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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    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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    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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    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 ---

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

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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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    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:

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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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    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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    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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    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:
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    Blog on the brown paper issue:

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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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    Since this was filmed, Holly has become a mathematics Lecturer at the University of Cambridge and the Corfield Fellow at Murray Edwards College.

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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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    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 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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    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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    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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    The 10,958 Problem - Numberphile

    8:24

    Featuring Matt Parker... Part 2 (solution) here:
    More links & stuff in full description below ↓↓↓

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    Inder J. Taneja papers...
    Single Digit Representations of Natural Numbers

    Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9


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    Math vs Physics - Numberphile

    13:53

    Robbert Dijkgraaf is a mathematical physicist. Extra footage from this interview:
    More links & stuff in full description below ↓↓↓

    Robbert Dijkgraaf website:

    Physics videos by Brady (who makes Numberphile):

    This video was filmed at the 2017 National Math Festival in Washington DC.

    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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    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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    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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    The Four Color Map Theorem - Numberphile

    14:18

    This video supported by Squarespace:
    The Four Color Map Theorem (or colour!?) was a long-standing problem until it was cracked in 1976 using a new method... computers!

    A little bit of extra footage from this:

    This video features Dr James Grime -
    More Grime videos:

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

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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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    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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    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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    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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    Illegal Numbers - Numberphile

    5:59

    Brown papers auction:
    Mona Lisa in binary:
    More links & stuff in full description below ↓↓↓

    This video features Dr James Grime -

    The hex should be: 4E554D, etc... We missed a digit copying it out!

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    Root 2 - Numberphile

    8:49

    The square root of two is a fascinating number with a long and sordid history. It also forms the basis of most office paper, such as A4, A3, etc.
    More links & stuff in full description below ↓↓↓

    This video features Professor Roger Bowley and Dr James Grime.

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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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    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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    Skewes Massive Number - Numberphile

    10:26

    Dr James Grime on the epic Skewes' Number.
    Lynda free trial (worth a look):
    More links & stuff in full description below ↓↓↓

    Prime numbers:
    Graham's Number:

    A small bit we chopped from this video:

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    70s James Grime drawn by Pete McPartlan...

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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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    Tau vs Pi Smackdown - Numberphile

    11:12

    Steve Mould (tau) and Matt Parker (pi) go head-to-head.
    More links & stuff in full description below ↓↓↓

    See our tau video:
    And check our Pi videos:
    Matt Parker:
    Steve Mould:

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    Is Zero Even? - Numberphile

    6:44

    A bit about zero - including a discussion of its even-ness!?
    More links & stuff in full description below ↓↓↓

    Featuring Dr James Grime ( and Professor Roger Bowley (University of Nottingham).

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    Partitions - Numberphile

    11:45

    Partitions are a major part of the Ramanujan story (as shown in the new film about his life) - but what are they?
    More links & stuff in full description below ↓↓↓

    Dr James Grime tackles the issue.
    Extra footage:
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    Young Tableau:
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    James discusses Good Will Hunting:

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    Christian Cooper
    Peggy Youell
    Ken Baron
    Today I Found Out
    Andrzej 'Yester' Fiedukowicz
    John Buchan
    Bill Shillito
    Thomas Buckingham
    Peter Kær
    Ole Kristian Merli
    Ayliean
    Thomas J.
    Alex Nordlund
    Jordan Smith
    Alfred Wallace
    Valentin
    Tryggve Johannesson
    George Greene
    Arnas
    Paul Bates
    Ian George Walker
    Tracy Parry
    Stan Ciprian
    Keith Vertrees
    Mark Klamerus
    Kristian Joensen

  • desc

    WARNING: Contains Numbers

    5:34

    More links & stuff in full description below ↓↓↓

    Primer on Kickstarter: Karl: Get an original Numberphile brown paper:

    Dr James Grime discusses The Primer sent to us by artist Karl Lautman.

    See our prime number videos...

    PLEASE NOTE: Numberphile is not associated with Karl's project and does not benefit from it. He sent us the sculptures without warning or promise of publicity... We just liked it and wanted to support a great numbery idea.

    Also note we do not vouch for Karl's product. In fact, the model sent to Brady has fallen out of sync on a couple of occasions and required re-calibration (using the instructions supplied by Karl with each model)... But we still think it's great and have had fun with it! Thanks Karl.

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  • desc

    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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  • desc

    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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  • desc

    Problems with Zero - Numberphile

    13:00

    Dividing by zero, zero divided by zero and zero to the power of zero - all pose problems!
    More links & stuff in full description below ↓↓↓

    This video features Matt Parker and James Grime - and

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  • desc

    666 - Numberphile

    11:06

    666 (and sometimes 616) is the notorious Number of the Beast... what's all that about? And what has roulette got to do with it!?
    More links & stuff in full description below ↓↓↓

    Pete Watts shares all sorts of other interesting bits of trivia from the Bible at Brady's Bibledex channel:

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  • desc

    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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  • desc

    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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  • desc

    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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  • desc

    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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  • desc

    Tau replaces Pi - Numberphile

    9:42

    Should Pi be replaced by Tau? Professor Phil Moriarty thinks so.
    More links & stuff in full description below ↓↓↓

    See our collection of Pi videos at:

    See ViHart's Tau video at:

    Tau manifesto:

    Professor Phil Moriarty is a physicist at the University of Nottingham. His scrawls from this video can be seen on Flickr at:

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  • desc

    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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  • desc

    The Last Digit of Prime Numbers - Numberphile

    9:44

    Dr James Grime on a new discovery in the Prime Numbers.
    More links & stuff in full description below ↓↓↓

    Audible:
    More Prime:
    More Grime:

    Read the paper discussed in this video:

    Support us on Patreon:

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  • desc

    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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