Prime Spirals


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    41 and more Ulams Spiral - Numberphile

    9:50

    More on prime numbers and Ulam's Spiral - this time focusing on 41 and Arthur C. Clarke.
    More links & stuff in full description below ↓↓↓

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

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

    The book discussed is The Garden of Rama.

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    Sloanes Gap - Numberphile

    7:27

    Thanks to
    More links & stuff in full description below ↓↓↓

    Here's the paper Dr Grime discusses:
    OEIS:
    Dr Grime:
    1729:

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    The Greatest Ever Infographic - Numberphile

    6:19

    Infographics are not new.. in 1862 Charles Joseph Minard created a much-praised infographic depicting Napoleon's invasion of Russia in 1812.
    More links & stuff in full description below ↓↓↓


    This video features Dr James Grime -
    More of James on Numberphile:

    Here is the info graphic:

    A book coming soon about the map:

    Destin puts great infographics on his Tumblr at

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    Fibonacci Mystery - Numberphile

    9:48

    Brady's view on people who write: FIRST -
    More links & stuff in full description below ↓↓↓

    Dr James Grime on the Pisano Period - a seemingly strange property of the Fibonacci Sequence.

    Available Brown papers:

    With thanks to

    James Grime on Twitter:

    The Alan interview:
    Lagrange Points:

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    63 and -7/4 are special - Numberphile

    12:13

    Dynamical sequences, prime divisors and special exceptions.
    More links & stuff in full description below ↓↓↓

    Featuring Dr Holly Krieger from MIT.
    More primes:

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    Goldbach Conjecture - Numberphile

    9:59

    Professor David Eisenbud on the famed Goldbach Conjecture.
    More links & stuff in full description below ↓↓↓

    Extra footage from this interview:

    Prime Playlist:

    Prime Number Theorem:

    Printing the largest known prime:

    New Numberphile merchandise (buttons and mugs) now available ---

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

    Professor Eisenbud is director at MSRI... See some of his favourite Numberphile videos:

    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

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    Primes are like Weeds - Numberphile

    8:41

    The Prime Number Theorem shows that primes are like weeds, popping up everywhere! Dr James Grime explains --- Little bit extra cut from this video:
    More links & stuff in full description below ↓↓↓

    Our prime number video collection:

    Follow James on Twitter at:

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    abc Conjecture - Numberphile

    6:44

    The abc Conjecture may have been proven by a Japanese mathematician - but what is it?
    More links & stuff in full description below ↓↓↓

    Feeling brave and want to read the papers by Shinichi Mochizuki - (scroll to the bottom)

    This video features Dr James Grime who tweets at

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    Encryption and HUGE numbers - Numberphile

    9:22

    Banks, Facebook, Twitter and Google use epic numbers - based on prime factors - to keep our Internet secrets. This is RSA public-key encryption.
    More links & stuff in full description below ↓↓↓

    Gold Vault:

    This video features Dr James Grime ( Message from James: Thanks to Dr Chris Hughes of the University of York who showed me how to find the RSA public key from my browser, and showed me how awesome they look when you print them out.

    Regarding the keys used for encryption:
    x, y prime
    Encode key E shares no factors with (x-1)(y-1)
    Decode key is D with E*D - 1 a multiple of (x-1)(y-1)

    Thanks to Drew Mokris for the animation:

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    Primes and Twin Primes: An Awesome Journey Pt.1 of 4

    14:31

    Part 1 of 4. These videos convey the thought process in discovering several methods to study Prime Numbers. Great visualizations will guide you through the beauty of the primes, while compelling insights will lay a foundation for the Twin Prime Conjecture. Recommended to watch in HD mode. Go to sievesofchaos.com for more information and visualizations.

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    Base 12 - Numberphile

    9:12

    We mark the date 12/12/12 with a video about the merits of the dozenal/duodecimal system.
    More links & stuff in full description below ↓↓↓

    Numberphile regular Dr James Grime makes the case. More about James at

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    Awesome Prime Number Constant - Numberphile

    7:26

    Have you ever heard of Mills' Constant? Video supported by (& free book):
    More links & stuff in full description below ↓↓↓

    Several people have pointed out the n=4 prime is 2521008887 (we missed an 8)

    More on prime numbers:

    This video features Dr James Grime -

    The Mills Proof is at:

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    One minus one plus one minus one - Numberphile

    11:10

    Discussing the brain-bending Grandi's Series and Thomson's Lamp - featuring Dr James Grime.
    More links & stuff in full description below ↓↓↓

    A little bit of extra footage from the very end of this interview at: (on Brady's own channel)

    See our Zeno's Paradox video at

    Check computerphile at

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    998,001 and its Mysterious Recurring Decimals - Numberphile

    9:47

    There has been some internet buzz about 998001, so Numberphile sheds some light on matters.
    More links & stuff in full description below ↓↓↓

    This video features Dr James Grime and we mention the YouTube channel vsauce.

    James' website:
    vSauce:

    Blog on the brown paper issue:

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    5040 and other Anti-Prime Numbers - Numberphile

    13:38

    Audible: (free trial)
    Dr James Grime discusses highly composite numbers.
    More links & stuff in full description below ↓↓↓

    Continues and extra footage:

    Prime numbers (more videos):



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    Number Trick - Numberphile

    3:29

    Just a quick number trick with Dr James Grime.
    More links & stuff in full description below ↓↓↓

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    Zero Factorial - Numberphile

    7:36

    0! = 1
    Dr James Grime tries to explain why this is the case - follow James on Twitter at
    More links & stuff in full description below ↓↓↓


    Regarding the equation at the end - James says it should be e^-t dt NOT e^-n dn ... sorry for the mix-up!

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    158,962,555,217,826,360,000 - Numberphile

    11:52

    The Nazi's Enigma Machine - and the mathematics behind it - was a crucial part of World War II. Flaw video at:
    More links & stuff in full description below ↓↓↓

    Brown papers on ebay: bit.ly/brownpapers

    Dr James Grime demonstrates the machine and discusses its many configurations.

    James' day job is touring with the Enigma machine - he could even visit you - see more at

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    Infinite Primes - Numberphile

    7:06

    How do we know there are an infinite number of primes?
    More links & stuff in full description below ↓↓↓

    Dr James Grime explains, with a bit of help from Euclid.

    Follow James at

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    Fermats Last Theorem - Numberphile

    9:31

    Simon Singh on Fermat's Last Theorem.
    Simpsons book: Fermat book:
    More links & stuff in full description below ↓↓↓

    EXTRA FOOTAGE:
    FERMAT IN SIMPSONS:

    Interview with Ken Ribet, who played a big role:

    Wiles' proof:

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    Why does 1=0.999...?

    1:59

    A common question, why does 1=0.999...

    If you want to know more, Wikipedia has a good article on the subject

    I take back the very last thing I said about it being an 'infinitesimal' - that's a 17th century idea that Newton and Leibniz were very keen on, but it was never mathematically rigorous. 200 years later that idea was entirely replaced with the modern definition of a limit, that the partial sums get closer and closer to the limit.

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    Riemann Hypothesis - Numberphile

    17:04

    Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis.
    More links & stuff in full description below ↓↓↓

    Prime Number Theorem:
    Fermat's Last Theorem:

    Prof Edward Frenkel's book Love and Math:
    Professor Frenkel is a mathematics professor at the University of California, Berkeley -

    The Millennium Prize at the Clay Mathematics Institute:

    Number Line:

    CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem)

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    210 is VERY Goldbachy - Numberphile

    6:35

    Carl Pomerance discusses 210 and its special relationship with Goldbach's Conjecture.
    More links & stuff in full description below ↓↓↓

    Goldbach's Conjecture:

    The paper discussed in this video:

    Professor Pomerance is based at Dartmouth College.

    More Prime number videos:

    Discuss on Brady's subreddit:

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

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    1 and Prime Numbers - Numberphile

    5:22

    Is 1 a prime number? Apparently not. Dr James Grime explains.
    More links & stuff in full description below ↓↓↓

    James Grime's website is:

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    Pi and the size of the Universe - Numberphile

    5:34

    Pi is famously calculated to trillions of digits - but Dr James Grime says 39 is probably enough. All our Pi videos:
    More links & stuff in full description below ↓↓↓

    An extra note from Dr Grime: Since pi39 ends in 0, you may think we could use pi38 instead - which has even fewer digits. Unfortunately, the rounding errors of pi38 are ten times larger than the rounding errors of pi39 - more than a hyrdogen atom. So that extra decimal place makes a difference, even if it's 0.

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    Gaps between Primes - Numberphile

    8:59

    An exciting paper about gaps between prime numbers - a step closer to proving the twin prime conjecture.
    More links & stuff in full description below ↓↓↓

    Extra footage at

    The proof was published by Yitang Tom Zhang from the University of New Hampshire.

    We're discussing it in simple terms with Numberphile regulars - physicists Ed Copeland and Tony Padilla from the University of Nottingham.

    Brown papers from this video available:

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    Glitch Primes and Cyclops Numbers - Numberphile

    13:32

    Audible:
    More links & stuff in full description below ↓↓↓

    Simon Pampena on Glitch Primes and Binary Cyclops Numbers.
    Simon on Twitter:

    Some book recommendations... Love & Math by Edward Frenkel, The Simpsons and their Mathematical Secrets by Simon Singh, The Mathematics of Love by Hannah Fry and Alex's Adventures in Numberland by Alex Bellos.

    Prime Playlist:

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    The Moving Sofa Problem - Numberphile

    13:00

    Featuring Dan Romik from UC Davis.
    More footage from this interview soon on Numberphile2.
    Dan's comprehensive page on this topic:

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

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    Transcendental Numbers - Numberphile

    13:41

    Numbers like e and Pi cannot be made using normal algebra.
    Featuring Australia's Numeracy Ambassador, Simon Pampena.
    Extra footage:
    More links & stuff in full description below ↓↓↓

    Discussing transendental numbers, algebraic numbers, pi, e and other stuff.

    Simon's website:

    Root 2:
    Pi Playlist:

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    Problems with French Numbers - Numberphile

    9:56

    French numbers can pose problems for non-native speaker - especially when you move beyond 70. Also discussing problems with phone numbers and commas!
    More links & stuff in full description below ↓↓↓

    Featuring Dr Paul Smith from the University of Nottingham.

    The French and marks out of 20:

    A little extra unlisted bit from this interview:

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    The problem in Good Will Hunting - Numberphile

    4:54

    We now have a Tumblr: Tumblr:
    This paper on ebay:
    More links & stuff in full description below ↓↓↓

    Just how hard was the second problem cracked by Will in Good Will Hunting? Matt Damon!

    And who doesn't love Homeomorphically Irreducible Trees?

    This video features Dr James Grime -

    Music by Alan Stewart -

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    The Worlds Best Mathematician - Numberphile

    10:57

    (*) Among current mathematicians, many people regard Professor Tao as the world's finest... Opinions on such things vary, of course.
    Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers.

    EXTRA FOOTAGE: (and more extras to come)

    The Legend of Question Six:
    Professor Tao's blog:

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

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    Is it Math or Maths? - Numberphile

    6:43

    An emotional subject for some - we ask a linguist about Math (US-style) and Maths (British-style).
    More links & stuff in full description below ↓↓↓

    More US-UK number conflict soon, including the mentioned CGP Grey interview - subscribe to Numberphile to ensure you see it:

    Dr Lynne Murphy writes a linguists blog in which she has dealt with Math vs Maths - visit her blog at:

    Fire up the UK-US rivalry by checking our video about miilions, billions, trillions:

    Aluminium and Aluminum:

    Should be facsimile but you get the point - Brady's bad!

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    What colour is 27? - Numberphile

    9:38

    More on number/color synesthesia, including your questions for with Alex Dainis.
    More links & stuff in full description below ↓↓↓

    Supported by: (numberphile5 for discount)

    Blog with graphs:

    Original video at:

    Alex's channel is:

    Huge thanks to Dave Wiley!

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    Squaring the Circle - Numberphile

    7:34

    Why squaring the circle - the old-fashioned way - was found to be impossible? Numblr:
    More links & stuff in full description below ↓↓↓

    This video featuring Dr James Grime:

    The paper from this video on ebay -

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    Apérys constant - Numberphile

    10:48

    Patreon:
    More links & stuff in full description below ↓↓↓

    Tony Padilla is an associate professor of physics at the University of Nottingham. Here he discusses the zeta function and Apéry's Constant.

    More Tony videos:

    Tony's Tweet:

    Roger Apéry pics courtesy of François Apéry

    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

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    Thanks to these Patreon supporters:
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    End credits music by Alan Stewart -

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    Dragon Curve - Numberphile

    7:04

    Beautiful Dragon Curves, Fractals and Jurassic Park. Featuring Rob Eastaway.
    More links & stuff in full description below ↓↓↓

    Rob's website:

    Thanks to Matthew Ward and Faraz Barzideh who helped Brady out with some curves!

    The book Jurassic Park is by the late Michael Crichton.

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    Phone Buttons - Numberphile

    7:42

    Get a free book from Audible:
    Why are phone buttons laid out as they are? Sarah Wiseman discusses.
    More links & stuff in full description below ↓↓↓

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    13532385396179 - Numberphile

    5:09

    A number which could earn its finder a $1000 prize.
    More links & stuff in full description below ↓↓↓

    John Conway videos:

    Read more at:

    With thanks to James Davis.

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    The Riemann Hypothesis

    19:36

    The Riemann Hypothesis is one of the Millennium Prize Problems and has something to do with primes. What's that all about? Rather than another hand-wavy explanation, I've tried to put in some details here. Some grown-up maths follows.

    More information:

    -----------------

    CORRECTION: The functional form of the zeta function is a reflection around the point 0.5, not the line x=0.5. But you can think of that as a reflection in the x-axis followed by a reflection in the line x=0.5.

    For example, if we start with zeta(x + iy) and reflect it in the x-axis we get zeta(x - iy). Reflect that in the x=1/2 line we get (junk)*zeta(1 - x - iy). And reflect that in the x-axis again we get (junk)*zeta(1 - x + iy). When zeta(x + iy) = 0 so are all the others.

    The zeros then look like this That's four zeros for the price of one.

    The zeros are still symmetric around the x=1/2 line. The reflection of zeta(x + iy) is (junk)*zeta(1 - x + iy). In the video I mixed up zeta(1 - x + iy) with zeta(1 - x - iy).

    But the point is the same, the error in the Prime Number Theorem is minimised if all the zeros lie on the line x=1/2.

    ---------------------

    Some people have asked about my final claim that you don't get the prize for a counterexample. Here is the rule from the Clay Institute:

    if a counterexample is proposed, the SAB will consider this counterexample after publication and the same two-year waiting period as for a proposed solution will apply. If, in the opinion of the SAB, the counterexample effectively resolves the problem then the SAB may recommend the award of the Prize. If the counterexample shows that the original problem survives after reformulation or elimination of some special case, then the SAB may recommend that a small prize be awarded to the author. The money for this prize will not be taken from the Millennium Prize Problem fund, but from other CMI funds.

    In other words, there are no guarantees either way.

  • desc

    Why -1/12 is a gold nugget

    15:17

    More links & stuff in full description below ↓↓↓

    Okay, the links...
    1. New vid on the Riemann Hypothesis explains where -1/12 comes from:
    2.The original videos at AND
    3. A useful blog from Tony Padilla:
    4. NY Times article on this:
    5. Terry Tao on this topic:

    Prof Edward Frenkel's book Love and Math:

    Professor Frenkel is a mathematics professor at the University of California, Berkeley -

    Animation by Pete McPartlan

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    Random Numbers - Numberphile

    11:39

    Using radioactive material to generate random numbers...
    Subscribe to our new channel COMPUTERPHILE here -
    More links & stuff in full description below ↓↓↓

    This video features James Clewett.

    Extra video about what happened next with our Strontium random numbers at
    And the Greek extra bit is at

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    Zenos Paradox - Numberphile

    12:05

    Dr James Grime is back and talking about tortoises.
    More links & stuff in full description below ↓↓↓

    In many ways this video follows on from and then

    James Grime's website is:

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    Why 381,654,729 is awesome - Numberphile

    9:06

    Discussing pandigital numbers with Dr James Grime (and a special guest).
    More links & stuff in full description below ↓↓↓

    With thanks to:

    Check out Dr Grime at:
    And on Tumblr at:

    And here is a hidden extra bit we cut from this video:

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    Pi and Four Fingers - Numberphile

    9:40

    Pi, Spigot Algorithms and why The Simpsons is not in Base 8? Simon Singh's book is at:
    More links & stuff in full description below ↓↓↓

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    The LONGEST time - Numberphile

    12:04

    A paper by Don Page claimed to use the longest finite time ever calculated by a physicist - it's the time it will take the Universe to reset itself!?!
    More links & stuff in full description below ↓↓↓

    Video featuring Tony Padilla from the University of Nottingham.

    Read the paper at

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    Collatz Conjecture in Color - Numberphile

    6:18

    The Great Courses Plus (free trial):
    This video features Alex Bellos. More info and links in full description.

    Extra footage with Alex and coloring:
    Or real-time video of the coloring:

    Our previous Collatz Conjecture video:

    The Collatz Colouring image is included in the book Visions of the Universe (USA NAME) and/or Visions of Numberland (UK NAME).

    Alex Bellos books on Amazon:

    More Alex Bellos videos:
    Edmund Harriss:

    Coloring by Tiffany Arment:
    Music by Alan Stewart.

    Talk about this video on Brady's subreddit if you like:

    Here's a blog post with everything neatly pulled together:

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    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

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    Note: The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US market. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally. Also note, with an annual membership, subscriptions are $14.99 per month as Brady mentioned. With a monthly membership, subscriptions are $19.99 per month.

  • desc

    Safe Cracking with Feynman - Numberphile

    8:23

    A chat about some of the ways legendary physicist Richard Feynman cracked safes (filing cabinets) at Los Alamos during the Manhattan Project.
    More links & stuff in full description below ↓↓↓

    Discussed by Professor Roger Bowley.

    My Favourite Scientist on Feynman:
    Feynman Diagrams:
    Enigma:

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    Squared Squares - Numberphile

    10:13

    Featuring Dr James Grime.
    More links & stuff in full description below ↓↓↓

    Extra footage from this interview:
    Blog post about the old photo:

    Check out for loads of great info.

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