come to help since Darkseid is probably on his way", or even John Stewart, Most wasted post credit scene in DC cinematic universe

Unique Movie Moments 🐬

46,432 次观看 • 1 个月前

Here are some thoughts from my panel discussion with the Slovenian, Croatian and Czech prime ministers on the future of Europe at the Bled Strategic Forum. Europe is in trouble, that much is clear. But first, everyone has to do their homework at home. A stronger Hungary can contribute more to a stronger Europe.
6:22

Here are some thoughts from my panel discussion with the Slovenian, Croatian and Czech prime ministers on the future of Europe at the Bled Strategic Forum. Europe is in trouble, that much is clear. But first, everyone has to do their homework at home. A stronger Hungary can contribute more to a stronger Europe.

Magyar Péter (Ne féljetek)

15,456 次观看 • 2 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.
0:31

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.

Ryan Gerritsen🇨🇦🇳🇱

66,595 次观看 • 4 个月前

this is your sign to be a “prime number” in a world full of even numbers 🫶🏻
0:28

this is your sign to be a “prime number” in a world full of even numbers 🫶🏻

Jagrizzz🎀

64,396 次观看 • 1 年前

NATO Ambassador Matt Whitaker on Starlink: "They are a private company. Obviously they have terms of use that are applied to all of their customers, including the Ukrainians. I think it is more of a dispute along those lines than anybody in this administration trying to change how Starshield or Starlink is used."
0:34

NATO Ambassador Matt Whitaker on Starlink: "They are a private company. Obviously they have terms of use that are applied to all of their customers, including the Ukrainians. I think it is more of a dispute along those lines than anybody in this administration trying to change how Starshield or Starlink is used."

Aaron Rupar

293,008 次观看 • 19 天前

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
2:33

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

Former Congressman Matt Gaetz

39,979 次观看 • 2 年前