Prime Spirals

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    Prime Spirals - Numberphile


    Prime numbers, Ulam Spirals and other cool numbery stuff with Dr James Grime.
    James Clewett on spirals at:

    And more to come soon...

    Numberphile on Facebook:
    Numberphile tweets:
    Google Plus:

    Videos by Brady Haran

    A run-down of Brady's channels:

    * subscribing to numberphile does not really change your physical appearance!

    And golden line in this context was made up by Brady!

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    Ulam Spiral Visualization - The Pattern of Prime Numbers


    The Ulam spiral is a way of visualizing the distribution of prime numbers (in blue). This pattern is one the great unsolved mysteries in mathematics and has important consequences in Cryptography.

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    Prime Spirals


    Inspired by the Prime Spiral video with Dr James Grime on Numberphile. I created this in Lightwave 3D and compiled it in After Effects. Explanation of what is going on is in the video itself. It basically shows how Prime numbers are distributed when varying an Archimedean spiral... I hope. I'm not really a mathematician.

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    Prime Spirals the 8 Adoni Prime Spirals


    The 8 Prime Spirals or 8 Adoni Prime Spirals were discovered in 1995 by Dr. Sol Adoni. The first prime spiral was discovered in 1963, the Ulam Spiral. All prime numbers over 5 exist on one of the 8 Adoni Prime Spirals. PROOF that Primes are not random. In 2012 the Prime Spirals were put into PyPrimes with other Prime Algorithms. The Prime Spirals beat all prime algorithms including the sieve of Eratosthenes.

    Dr. Sol Adoni called the paper in 1995 the Ennisa Prime Formula and he described the 30Mod Algorithm with 8 prime distribution channels or 8 prime prime spirals in 1995.

    Dr. Sol Adoni has created Helix Equations and HelixQ a new computer language to run complex dimensional math equations such as the 8 Prime Spirals. The 8 Adoni Spirals are also called the Sollog Primes.

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    Prime Spiral Beta


    There are some prime numbers and some other things going on here... still in development / sorry for the quality.

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    41 and more Ulams Spiral - Numberphile


    More on prime numbers and Ulam's Spiral - this time focusing on 41 and Arthur C. Clarke.

    This video features Dr James Clewett. More Clewett videos at:

    See our other Ulam Spiral video at:
    And more to come soon...

    Numberphile on Facebook:
    Numberphile tweets:
    Google Plus:

    Videos by Brady Haran
    A run-down of Brady's channels:

    The book discussed is The Garden of Rama.

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    Prime numbers on an archimedes spiral.


    Here is the MATLAB script I used to create this:

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    Prime Spiral: Sieve of Eratosthenes


    Video shows the Sieve of Eratosthenes in action.

    All numbers are first assumed to be prime - drawn in black.
    Then all those with factors are systematically eliminated.

    In the end...
    Prime numbers, and one, are shown black.
    Numbers with one prime factor are shown white.
    Numbers with two prime factor are shown blue.
    Numbers with three prime factor are shown dark red.
    Numbers with four prime factor are shown greeny yellow.

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    Super Prime Algorithm by Dr. Sol Adoni 30 Mod Prime Algorithm 8 Prime Spirals


    Super Prime Algorithm by Dr. Sol Adoni 30 Mod Prime Algorithm 8 Prime Spirals.

    Learn about the 8 Prime Spirals 30 Mod Prime Algorithm that creates SUPER PRIMES

    See how the NSA hacked ECC Crypto and Bitcoin

    NSA Snowden Documents Wiki Leaks

    Backdoor for ECC Encryption

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    Golden Ratio And Prime Number Spirals - An Amazing Pattern


    I showed you how to make the seed arrangement using the golden ratio here:

    If you remove all of the seeds whose index numbers are NOT prime numbers, the pattern that remains is really friggin' cool.

    If you have any more information on this than what I mention in the video please let me know.

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    1 and Prime Numbers Numberphile


    Is 1 a prime number? Apparently not. Dr James Grime explains. Website: Numberphile on Facebook: .

    Matt Parker on the latest Mersenne Prime to take the title of world's biggest prime. He had it printed! More from this interview very soon, including details of how .

    Prime numbers, Ulam Spirals and other cool numbery stuff with Dr James Grime. James Clewett on spirals at: And more to come .

    Banks, Facebook, Twitter and Google use epic numbers - based on prime factors - to keep our Internet secrets. This is RSA public-key encryption. This video .

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    Gaussian Prime Spirals


    The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.

    Start a loop with a point having integer coordinates in the complex plane (called a Gaussian integer) and trace a path as follows: ? Move right until a Gaussian prime p is encountered, then turn left 90. ? Continue, always moving straight in the curren...

    Contributed by: Joseph O'Rourke and Stan Wagon

    Audio created with WolframTones:

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    Prime numbers: A PATTERN!


    The graph at the end of this video shows an impressive truth about prime numbers (calculated out to the first 10 million primes, roughly). This pattern is solid, unchanging, and beautiful truth about prime numbers that may help us break the code of prime numbers and the fundamental properties of our mathematical system

    Cool stuff on Ulam Spiral:

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    :) On Prime Spirals and Gravitational Lensing, Etc.


    notes at night

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    Prime Number Logarithmic Spiral


    Spiral generated in the same manner as the Golden Spiral, but instead of using the Fibonacci sequence, the sequence of all prime numbers less than 1000 is plotted

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    The Ulam Prime Spiral


    The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.

    Inspired by the square spiral of Stanislaw Ulam, the prime numbers are plotted on a spiral number line. Each prime on the wound line is marked with a dot. Adjusting the tightness of the winding and the density allows different patterns to emerge.

    Contributed by: Christopher Skiscim
    Based on a program by: Greg Keogh

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    Prime Number Theorem: the density of primes


    The Prime Number Theorem is explained. The natural logarithm is introduced using the logarithmic spiral to give you a better feeling for this type of growth. These come together to give us an intuitive feeling AND formula for how many primes exist as we look towards infinity.

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    TFP AMV - Optimus Prime Spiral


    The more I listened to this song, the more it reminded me of Optimus. And so my first Transformers AMV is for my favorite Autobot. c:

    Note: The full song is actually almost eight minutes long; I edited it to use only the third verse, chorus, and bridge.


    Song: Spiral (ft. Beth Bullock)
    Artist: Andy Hunter
    Album: Glow

    Transformers Prime
    Transformers: Fall of cybertron
    The Transformers (G1)
    The Transformers: The Movie (G1)
    Beast Wars: Transformers

    Transformers (c) Hasbro

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    A variation on an Ulam Spiral: a Sacks Spiral


    Simplicity making complexity. In one word: Emergence.
    Using the same process as my Ulam Spiral video,

    but this time in a Sacks Spiral,
    Animation made with FMS Logo.

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    Photoshop Tutorial #3 - Prime Spiral


    - Be sure to follow me!

    In this Photoshop tutorial, I give you a detailed explanation on how to create a Prime Spiral effect. If you have any questions, please feel free to leave it in the comment section below, and I'll be more than happy to answer. And also feel free to subscribe if you found this helpful :) More to come!

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    Polar Prime Spiral


    The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.

    The integers can be arranged on a spiral while keeping square numbers on the positive x axis. Prime numbers concentrate on trajectories of quadratic functions like x^2 + x + 41. The green line shows the sequence generated by x^2 + a x + b. A blue curve ...

    Contributed by: Michael Schreiber

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    素数のハニカム螺旋 - prime spiral on honeycomb grid -




    drawing prime number sequence on honeycomb grid with growing from the center of the grid.

    see more.

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    Prime Algorithm 30 Mod Prime Algorithm by Dr. Sol Adoni


    Prime Algorithm 30 Mod Prime Algorithm by Dr. Sol Adoni

    Video by Dr. Sol Adoni the mathematician that discovered the 30Mod Prime Algorithm or 8 Prime Spirals also known as Adoni Prime Spirals in the 1990's.

    Learn about the fastest prime generator as tested against prime algorithms by PyPrimes.

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    Day & Night News - Prime - Spiral Of Aids - Part 1


    Follow Day & Night News on Facebook

    Visit Day & Night News for latest news

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    Ulam Spirals


    Ulam's Spirals are a pretty and potentially mathematically significant way of viewing patterns among the prime numbers. The idea is to start with any natural number at a point on a square grid and proceed in a vaguely helical manner; assign each subsequent square the next number, and color squares according to whether or not their numbers are prime.

    The first half of this video demonstrates this construction on a 31 x 31 grid starting with 1 at the center (green squares are prime, blue squares aren't). In the second half (once my regrettably finite grid is filled in), each subsequent frame displays the Ulam's Spiral with a central initial value 1 more than the frame before. What follows, in addition to a nice primes-in-a-whirlpool effect, is a visual manifestation of the apparent order underlying that venerable mathematical quandary of the distribution of prime numbers.

    Images created using PLT-Racket. Much love to lambda.

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    Doodling in Math: Sick Number Games


    I don't even know if this makes sense. Boo cold.
    Try playing with this:

    My personal website, which you might like:

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    Doodling in Math: Spirals, Fibonacci, and Being a Plant 1 of 3


    Part 2:
    Part 3:
    Re: Pineapple under the Sea:

    My personal website, which you might like:

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    Ulam Spiral Fun


    Explanation of Sal's Ulam Sprial code

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    Prime Number Sieve and the Ulam Spiral


    The Ulam Spril was publicized by Stanislaw Ulam in 1963. The spiral can be generated using the sieve of Eratosthenes to etch out the prime numbers. This animation depicts 123 iterations of the sieve. Initially, the Ulam Spiral is drawn and the primes are colored dark red. Those primes that have a rank, the order that the prime appears in the prime number sequence, that is also prime are colored yellow, and those that have a rank that is a prime with a rank that is also prime are colored blue. The sieve begins with 2 and 'evaporates' every other cell. When a cell is evaporated, the cells ahead of it in the spiral shift back to fill the vacant space but they retain their original value for future division tests. The next iteration evaporates those cells divisible by 3, and then 5, 7 and so on. Red cells(primes) change to black when they are less than p^2. Thus, the area of the inner square is π(x)^2 (the prime counting function). What is left after all composites have been evaporated and the newly created black cells are interperted as composites is an exact replica of what we started with, only shifted in the hierarchy of primeness so to speak. The path of a couple of prime points is traced as they move to their final destination. Music by: cloudtalk, Austin Texas.

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    3D Ulam Spiral


    Ulam spiral with prime numbers projected in the z-axis to their values.

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    spirals 8000


    The fractal set of x*ln(x), the generating function for entropy and the prime numbers, generated by laying a lattice onto the function (implemented by decimating it) with values between 1 and 8 and a step size of 0.001. Copyright (c) John Schutkeker, 2016, Royal Oak, MI.

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    Aikatsu Prism Spiral Lyrics


    this took forever and please don't take it down.

    This is Aikatsu - Prism Spiral
    with japanese and english lyrics

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    How the NSA Hacked ECC CRYPTO and BITCOIN


    How the NSA Hacked ECC CRYPTO and BITCOIN

    The special relationships between primes is how the NSA cooked seed keys for ECC crypto. Since 1995 the NSA has known that all primes exist on only 8 Prime Spirals and the relationships between numbers on these spirals is special and that relationship allows seed keys for ECC to be backdoored or cooked.

    Wiki and NSA are actively banning any info about the PRIME ALGORITHM or 8 Prime Spirals as well as any info about Dr. Sol Adoni the mathematician that discovered them in 1995.

    Wiki is under obvious NSA control and banning any information about the PRIME ALGORIRTHM

    They have deleted the 8 PRIMES SPIRALS page and banned all users who have tried to put information about how the NSA used the 8 Prime Spirals to backdoor ECC Crypto.

    Look for yourself

    They even deleted a page about the mathematician that discovered it in 1995

    They have banned anyone posting positive information about the original user that created the page. Go create a wiki account and post on the page below something positive, you will be accused of being a sock puppet of that user by NSA Mods that control wiki.

    Try it, here is the original user that got banned and all positive posts on his page get banned too.

    You can view info about this major new discovery for prime theory at

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    Ulam Spiral w/ a Twist


    A pattern arranged like the Ulam spiral only instead of a dot for every prime, we use different sized circles to represent the number of divisors. Notice the pattern is almost exactly like the classic Ulam spiral only the mystery lines are way more pronounced.

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    【HD】Aikatsu! - episode 05 - Ichigo & Ran - prism spiral【中文字幕】



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    Aikatsu! Music Video Prism Spiral ♪


    Lagu cool dan keren banget yang dipersembahkan oleh Aoi☆
    Lihat juga premium dress warna biru Aoi yang charming♪

    Cek juga info terkini Aikatsu! Indonesia di website resmi↓

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    Prime Numbers, the Ulam Spiral, and the Flaming Lips.


    The Ulam Spril was publicized by Stanislaw Ulam in 1963. The spiral can be generated using the sieve of Eratosthenes to etch out the prime numbers. This animation depicts 51 iterations of the sieve. Initially, each pixel is blue.With each successive iteration, the composite numbers (black) are etched from the blue background leaving the Ulam Spiral. This square is 240 by 240. White pixels indicate the composites identified during the current iteration. Red pixels are composites not yet discovered by the sieve. After 51 iterations the rendering is only gauranteed to be exact up to 233^2. Even so, the fraction (total number of red pixels/total number of pixels) decreases dramatically with the first few iterations.

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    An Ulam Spiral


    Simplicity making complexity. In one word: Emergence.
    Ulam Spiral is when you mark the integers on a grid, in a square spiral pattern, and then retain only prime numbers.
    For this variation, I retained multiples of 1, then multiples of 2, etc.
    I was inspired by


    from the EmergentDesign channel.
    What I wondered was the relation between two consecutive patterns, i.e. what happens between the paterns for the multiples of 2 and 3, 3 and 4, etc.
    So I imagined that each dot was moving. The first dot moving from 1 to 2 to 3..., the second one from 2 to 4 to 6..., the 3rd from 3 to 6 to 9... etc. The result is this animation where you can see the transitions between each of the multiples.
    Animation made with FMS Logo.

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    Prime Number Fractal on the Ulam Spiral


    The Ulam Spril was publicized by Stanislaw Ulam in 1963. The spiral can be generated using the sieve of Eratosthenes to etch out the prime numbers. This animation depicts 123 iterations of the sieve. Initially, the Ulam Spiral is drawn and the primes are:

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    Ulam Spiral


    Illustration of the Ulam spiral, with tink sounds for the composite numbers and sosumi sounds for 1 and the primes.

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    ⭐️素数銀河⭐️ Prime numbers formed a line on the spiral neatly.



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    اعداد اولیه و فنر اولم Prime Numbers and Ulams Spiral


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    Warframe Stances - Reaping Spiral & Stalking Fan


    In-game name : Hellmanz
    Patreon -

    Warframe Stances - Playlist -

    Play Warframe now :

    Get a 7 day EXP boost By using my referral link -

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    Ulam Spiral - Constant Composites


    The Ulam spiral is a method of visualizing the prime numbers, that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a long and very boring paper at a scientific meeting.

    Source code:

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    Long Lost Nikola Tesla Drawings Reveal Map To Multiplication


    A recently discovered set of original Nikola Tesla drawings reveal a map to multiplication that contains all numbers in a simple to use system. The drawings were discovered at an antique shop in central Phoenix Arizona by local artist, Abe Zucca. They are believed to have been created during the last years of Tesla’s Free Energy lab, Wardenclyffe. The manuscript is thought to contain many solutions to unanswered questions about mathematics.

    The Sketches were hidden in a small trunk with numerous other drawings and manuscripts ranging from hand-held technological devices to free-energy systems, many with notes scrawled all over them. Some of the pieces are already familiar to the public, but a few others are not. Most notably is the Map to Multiplication or the Math Spiral. Zucca made a few copies and showed the drawings around to different thinkers, dreamers, and mathematicians.

    A few days later a Local High School Mathematics Instructor, Joey Grether, had been working on deciphering the system and had a few breakthroughs. Grether suggests that the Spiral not only explores Multiplication as an interwoven web, but that it, “offers a comprehensive visual understanding of how all numbers are self-organized into 12 positions of composability.”

    “This device allows us to see numbers as patterns, the formation of prime numbers, twin primes, Highly composite numbers, multiplication and division, as well as few other systems, I imagine, that are yet to be discovered.”

    The diagram itself is very intuitive, allowing students to see how numbers all work together based on a spiral with 12 positions. 12, or 12x (multiples of 12) is the most highly composite system, which is why we have 12 months in a year, 12 inches in a foot, 24 hours in a day, etc. 12 can be divided by 2, 3, 4, and 6. So can all multiples of 12. For every 12 numbers there is a chance of 4 numbers being prime. They happen to fall in positions (think clock positions) 5, 7, 11, and 1.

    Tesla is known for the quote “If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.” It turns out that when the device is examined, the digital roots of the numbers in positions 3, 6, 9, and 12 constantly repeat the same sequence 3, 6, 9! Is this what Tesla was referring too? The self-organization of numbers and their digital roots?

    Its hard to say, but Grether seems to think so. “This breakthrough is phenomenal. If we could get students all over the globe to use this technique, to play with it, and help figure out how to use it, we could overcome our cultural aversion to Mathematics. Instead of memorizing the multiplication table, we could learn the positions of numbers and have a better understanding of how they work.”

    Juan Zapata, One of Mr. G’s students believes so as well… “I used to say I’m bad at Math… cause that's what everyone says, but now, I’m like, dude, this is too easy.”

    Theres one other fact about the Tesla Spiral that make it interesting. The diagram is dated 12/12/12! 1912. Grether and his students want to turn December 12 into a national holiday. So grab a 12 pack, get a dozen donuts, and celebrate the power of 12x.


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    Waltz of Primes


    The video shows a visualization of a complex function, whose nulls are located at all primes on the real axis. Inspired by Ulam’s prime spiral, the real axis was winded up to an Archimedes spiral.
    Music by Bill Schaeffer, “The Happy Song”, 2008, available at

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    A Pattern in Prime Numbers ?


    An interesting phenomenon I stumbled upon recently.

    Hope you find it as fascinating as me.

    If there are any mathematicians in the audience who can explain this,
    (in a simple way) feel free to comment.

    (Oh, and yes, I returned the voice to Professor Hawking, but he left me a copy ;)
    ...ok, I made it with speakonia :) )

    Also I made a large rendering of the pattern available for download here:

    (It is the smallest download button on the page...,
    and please let me know when the link expired.)
    Could be a nice poster :) as suggested by user bobbooty.


    e-world by zero-project

    is licensed under a Creative Commons license:

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    Spiral Prime Numbers


    * Spiral Prime Numbers :
    * Spiral Prime Numbers - Projection :

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