Formulas for primes
Magic squares
- Multimagie.com
- Fituvalu: tools for finding a 3x3 square-of-squares
Articles and videos
- Natural numbers
- 163 and Ramanujan Constant - Numberphile by (2 March 2012) ► Heegner numbers and Ramanujan’s constant.
- 6,000,000 and Abel Prize - Numberphile by (31 March 2012) ► Some information about the Abel Prize and Szemerédi’s theorem.
- Is Zero Even? - Numberphile by and (2 December 2012) ► The invention of zero.
- The Legend of Question Six - Numberphile by (16 August 2016) ► Question 6 from the 1988 International Mathematical Olympiad and solving it using Vieta jumping.
- ↪The Return of the Legend of Question Six - Numberphile by (16 August 2016) ► The continuation of the previous video.
- Savez-vous compter les choux ? (A la mode de Peano) by (18 August 2017) ► An introduction to Peano axioms.
- Catalan's Conjecture - Numberphile by (14 February 2018) ► Catalan’s Conjecture has been proven by in 2002 and proving that £[x^2-y^3=1£] has no odd solutions.
- Finding the general formula for nth octagonal number | Visual proof | by (26 April 2018) ► The title says it all.
- Il n'y a pas de question stupide #02 : Là où les nombres s'arrêtent by (29 June 2018) ► Some very basic mathematics: why there is no last number.
- Comment monter un escalier - Micmaths by (17 July 2018) ► Counting how many ways we can sum 1s and 2s to get a given number.
- ↪Comment monter un escalier - Bonus - Micmaths by (17 July 2018) ► The continuation of the previous video.
- The Centrifuge Problem - Numberphile by (3 December 2018) ► How many test tubes can be balanced in a centrifuge?
- Solving An Incredibly Hard Problem From Australia by (4 June 2019) ► Finding the maximum of £[ab+bc+cd£] for £[a+b+c+d=63£].
- La complexité, mystère des nombres entiers by (September 2019) ► The definition of the complexity of an integer.
- Russian Multiplication - Numberphile by (4 February 2020) ► A description of the Egyptian/Ethiopian/Russian multiplication and why it works.
- Why We Might Use Different Numbers in the Future↓ by (18 April 2020) ► Some basic information about numeral systems.
- Landmark Math Proof Clears Hurdle in Top Erdős Conjecture — Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns. by (3 August 2020) ► and proved that whenever a number list’s sum of reciprocals is infinite, it must contain infinitely many evenly spaced triples.
- ↪Surprise Computer Science Proof Stuns Mathematicians — For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results. by (21 March 2023) ► The upper bound of the maximum size of triple-free set has been largely decreased.
- MegaFavNumbers - The Even Amicable Numbers Conjecture by (19 August 2020) ► Poulet’s pair £[(666030256, 696630544)£] are the smallest amicable numbers whose sum is not divisible by £[9£].
- [AVENT MATHS] : 5 est intouchable🚫 by (5 December 2020) ► Untouchable numbers and Goldbach’s conjecture.
- [AVENT MATHS] : 11 dans vos livres🚫 by (11 December 2020) ► The CRC of ISBN.
- ★★★ Les règles de l'Infini - La Classification des Nombres #6↑ by and (20 December 2020) ► The history of the notion of infinity and using the projective line to complete £[\mathbb{Q}£] with £[\infty£].
- The Moessner Miracle. Why wasn't this discovered for over 2000 years? by (17 July 2021) ► A presentation of Moessner’s Theorem.
- Secrets of the lost number walls by (27 August 2022) ► A presentation of number walls.
- Problems with Powers of Two - Numberphile by (21 September 2022) ► Trying to get as many as possible powers of 2 by adding two numbers from a set of n numbers.
- ↪Powers of 2 (extra) - Numberphile by (15 November 2022) ► The continuation of the previous video.
- From Systems in Motion, Infinite Patterns Appear — Mathematicians are finding inevitable structures in sufficiently large sets of integers. by (5 December 2022) ► Some extensions of Erdős sumset conjecture have been proven using ergodic theory.
- Animating Nicomachus's 2000 year old mathematical gem (Mathologer Christmas video) by (24 December 2022) ► £[\begin{matrix}1=1^1&1=1^2&1=1^3 \\1+1=2^1&1+3=2^2&3+5=2^3 \\1+1+1=3^1&1+3+5=3^2&7+9+11=3^3 \\1+1+1+1=4^1&1+3+5+7=4^2&13+15+17+19=4^3 \\\cdots&\cdots&\cdots \\\end{matrix}£]
- Practical Numbers - Numberphile by (18 May 2023) ► A presentation of practical numbers.
- I designed a silly but semi-functional computer. by (27 November 2023) ► Some objects implementing the Irish logarithm.
- A Triplet Tree Forms One of the Most Beautiful Structures in Math — The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century. by and (12 December 2023) ► A short presentation of Markov numbers.
- Is this the most beautiful proof? (Fermat's Two Squares)↑ by (22 December 2023) ► An explanation of ’s one-sentence proof of a theorem of Fermat’s Two Squares Theorem.
- La constante de Kaprekar by (21 January 2024) ► Kaprekar’s routine.
- When a complicated proof simplifies everything by (17 May 2024) ► A simple proof that £[b^n-1£] divides £[b^n-1£].
- 343867 and Tetrahedral Numbers - Numberphile by (21 May 2024) ► Cauchy’s Polygonalnumber Theorem and ’s conjecture.
- Erdős–Woods Numbers - Numberphile by (30 June 2024) ► A presentation of Erdős–Woods numbers.
- What's the next freak identity? A new deep connection with Sophie Germain primes by (9 November 2024) ► Some analysis on the number of finite sequences of integers whose sum and product are equal.
- Jean-Pierre Escofier - L’intérêt de déjeuner ensemble by (26 June 2025) ► From a lunch between , , and to Green–Tao theorem.
- Euclid's Algorithm - Numberphile by (16 January 2026) ► Euclid’s Algorithm, a proof that it computes the GCD, Bézout’s identity, and the fact that the worst case is with two consecutive Fibonacci numbers.
- Large numbers
- Des nombres grands, TRÈS grands - Micmaths by (17 September 2014) ► From a billion to Graham’s number.
- Calculer les derniers chiffres du nombre de Graham by (13 April 2017) ► Computing the last digit of Graham’s number.
- The Enormous TREE(3) - Numberphile by (19 October 2017) ► Kruskal’s tree theorem and the enormous numbers it implies.
- ↪TREE(3) (extra footage) - Numberphile by (19 October 2017) ► The continuation of the previous video.
- How big is Rayo's Number 拉約數 by (25 March 2018) ► The silly definition of Rayo’s Number.
- TREE(3) explained in layman terms 樹函数 by (20 August 2018) ► Some unexplained information about TREE(3).
- TREE vs Graham's Number - Numberphile by (26 October 2019) ► Comparing sequences using a fast-growing hierarchy.
- ↪TREE(Graham's Number) (extra) - Numberphile by (26 October 2019) ► The continuation of the previous video.
- The Daddy of Big Numbers (Rayo's Number) - Numberphile by (12 April 2020) ► The story of the Big Number Duel between and .
- Katie's #MegaFavNumbers - the MEGISTON, and Steinhaus-Moser notation by (19 August 2020) ► The title says it all.
- Théorème de Kruskal et des arbres, LMSB#5 by (13 December 2020) ► Yet another explanation of the TREE function, this one is better than the ones above, but still not perfectly explained.
- Le plus grand de tous les nombres ?! - Deux (deux ?) minutes pour... by (23 April 2024) ► A presentation of the usual large numbers.
- The Hyper Moser (and other Mega Numbers) - Numberphile by (14 March 2025) ► Yet another useless, because it contains little information, video about large numbers: this one is about the Steinhaus–Moser notation.
- ↪Mega and Moser (extra footage) - Numberphile by (16 March 2025) ► The continuation of the previous video.
- The Original Biggest Numbers - Numberphile by (31 March 2026) ► Some very large numbers appear in the Jainism tradition in India.
- How to break Magic the Gathering. by (1 April 2026) ► How to create huge numbers with Magic the Gathering.
- Busy Beaver
- Busy Beaver Turing Machines - Computerphile by (2 September 2014) ► A not-so-clear presentation of Busy Beaver.
- The Boundary of Computation by (10 July 2023) ► Busy Beaver is better explained in this video, but ’s example of a fast growing series adds little value.
- With Fifth Busy Beaver, Researchers Approach Computation’s Limits — After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get. by (2 July 2024) ► The value of BB(5) has been proven by a group of amateurs using Coq.
- ↪How a Group of Amateurs Solved an Impossible Problem (21 April 2025) ► The same.
- Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math — The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation. by (22 August 2025) ► Some huge numbers have been found while looking for BB(6), but this one will be very difficult to solve since some Turing machines are equivalent to the Collatz conjecture.
- Bernoulli numbers
- Les nombres de Bernoulli et le programme de Lovelace by (15 June 2020) ► A presentation of Bernouilli numbers and ’s "program" to compute them.
- Faulhaber's Fabulous Formula (and Bernoulli Numbers) - Numberphile⇊ by (17 October 2023) ► This description of Bernoulli numbers is impossible to understand.
- Chinese Remainder Theorem
- Chinese Remainder Theorem and Cards - Numberphile by (8 August 2018) ► A trick using simple modular arithmetic.
- How Ancient War Trickery Is Alive in Math Today — Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research. by (14 September 2021) ► A presentation of the Chinese remainder theorem.
- What Hot Dogs Can Teach Us About Number Theory — The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples. by (18 November 2021) ► Yet another presentation of the theorem.
- Base 12
- Base 12 - Numberphile by (12 December 2012) ► About the proposal of the Dozenal Society of Great Britain.
- [AVENT MATHS] : 12 est une base🚫 by (12 December 2020) ► The advantage of base 12.
- Casting out nines
- Casting Out Nines - Numberphile by (13 September 2017) ► The title says it all.
- ↪Casting Out Nines (extra footage) - Numberphile by (14 September 2017) ► The continuation of the previous video.
- [AVENT MATHS] : 9 est une preuve ?🚫 by (9 December 2020) ► An explanation of why casting out nines works.
- Integers
- How real men solves a simple equation (when Ramanujan gets bored)↓ by (27 April 2021) ► A painfully slow resolution of £[\left\{\begin{array}{@{}l@{}}\sqrt{x}+y=7\\x+\sqrt{y}=11\end{array}\right.£].
- The operation before the addition
- À vous de chercher : avant l'addition ? - Micmaths by (9 November 2017) ► What is the preceding element in the series addition / multiplication / exponentiation / tetration / …
- ↪Réflexions : Qu’est-ce qui vient avant l’addition ?↓ by (9 November 2017) ► Trying to answer to the previous question, but the analysis is too narrow and, so, it is a failure. (The strange thing is that the guy knows Peano and does not think about the successor function.)
- ↪Le live final des 10 ans de micmaths by (30 November 2017) ► Several subjects (42, graphs, books…), the last one being the operation before the addition.
- Comment résoudre un exercice d'arithmétique [TN-AB-19] (10 January 2023) ► A very simple arithmetic problem.
- Multiplication
- Comment multiplier rien du tout ? - Micmaths by (26 March 2014) ► 1 is the neutral element of the multiplication.
- Geometry of Binomial Theorem | Visual Representation | 2 examples by (19 January 2018) ► Visualisations of £[(a+b)^2=a^2+2ab+b^2£] and of £[(a+b)^3=a^3+3a^2b+3ab^2+b^3£].
- Former McDonald's Worker Does a Number Theory Proof by (23 February 2019) ► Proving that £[2019^4+4^{2019}£] is not prime using Sophie Germain Identity (£[a^4 + 4b^4 = (a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab)£]).
- a BIG prime factor problem! by (30 March 2019) ► Partial factorisation of £[1002004008016032£].
- Mathematicians Discover the Perfect Way to Multiply — By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit. by (11 April 2019) ► An algorithm to multiply two numbers with complexity £[n log(n)£] has been found.
- The Difference of Two Squares by and (7 May 2019) ► Proving that the set of integers being the difference of two squares is the set of integers which are not of the form £[4k+3£].
- One of the easiest Putnam Exam questions! by (29 July 2019) ► Computing the number of integers that are divisors of £[10^{40}£] or of £[20^{30}£].
- MP^2 | Number City: the city a maths grant built by (10 July 2025) ► A real-life representation of integer factorisation.
- Divisibility criteria
- Divisibility Tricks - Numberphile by (17 January 2019) ► Divisibility trick from 2 to 11 and the generalised divisibility rule.
- ↪Divisible by Seven (worst card trick ever?) - Numberphile by (18 January 2019) ► The continuation of the previous video.
- Un jeune nigérian de 12 ans dévoile une propriété de maths by (14 November 2019) ► A criteria of divisibility by 7.
- Fabriquez vos propres critères de divisibilité by (11 April 2020) ► How to use modular arithmetic to define divisibility criteria.
- Why 7 is Weird - Numberphile by (22 August 2022) ► Yet another video about the divisibility tricks from 2 to 11.
- Solving Seven - Numberphile by (25 June 2024) ► A presentation of division graphs.
- New divisibility rule! (30,000 of them) by (21 November 2024) ► How to create many unusable divisibility tests.
- Modular times tables
- La face cachée des tables de multiplication - Micmaths by (19 June 2015) ► Graphical representation of multiplication in modular arithmetic.
- Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe? by (19 February 2022) ► Debunking the bullshit around ’s 3-6-9 vortex.
- Factorial
- Zero Factorial - Numberphile by (8 June 2013) ► Some reasons why £[0!=1£].
- Hyperfactorial introduction by (18 November 2018) ► The definition (£[H(n)=\prod_{i=1}^{i=n}i^i£]), £[H(5)£] is the number of milliseconds in a day, and £[H(0)=1£].
- Superfactorial 4$=4!3!2!1! by (19 November 2019) ► The definitions of superfactorial and hyperfactorial.
- 7 factorials you probably didn't know by (5 August 2021) ► Double factorial, subfactorial, primorial, two super factorials, exponential factorial, and hyper factorial.
- Big Factorials - Numberphile by (24 March 2022) ► A presentation of Stirling’s formula.
- What's special about 288? - Numberphile by (24 October 2023) ► Some very little information about superfactorial.
- Subfactorial
- Subfactorial, a recursive approach by (13 November 2018) ► The definition of derangements and the expression £[!n=(n - 1)(!(n-1)+!(n-2))£].
- subfactorial & derangement, an explicit approach by (25 November 2018) ► £[!n = n!\sum_{i=0}^{i=n}\frac{(-1)^i}{i!}£] and £[!n\approx\frac{n!}{e}£] for large n.
- Primes
- Prime Spirals - Numberphile by (9 July 2013) ► Ulam and Sacks spirals.
- Awesome Prime Number Constant (Mills' Constant) - Numberphile by (18 July 2013) ► Mills’ constant.
- Primes are like Weeds (PNT) - Numberphile by (13 August 2013) ► The Prime Number Theorem.
- ↪Prime Number Theorem (little extra bit) by (19 August 2013) ► The continuation of the previous video.
- Liar Numbers - Numberphile by (3 February 2014) ► Carmichael numbers.
- What do 5, 13 and 563 have in common? by (3 August 2014) ► Wilson’s theorem and Wilson’s primes.
- ↪Wilson's Theorem (extra footage) by (4 August 2014) ► The continuation of the previous video.
- Skewes' Massive Number - Numberphile by (23 October 2015) ► Skewes determined that £[10^{10^{10^{34}}}£] is a upper bound for the smallest natural number £[{\displaystyle x}£] for which £[\displaystyle \pi (x)>\operatorname {li} (x)£] (but this video does not say that he assumed the Riemann hypothesis is true).
- ↪Skewes' Number (tiny bit we cut) by (24 October 2015) ► The continuation of the previous video.
- Glitch Primes and Cyclops Numbers - Numberphile by (7 December 2015) ► Some simple maths with prime numbers having some characteristics with their decimal representation.
- The Last Digit of Prime Numbers - Numberphile by (4 May 2016) ► A bias in the last digit of prime numbers has been found.
- 5040 and other Anti-Prime Numbers - Numberphile by (6 July 2016) ► Highly composite number.
- ↪Failed Anti-Prime Conjecture (extra footage) - Numberphile by (8 July 2016) ► The continuation of the previous video.
- ↪Infinite Anti-Primes (extra footage) - Numberphile by (8 July 2016) ► The continuation of the previous video.
- 383 is cool - Numberphile by (15 February 2017) ► 383 is a Woodall prime.
- The Trinity Hall Prime - Numberphile by (7 September 2017) ► A nicely printed prime.
- 78557 and Proth Primes - Numberphile by (13 November 2017) ► Proth numbers and Sierpiński numbers.
- Les nombres premiers respectent la parité by (February 2018) ► A conjecture of on the equidistribution of the sums of the digits of prime numbers was proven by and .
- What was Fermat’s “Marvelous" Proof? | Infinite Series by (9 March 2018) ► The difference between primality and irreducibility.
- A Chemist Shines Light on a Surprising Prime Number Pattern — When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory. by (14 May 2018) ► The diffraction of prime numbers shows some patterns, but does this have any interest?
- Squaring Primes - Numberphile by (20 November 2018) ► Two proofs that 24 divides £[p^2-1£] for any prime greater than 3.
- Big Question About Primes Proved in Small Number Systems — The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems. by (26 September 2019) ► The title says it all.
- Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations by (8 October 2019) ► Explaining some drawing artefacts with rational approximations of π and Dirichlet’s theorem.
- Primes without a 7 - Numberphile by (20 November 2019) ► proved that there is an infinite number or primes without a given digit, but there is no information about the proof.
- A Prime Surprise (Mertens Conjecture) - Numberphile by (23 January 2020) ► The Mertens Conjecture has been proven wrong.
- 906,150,257 and the Pólya conjecture (MegaFavNumbers) by (19 August 2020) ► £[906150257£] is the smallest counterexample of Pólya conjecture.
- 2.920050977316 - Numberphile by (26 November 2020) ► Encoding the sequence of primes in a single number.
- ↪Prime Generating Constant (extra) - Numberphile by (4 December 2020) ► The continuation of the previous video.
- [AVENT MATHS] : 1 n'est pas premier🚫 by (1 December 2020) ► A short history of the primality of one.
- La conjecture de Legendre by and (10 May 2021) ► A very short and basic presentation of Legendre’s conjecture.
- Mathematicians Outwit Hidden Number Conspiracy — Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now. by (3 January 2022) ► and proved the logarithmic Chowla conjecture: the parity of the number of prime factors of an integer is not correlated with that of its neighbours.
- How Can Infinitely Many Primes Be Infinitely Far Apart? — Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be. by (21 July 2022) ► Some facts about the density of primes: gaps between primes, digitally delicate primes, and widely digitally delicate primes.
- An Exact Formula for the Primes: Willans' Formula by (22 September 2022) ► A detailed explanation of C. P. Willans’ formula to compute the n-th prime.
- Teenager Solves Stubborn Riddle About Prime Number Look-Alikes — In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician. by (13 October 2022) ► A 17-years old boy gets some results about the density of Carmichael numbers.
- Paterson Primes (with 3Blue1Brown) - Numberphile by (4 November 2022) ► An obviously wrong conjecture about primes.
- ↪Prime Pyramid (with 3Blue1Brown) - Numberphile by (6 November 2022) ► Farey sequence, Euler’s totient function…
- ↪The Prime Number Race (with 3Blue1Brown) - Numberphile by (23 February 2023) ► The 4k-1 vs. 4k+1 prime race.
- Why Mathematicians Re-Prove What They Already Know — It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another. by (26 April 2023) ► Using complex mathematical results to prove, once again, that there are infinitely many prime numbers.
- How to Build a Big Prime Number — A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers. by (13 July 2023) ► Some mathematicians found a polynomial-time and pseudodeterministic (producing the same solution with high probability) algorithm to find prime numbers of length n or, more generally, numbers having a property decidable in polynomial time.
- A New Generation of Mathematicians Pushes Prime Number Barriers — New work attacks a long-standing barrier to understanding how prime numbers are distributed. by (26 October 2023) ► The progress on knowing better the distribution of primes.
- ↪23% Beyond the Riemann Hypothesis - Numberphile by (29 October 2023) ► The same with less information.
- Mathematicians Uncover a New Way to Count Prime Numbers — To make progress on one of number theory’s most elementary questions, two mathematicians turned to an unlikely source. by (11 December 2024) ► and used ’s norm to prove that there infinitely are many primes that can be written, for example, as £[p^2+4q^2£].
- 100000001 is divisible by 17 - Numberphile by (9 December 2025) ► Analysing the primality of £[10^n + 1£].
- 3867632931 × 10^10001 +1 - Numberphile by and (16 February 2026) ► £[3867632931 \times 10^{10001} + 1£] is a reversible prime.
- ↪Addicted to Prime Numbers (full interview) - Numberphile by and (16 February 2026) ► An interview of .
- Awkward Primes - Numberphile by (7 April 2026) ► Looking at the minimal number of straight lines needed to cover the first (n, n-th prime) points.
- ↪Prime at the End of the Line (extra) - Numberphile by (8 April 2026) ► The continuation of the previous video.
- Gaps between primes
- Exploring the mysteries of the Prime (gaps!) Line. by (6 April 2021) ► Some facts about the gaps between prime numbers.
- ↪Predicting primes using the Prime (gaps) Line equation [DELETED SCENE] by (9 April 2021) ► The continuation of the previous video.
- Bounded gap between primes
- Unheralded Mathematician Bridges the Prime Gap — A virtually unknown researcher has made a great advance in one of mathematics’ oldest problems, the twin primes conjecture. by (19 May 2013) ► An unknown mathematician proves that there is an infinity of pairs of primes such as their difference is smaller than 70,000,000.
- Gaps between Primes - Numberphile by and (27 May 2013) ► Some information about ’s paper.
- ↪Gaps between Primes (extra footage) - Numberphile by and (27 May 2013) ► A complement of the previous video.
- Les nombres premiers by (30 September 2016) ► The improvement on ’s bounded gaps between primes and Hardy-Littlewood’s conjectures.
- ↪Les nombres premiers by (30 September 2016) ► Some information additional to the previous video.
- Twin Prime Conjecture - Numberphile by (13 April 2017) ► speaks about the history of studying prime gaps and about his own work.
- Twin Proofs for Twin Primes - Numberphile by (27 March 2022) ► Two proofs that if £[p£] and £[q£] are twin primes, then £[p \times q \equiv 8 \pmod 9£].
- Something strange happens when you look at the primes by and (29 November 2025) ► The story of trying to prove the Twin Prime conjecture.
- Large gap between primes
- Large Gaps between Primes - Numberphile by (19 July 2017) ► Estimating the largest gap between consecutive primes below a given number.
- ↪Love Prime Numbers - Numberphile by (20 July 2017) ► The continuation of the previous video: explains his interest in prime numbers.
- Fermat’s theorem on sums of two squares
- The Prime Problem with a One Sentence Proof - Numberphile by (18 July 2016) ► There is a simple proof of Fermat’s theorem on sums of two squares.
- ↪The One Sentence Proof (in multiple sentences) - Numberphile by (18 July 2016) ► The continuation of the previous video.
- Why was this visual proof missed for 400 years? (Fermat's two square theorem) by (25 January 2020) ► The title says it all.
- 274207281-1
- New World's Biggest Prime Number (PRINTED FULLY ON PAPER) - Numberphile by (21 January 2016) ► The race to find the largest prime number and GIMPS.
- How they found the World's Biggest Prime Number - Numberphile by (21 January 2016) ► A description of Lucas-Lehmer primality test for Mersenne numbers.
- More details about the World's Biggest Prime by (21 January 2016) ► Useless facts about 274207281-1 digits.
- 282589933-1
- MegaFavNumbers - 82589933 and The Biggest Prime Ever Known by (20 August 2020) ► 282589933-1 is the current biggest known (Mersenne) prime.
- 2136279841-1
- New largest prime number found! See all 41,024,320 digits. by (21 October 2024) ► A new record has been found. describes the strategy changes of the Great Internet Mersenne Prime Search.
- The Man Who Found the World's Biggest Prime - Numberphile by , , and (22 October 2024) ► Interviews of who paid for running the GPUs and who created GIMPS.
- ↪Largest Known Prime discovered by Luke Durant (Full Interview) - Numberphile (22 October 2024) ► The full interview of .
- ↪GIMPS's George Woltman on discovery of 52nd Mersenne Prime (Full Interview) - Numberphile (22 October 2024) ► The full interview of .
- New Largest Known Prime with Matt Parker (Full Interview) - Numberphile by (24 October 2024) ► describes his feeling about the new Mersenne Prime and explains how he created his video.
- Erdős primitive set conjecture
- Graduate Student’s Side Project Proves Prime Number Conjecture — Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.” by (6 June 2022) ► Erdős primitive set conjecture has been proven.
- Primes and Primitive Sets (an Erdős Conjecture is cracked) - Numberphile by (16 June 2022) ► speaks about the conjecture he proved.
- ↪Primitive Sets (extra) - Numberphile by (16 June 2022) ► The continuation of the previous video.
- A Breakthrough with Fingerprint Numbers - Numberphile by (10 October 2023) ► Some new results on the asymptotic behaviour of density functions of the set of primes.
- Riemann Hypothesis
- Riemann Hypothesis - Numberphile by (11 March 2014) ► Presentation of complex numbers, the ζ function and Riemann hypothesis.
- Deux (deux ?) minutes pour... l'hypothèse de Riemann by (4 April 2016) ► A similar video.
- The Key to the Riemann Hypothesis - Numberphile by (10 May 2016) ► L-Functions and Riemann Hypothesis.
- But what is the Riemann zeta function? Visualizing analytic continuation by (9 December 2016) ► The title says it all: some good graphics to get some feeling on the behaviour of ζ function.
- Euler’s Pi Prime Product and Riemann’s Zeta Function by (8 September 2017) ► The Euler product formula for the Riemann zeta function.
- L'Hypothèse de Riemann by (4 October 2019) ► A basic explanation of the Riemann hypothesis introduced via the prime-counting function.
- Attempts Made to Prove the Riemann Hypothesis by (4 December 2019) ► A list of failed attempts at proving Riemann hypothesis.
- The Riemann Hypothesis, Explained by (4 January 2021) ► Yet another presentation of the Riemann hypothesis. This one is rather basic, short, and clear.
- L’hypothèse de Riemann (⧉) by (15 November 2021) ► A basic presentation of the conjecture.
- What is the Riemann Hypothesis REALLY about? by (13 December 2022) ► Some nice graphs and formulas, but nothing is really explained.
- The Search for Siegel Zeros - Numberphile by (19 December 2022) ► A presentation of the Generalised Riemann hypothesis and ’s result on Landau-Siegel zeros.
- Thomaths 26 : La fonction Zêta de Riemann by (6 March 2024) ► Some information about the ζ function.
- ‘Sensational’ Proof Delivers New Insights Into Prime Numbers — The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis. by (15 July 2024) ► As usual with Quanta Magazine articles, the description is limited to so basic mathematics so you have very little information about and result.
- Goldbach’s conjecture
- Goldbach Conjecture - Numberphile by (24 May 2017) ► A description of the conjecture.
- ↪Goldbach Conjecture (extra footage) - Numberphile by (25 May 2017) ► The continuation of the previous video.
- 210 is VERY Goldbachy - Numberphile by (28 May 2017) ► 210 is the largest number such that the difference between itself and a prime larger than its half is a prime.
- Goldbach Conjecture (but with TWIN PRIMES) - Numberphile by (14 September 2024) ► A Goldbach Conjecture Using Twin Primes and OEIS A007534.
- ↪Twin Prime Goldbach Conjecture (extra footage) - Numberphile by (14 September 2024) ► The continuation of the previous video.
- The Obviously True Theorem No One Can Prove by (20 June 2025) ► The story of Goldbach’s conjecture and the proof of Goldbach’s weak conjecture.
- Fermat’s little theorem
- Fermat’s HUGE little theorem, pseudoprimes and Futurama by (27 October 2018) ► A "proof" of the theorem and two applications.
- The Freshman's Dream (a classic mistake) - Numberphile by (16 July 2024) ► presents some simple facts about modular arithmetic.
- ↪The Freshman's Dream (extra) - Numberphile (18 July 2024) ► The continuation of the previous video: a quick proof of Fermat’s little theorem.
- Miller–Rabin primality test
- Witness Numbers (and the truthful 1,662,803) - Numberphile by (28 November 2021) ► A description of Miller–Rabin primality test, but there is no mathematical explanation of how it works.
- How To Find Massive Primes in Seconds | Miller-Rabin Primality Test by (9 May 2025) ► A presentation of Miller–Rabin primality test, but the explanations are not mathematically sound and the complex stuff is skipped.
- Digitally delicate primes
- Mathematicians Find a New Class of Digitally Delicate Primes — Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite. by (30 March 2021) ► The study of "digitally delicate" and "widely digitally delicate" primes. This seems first to be some fun rather than mathematical results that will be built upon.
- How do you prove a prime is infinitely fragile? by (28 July 2021) ► The proof that there are infinitely many widely digitally delicate primes.
- ↪Infinitely Fragile Primes: bonus content! by (28 July 2021) ► Some little additional explanation.
- Théo Untrau - Délicatesse des nombres premiers by (30 January 2025) ► Some information about ’ proof that there are infinitely many delicate primes.
- abc Conjecture
- abc Conjecture - Numberphile by (12 October 2012) ► proposes a proof of Oesterlé-Masser conjecture.
- Titans of Mathematics Clash Over Epic Proof of ABC Conjecture — Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years. by (20 September 2018) ► and consider that Shinichi Mochizuki’s proof is incorrect.
- Find your own ABC Conjecture Triple by (8 October 2021) ► A clear description of the ABC conjecture.
- Benoît Claudon - Le b.a.-ba de l'abc by (15 April 2024) ► The Mason-Stothers theorem and the abc conjecture.
- Magic squares
- The magic, myth and math of magic squares | Michael Daniels | TEDxDouglas↓ by (17 December 2014) ► There is no mathematics here, only some little history (the presenter seems to be pseudoscience bullshit guru).
- The Parker Square - Numberphile by (18 April 2016) ► A miserable failure at trying to find a magic square containing squares.
- Magic Square Party Trick - Numberphile by (19 April 2016) ► A trick to create a magic square with a given sum.
- ↪Magic Square Party Trick (extra footage) by (19 April 2016) ► The continuation of the previous video.
- Magic Squares, Including Frenicle's 880 of Order Four –John Conway by (27 July 2016) ► Some methods to generate magic squares of any size.
- Autour du nombre 34, avec Roger Mansuy - Myriogon #5 by and (23 March 2020) ► 4x4 magic squares.
- Les carrés magiques et les suites mathématiques : comment ça marche ? 🧙🏼♂️➕🧮 (29 April 2020) ► Miscellaneous simple facts about magic squares.
- Finite Fields & Return of The Parker Square - Numberphile by (7 October 2021) ► Magic squares of squares in £[\mathbb{Z}/n\mathbb{Z}£].
- ↪Become a MILLIONAIRE by winning The Parker Prize (extra footage) by (8 October 2021) ► The continuation of the previous video.
- How to make a Birthday Magic Square by (20 November 2022) ► How to create a magic square by using two 4x4 mutually orthogonal Latin squares.
- The Korean king's magic square: a brilliant algorithm in a k-drama (plus geomagic squares) by (4 February 2023) ► A "proof" that ’s method generates a magic square and applying magic squares to geometrical shapes.
- Magic Squares of Squares (are PROBABLY impossible) - Numberphile by (13 June 2023) ► Using some theorems and a conjecture to explain why there may be no 3x3 magic square-of-squares.
- Magic Chess Tours (with Knights and Kings) - Numberphile by (1 April 2024) ► Knight tours and king tours that are magic.
- The Anti-Parker Square - Numberphile by (17 December 2024) ► is trying to build a square-of-squares and she is musing about some relationship with perfect Euler bricks.
- A Magic Square Breakthrough - Numberphile by (9 February 2025) ► A new paper ("On the existence of magic squares of powers") proves that, for each £[n≥2£], there exists an integer £[n_0(d)£] such that there exists an n×n magic square of £[d^{th}£] powers for all £[n≥n_0(d)£]. So is believing more that there is no square-of-squares, and he decides to propose $10000 bounty to the person who find one.
- ↪A warning about hunting for 'Parker Squares' - Numberphile by (11 February 2025) ► An advice for the wannabe square-of-squares researchers: take care of rounding errors.
- Magic hexagons
- Magic Hexagon - Numberphile by (26 August 2014) ► There is only one magic hexagon.
- [AVENT MATHS] : 19 cases d'un hexagone magique🚫 by (19 December 2020) ► The same.
- Sums
- Sum of n squares | explained visually | by (20 June 2017) ► A visualisation of the £[1^2+2^2+3^2+…+n^2 = \frac{n(n+1)(2n+1)}{6}£] formula.
- Beautiful visualization | Sum of first n Hex numbers = n^3 | animation by (9 July 2017) ► The title says it all.
- Sum of cubes by (8 June 2019) ► Using a 2D figure to prove £[\sum_{i=1}^{n}i^3=\left(\sum_{i=1}^{n}i\right)^2£].
- How to evaluate a double summation (change the order first) by (8 June 2019) ► £[\sum_{m=0}^{∞}\sum_{n=1}^{m}\frac{1}{2^{m+n}}=\frac{2}{3}£].
- Diophantine equations
- 87,539,319 - Numberphile by (27 November 2013) ► Futurama contains several references to Ramanujan’s 1729 and another taxicab number.
- Hasse Principle - Numberphile by (1 June 2016) ► A demonstration why £[9m+4£] or £[9m+5£] cannot be the sum of three cubes.
- Secret Link Uncovered Between Pure Math and Physics — An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics. by (1 December 2017) ► The work of on Diophantine equations is based on analogies with gauge theory.
- Euler's and Fermat's last theorems, the Simpsons and CDC6600 by (24 March 2018) ► A counterexample of Euler’s conjecture and the proof that £[A^4+B^4= C^2£] has no solution.
- A number theory proof by (4 April 2018) ► Proving that £[a^2+b^2=4c+3£] has no solution.
- Superhero Triangles - Numberphile by (28 January 2020) ► A presentation of Heronian triangles.
- Impossible Squares - Numberphile by (4 April 2020) ► Drawing squares on an integer lattice and solving £[a^2+b^2=c^2£].
- a RARE mistake from Euler (AIME 1989) by (7 April 2020) ► Finding £[n£] such that £[133^5+110^5+84^5+27^5=n^5£].
- Mathematicians Prove 30-Year-Old André-Oort Conjecture — A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties. by (3 February 2022) ► The subject is complex, so the article does not give much details.
- Le Théorème des 5 Cubes [TN-AB-18] (7 November 2022) ► The proof that any number can be written as the sum of 5 cubes.
- Mathematical Trio Advances Centuries-Old Number Theory Problem — The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.” by (29 November 2022) ► Lower and upper bounds have been found on the number of integers that can be written as the sum of two cubed fractions.
- What's hiding beneath? Animating a mathemagical gem by (17 December 2022) ► £[3^2+4^2=5^2£], £[10^2+11^2+12^2=13^2+14^2£], £[21^2+22^2+23^2+24^2=25^2+26^2+27^2£]…
- Two Students Unravel a Widely Believed Math Conjecture — Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall. by (10 August 2023) ► The local-global conjecture for Apollonian circle packings has been proven to be false.
- ★★ L'Équation de Pell, un problème millénaire - Hors-Série by and (19 August 2023) ► The history of the study of Pell’s equation, from the Pythagoreans, to India, and to Gauss.
- A simple equation that behaves weirdly - Numberphile by (17 June 2025) ► Analyzing the asymptotic number of solutions of the Diophantine equation £[x^2+y^2+z^2+w^2=xyzw£].
- Pythagorean triples
- All possible pythagorean triples, visualized by (26 May 2017) ► Using the complex plane to visualise the Pythagorean triples.
- finding ALL pythagorean triples (solutions to a^2+b^2=c^2) by (9 July 2018) ► Computing the well-known formula to generate Pythagorean triples: (2mn, m2-n2, m2+n2).
- Fibonacci = Pythagoras: Help save a beautiful discovery from oblivion↑ by (3 December 2022) ► A tree generating all primitive Pythagorean triples.
- Congruent numbers
- Tobias Schmidt - Le plus ancien problème mathématique non résolu by (13 May 2019) ► A presentation of the congruent number problem.
- My #MegaFavNumber: 224,403,517,704,336,969,924,557,513,090,674,863,160,948,472,041 by (19 August 2020) ► A short and (too) fast presentation of congruent numbers.
- Sum of three cubes
- The Uncracked Problem with 33 - Numberphile by (6 November 2015) ► What numbers can be represented as the sum of three cubes?
- 74 is cracked - Numberphile by (31 May 2016) ► £[74=-284650292555885^3+66229832190556^3+283450105697727^3£].
- 42 is the new 33 - Numberphile by (12 March 2019) ► explains how he found £[33=8866128975287528^3−8778405442862239^3−2736111468807040^3£].
- How Search Algorithms Are Changing the Course of Mathematics — The sum-of-three-cubes problem solved for “stubborn” number 33. by (28 March 2019) ► This article tells about the same subject and about the usefulness of using computers to find some solutions of Diophantine equation.
- The Mystery of 42 is Solved - Numberphile by (6 September 2019) ► £[42=−80538738812075974^3+80435758145817515^3+12602123297335631^3£].
- 3 as the sum of the 3 cubes - Numberphile by (24 September 2019) ► £[3=569936821221962380720^3-569936821113563493509^3-472715493453327032^3£].
- Why the Sum of Three Cubes Is a Hard Math Problem — Looking for answers in infinite space is hard. High school math can help narrow your search. by (5 November 2019) ► A simple explanation of the search method.
- 569936821221962380720 - Numberphile by (19 August 2020) ► The latest findings about the problem of the sum of three cubes.
- Fermat’s last theorem
- Fermat's Last Theorem - Numberphile by (24 September 2013) ► The history of Fermat’s last theorem.
- Homer Simpson vs Pierre de Fermat - Numberphile by (29 September 2013) ► Simpson episodes contain some Fermat near-misses.
- How Math’s Most Famous Proof Nearly Broke — Andrew Wiles thought he had a solution to an age-old puzzle. Until it began to unravel. by (28 May 2015) ► The initial proof of Fermat’s Last Theorem contained an error.
- The Heart of Fermat's Last Theorem - Numberphile by (6 April 2016) ► Trying to transmit some feeling about the link between elliptic curves and modular forms.
- ‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem — Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world. by (6 April 2020) ► Two new papers continue to build the bridge between Diophantine equations and automorphic forms.
- Avec Pierre de Fermat - Myriogon #17 by and (15 April 2020) ► There are little mathematics here, just a mad .
- L'INCROYABLE HISTOIRE DE LA CONJECTURE DE FERMAT CMH#14 by (9 September 2022) ► Yet another telling of the history of Fermat’s last theorem.
- Useless number facts
- 153 and Narcissistic Numbers - Numberphile↓ by (3 January 2012) ► About the narcissistic numbers (a.k.a. Armstrong numbers).
- 3435 - Numberphile by (13 January 2012) ► About the Munchausen numbers (a.k.a. perfect digit-to-digit invariant).
- 7 and Happy Numbers - Numberphile↓ by (10 February 2012) ► About the happy numbers.
- 145 and the Melancoil - Numberphile by (26 February 2012) ► About the unhappy numbers.
- 998,001 and its Mysterious Recurring Decimals - Numberphile by (6 March 2012) ► Explaining the digits of £[\frac{1}{999…9^n}£].
- 37 - Numberphile by (20 July 2012) ► The usual trick using the fact that £[3 \times 37 = 111£].
- Illegal Numbers - Numberphile by (13 May 2013) ► When some companies try to copyright some numbers.
- Why 381,654,729 is awesome - Numberphile by (21 May 2013) ► Pandigital numbers.
- Six Sequences - Numberphile by (22 July 2013) ► Khintchine’s constant, Wieferich primes, Golomb’s sequence, largest metadrome in base n, all 7’s, and Wild Numbers.
- Curiosités mathématiques #2 - Nombres renversés- Micmaths by (21 May 2015) ► The 1089 trick.
- Why 82,000 is an extraordinary number - Numberphile by (12 June 2015) ► 2 (resp. 3 / 4 / 82000) is the smallest number written with 0 and 1 in base 2 (resp. 3 / 4 / 5).
- Why 1980 was a great year to be born... but 2184 will be better↓ by (29 June 2015) ► Silly simple arithmetical facts.
- What's special about 196? by (28 August 2015) ► The reverse and-add-process and Lychrel numbers.
- 2016, les propriétés mathématiques - Micmaths by (1 January 2016) ► Some characteristics of 2016.
- Incredible Formula - Numberphile by (23 December 2016) ► A pandigital formula approximating e.
- 2016+1 (Cette nouvelle année est-elle intéressante ? Episode 08) by (1 January 2017) ► Some characteristics of 2017.
- The 10,958 Problem - Numberphile by (18 April 2017) ► Trying to create all integers by combining each digits from 1 to 9 (or from 9 to 1) and the kludge about digit concatenation.
- ↪A 10,958 Solution - Numberphile by (18 April 2017) ► The continuation of the previous video.
- ↪Concatenation (extra footage) - Numberphile by (19 April 2017) ► The continuation of the previous video.
- 13532385396179 - Numberphile by (8 June 2017) ► Someone found a counterexample to Conway’s fifth problem (see Five $1,000 Problems - John H. Conway).
- The Square-Sum Problem - Numberphile by (11 January 2018) ► Is it possible to order the n first integers so the sum of any two adjacent numbers is a square?
- ↪The Square-Sum Problem (extra footage) - Numberphile by and (11 January 2018) ► The continuation of the previous video.
- ↪Numberphile's Square-Sum Problem was solved! #SoME2 by (30 July 2022) ► Proving that a chain exists for all lengths greater than 25.
- 357686312646216567629137 - Numberphile by (27 July 2018) ► Right-truncatable primes and left-truncatable primes.
- Every Number is the Sum of Three Palindromes - Numberphile by (17 September 2018) ► , , and have created an algorithm to generate a triplet of palindromes whose sum is a given number.
- The Most Evil Number (Belphegor's Prime) - Numberphile by (31 October 2018) ► Belphegor’s Prime: £[1000000000000066600000000000001£].
- ↪Evil Numbers (extra footage) - Numberphile by (31 October 2018) ► The continuation of the previous video.
- 2018+1 (Cette nouvelle année est-elle intéressante ? Episode 10) by (1 January 2019) ► Some characteristics of 2019.
- Trois cent trente-trois mille trois cent trente-trois - Micmaths by (13 February 2019) ► Some properties of 3, 33, 333…
- 90,525,801,730 Cannon Balls - Numberphile by (8 April 2019) ► Wasting electricity to find sums of polygonal numbers which are equal to a polygonal number.
- Calculator Number Trick: rectangle patterns by (31 May 2019) ► A number generated by punching the corners of a rectangle on a calculator is a multiple of 11.
- The Archimedes Number - Numberphile by (24 November 2019) ► Solving of Archimedes’ Cattle Problem.
- 2010+10 (Cette nouvelle année est-elle intéressante ? Episode 11) by (1 January 2020) ► Some characteristics of 2020.
- Strings and Loops within Pi - Numberphile by (20 February 2020) ► Looking for "self-locating" numbers in the decimals of π.
- #MegaFavNumbers Self-Descriptive Numbers (the beauty 6210001000) by (19 August 2020) ► The title says it all.
- What is the biggest tangent of a prime? by (20 August 2020) ► Looking for primes such that £[tan(p)>p£].
- [AVENT MATHS] : 10, tout en formes !🚫 by (10 December 2020) ► 10 is both a triangular number and a tetrahedral number.
- [AVENT MATHS] : 16 avec Bobby🚫 by (16 December 2020) ► ’s Bibi-binary system.
- 2020+1 (Cette nouvelle année est-elle intéressante ? Episode 12) by (1 January 2021) ► Some characteristics of 2021.
- A Video about the Number 10 - Numberphile by (11 November 2021) ► A presentation of friendly numbers.
- The Most Wanted Prime Number - Numberphile by (15 December 2021) ► Trying to find primes having the format £[123456789101112…121110987654321£] or £[123456789101112…£].
- 2021+1 (Cette nouvelle année est-elle intéressante ? Episode 13) by (1 January 2022) ► Some characteristics of 2022 and the proof that there is no equilateral triangle with integer coordinates.
- 2022+1 (Cette nouvelle année est-elle intéressante ? Episode 14) by (1 January 2023) ► Some facts about 2023.
- 2023+1 (Cette nouvelle année est-elle intéressante ? Episode 15) by (1 January 2024) ► Some facts about 2024.
- Why is this number everywhere? by (28 March 2024) ► Some random facts about 37.
- Apocalyptic Numbers - Numberphile↓ by (6 April 2024) ► Apocalyptic Numbers.
- ↪Goliath & Leviathan Numbers - Numberphile↓ by (7 April 2024) ► Even more stupid numbers.
- ↪Interesting 666-digit Numbers - Numberphile↓ by (8 April 2024) ► The same.
- ↪James Stirling (extra clip) - Numberphile by (9 April 2024) ► Some little information about .
- Absolute Primes - Numberphile by (22 September 2024) ► The useless Circular Primes and Permutable Primes (a.k.a. Anagrammatic Primes).
- 2024+1 (Cette nouvelle année est-elle intéressante ? Episode 16) by (1 January 2025) ► Some facts about 2025.
- 2016502858579884466176 - Numberphile by (24 September 2025) ► Harshad numbers (a.k.a. Niven numbers).
- ↪Harshad Phone Numbers - Numberphile by (25 September 2025) ► The continuation of the previous video.
- Super Facts about 6-7 - Numberphile by (22 December 2025) ► Some facts about 6, 7, and 67.
- ↪Almost Interesting Facts about 6-7 - Numberphile by (22 December 2025) ► The continuation of the previous video.
- ↪6-7 Origin Story (extra footage) - Numberphile by (18 December 2025) ► The continuation of the previous video: the 6-7 meme.
- 2025+1 (Cette nouvelle année est-elle intéressante ? Episode 17) by (1 January 2026) ► Some facts about 2026.
- ↪2026 est un nombre eulérien by (1 January 2026) ► AN extract of the blog article: 2026 is an Eulerian number of the second order.
- Perfect numbers
- The Six Triperfect Numbers - Numberphile by (29 June 2018) ► The title says it all.
- Mathematicians Open a New Front on an Ancient Number Problem — For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things. by (10 September 2020) ► studies spoof numbers (numbers which do not fully respect the criteria of a perfect number) in order to find properties that could prove the impossibility of an odd perfect number.
- [AVENT MATHS] : 6 est parfait🚫 by (6 December 2020) ► A short presentation of perfect numbers.
- The Mysterious Math of Perfection — Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.↑ by (15 March 2021) ► A good and simple introduction to perfect numbers.
- The Oldest Unsolved Problem in Math by (8 March 2024) ► The hunt for an odd perfect number.
- Powerful numbers
- Des nombres puissants (et un échange stupéfiant)↑ by (12 October 2024) ► Some ideas around an anecdote about and : the fact that £[x^2 - 8 y^2 = 1£] has an infinity of solutions quickly demonstrates that there is an infinity of pairs of consecutive powerful numbers.
- Multiplicative persistence
- La persistance des nombres by (August 2013) ► A good overview about the multiplicative persistence.
- La persistance des nombres - Automaths #09🚫 by (13 November 2018) ► Is there a number with a multiplicative persistence (base 10) greater than 11?
- What's special about 277777788888899? - Numberphile by (21 March 2019) ► The same, with a small Python program.
- ↪Multiplicative Persistence (extra footage) - Numberphile by (24 March 2019) ► The continuation of the previous video.
- The Four 4s
- The Four 4s - Numberphile by (6 February 2017) ► ’s solution to the four 4s problem.
- ↪The Four 4s (extra footage) by (8 February 2017) ► The continuation of the previous video.
- Make Any Number From Four π's! by (14 March 2020) ► The same with π.
- Minimal Primes
- Minimal Primes by (16 July 2001) ► The proof that we can remove some digits in any prime to get a number appearing in the list £[2,3,5,7,11,19,41,61,89,409,449,499,881,991,6469,6949,9001,9049,9649,9949,60649,666649,946669,60000049,66000049,66600049£].
- Prime game by (19 December 2020) ► A short presentation of the previous theorem.
- The Collatz conjecture
- La conjecture de Syracuse by (27 June 2011) ► A presentation of Collatz conjecture.
- UNCRACKABLE? The Collatz Conjecture - Numberphile by (8 August 2016) ► Yet another presentation of the conjecture and the failure to prove it.
- ↪Collatz Conjecture (extra footage) - Numberphile by (9 August 2016) ► The continuation of the previous video.
- Collatz Conjecture in Color - Numberphile by (28 March 2017) ► A nice graphical representation of Collatz sequences.
- ↪Coloring Collatz Conjecture (extra footage) - Numberphile by (29 March 2017) ► The continuation of the previous video.
- Mathematician Proves Huge Result on ‘Dangerous’ Problem — Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades. by (11 December 2019) ► The title says it all.
- The Simple Math Problem We Still Can’t Solve — Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop. by (22 September 2020) ► An introduction to the conjecture.
- La conjecture de Syracuse - Deux (deux ?) minutes pour... by (15 December 2020) ► Yet another presentation of the conjecture, but as usual with , this one is more effective than most other ones.
- The Simplest Math Problem No One Can Solve - Collatz Conjecture by (30 July 2021) ► Yet another one.
- SYRACUSE : LA PREUVE À 850 000 DOLLARS ! CMH#26 by (23 December 2023) ► This presentation is very basic.
- Aliquot Sequences
- Suites de diviseurs by (8 August 2019) ► An introduction to aliquot sequences.
- An amazing thing about 276 - Numberphile by (1 May 2024) ► A presentation of the aliquot sequences and the fact there are still some unknowns about them.
- ↪Untouchable Numbers - Numberphile by (1 May 2024) ► The continuation of the previous video.
- The Kolakoski Sequence
- The Kolakoski Sequence - Numberphile by (24 July 2017) ► A short description of the sequence.
- The Recamán Sequence
- The Slightly Spooky Recamán Sequence - Numberphile by (14 June 2018) ► A description of the sequence and the "music" generated from it.
- Somos Sequences
- The Troublemaker Number - Numberphile by (23 May 2022) ► A presentation of Somos sequences.
- The Astonishing Behavior of Recursive Sequences — Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians. by (16 November 2023) ► The Somos sequences and the Göbel sequences.
- On-Line Encyclopedia of Integer Sequences
- Sloane's Gap - Numberphile by (15 October 2013) ► oeis.org, 1729, interesting and uninteresting numbers.
- How to Build a Search Engine for Mathematics — The surprising power of Neil Sloane’s Encyclopedia of Integer Sequences. by (22 October 2015) ► The history of the creation of oeis.org by Neil Sloane.
- Amazing Graphs - Numberphile by (8 August 2019) ► Two sequences which have an unexpected graphical representation.
- ↪Amazing Graphs II (including Star Wars) - Numberphile by (14 August 2019) ► The continuation of the previous video with some other sequences.
- ↪Amazing Graphs III - Numberphile by (22 August 2019) ► Yet other sequences.
- A Not So Amazing Graph (extra footage) - Numberphile by (22 August 2019) ► The graph of Fibonacci sequence is not interesting.
- Dungeon Numbers - Numberphile by (29 July 2020) ► Still more useless series, these ones are based on using different counting bases.
- ↪Dungeon Numbers (extra) - Numberphile by (30 July 2020) ► The continuation of the previous video.
- Exciting Number Sequences by (11 March 2021) ► Some miscellaneous sequences.
- The Levine Sequence - Numberphile by (31 March 2021) ► Yet another useless series.
- A Sequence with a Mistake - Numberphile by (12 May 2021) ► Finding the rule of a sequence containing an error.
- Planing Sequences (Le Rabot) - Numberphile by (3 June 2021) ► Yet another series which seems of no interest.
- A Number Sequence with Everything - Numberphile by (10 November 2022) ► This series could be interesting to study.
- The Yellowstone Permutation - Numberphile by (29 January 2023) ► This proof that all numbers appear in the Yellowstone Permutation is rather messy.
- Cardinal/ordinal numbers
- How to Count Infinity by (12 May 2012) ► A very short explanation of Cantor’s proof that real numbers are uncountable.
- Infinity is bigger than you think - Numberphile by (6 July 2012) ► An introduction to Cantor’s theorem.
- The Deepest Uncertainty — When a hypothesis is neither true nor false. by (6 June 2013) ► A simple presentation of the Continuum Hypothesis.
- Deux (deux ?) minutes pour l'hôtel de Hilbert by (6 February 2015) ► Hilbert’s hotel and Cantor’s diagonal.
- How To Count Past Infinity by (9 April 2016) ► A mind-boggling presentation of ordinal numbers.
- A Hierarchy of Infinities | Infinite Series | PBS Digital Studios by (8 December 2016) ► The Continuum hypothesis.
- How Big are All Infinities Combined? (Cantor's Paradox) | Infinite Series by (23 March 2018) ► This presentation of Cantor paradox is too fast-paced.
- Defining Infinity | Infinite Series by (13 April 2018) ► About infinite ordinals and cardinals.
- Ordinals vs Cardinals (and how many algebraic numbers are there?) by (26 September 2018) ► The difference between cardinal and ordinal numbers and a proof that algebraic numbers are countable.
- Mathias Rousset - Un algorithme dont l’arrêt n’est pas Peano-prouvable by (4 July 2019) ► A short presentation of Goodstein’s theorem.
- How An Infinite Hotel Ran Out Of Room by (10 May 2021) ► The usual description of Hilbert’s hotel and Cantor’s diagonal.
- How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer. — For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. by (15 July 2021) ► The description of the current progress on defining the axioms that would enable to prove or disprove the continuum hypothesis.
- Sur la route de l’infini | Voyages au pays des maths | ARTE by (30 October 2021) ► Yet another classic presentation of Hilbert’s hotel and Cantor’s diagonal.
- How Big Is Infinity? — Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size. by (27 September 2022) ► A classic presentation of Cantor’s diagonal, the continuum hypothesis…
- An infinite number of $1 bills and an infinite number of $20 bills would be worth the same by (31 October 2022) ► is making fun of the ones who have trouble dealing with infinity.
- Ordinal Numbers - Numberphile by (22 October 2025) ► A clear, but not rigorous, description of ordinal numbers.
- The Man Who Stole Infinity — In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism. by (25 February 2026) ► A letter proves that used the proof that algebraic numbers are countable and an improved version of his proof that real numbers are uncountable with any recognition to .
- The hydra theorem
- Deux (deux ?) minutes pour... l'hydre de Kirby & Paris by (8 February 2016) ► An introduction to ordinal numbers, using them to prove the hydra theorem, and Paris-Harrington Theorem which demonstrates that the hydra theorem cannot be proven using Peano arithmetic.
- Kill the Mathematical Hydra | Infinite Series by (26 January 2017) ► The hydra theorem and ordinal numbers.
- ↪How Infinity Explains the Finite | Infinite Series by (2 February 2017) ► The continuation of the previous video: Goodstein Sequence and Paris-Harrington Theorem.
- The Hydra Game - Numberphile by (18 April 2024) ► A simpler version of the problem.
- Goodstein’s theorem
- The sequence that grows remarkably large, then drops to zero! by (29 July 2022) ► A presentation of Goodstein’s theorem that is unprovable in Peano arithmetic.
- Way Bigger Than Graham's Number (Goodstein Sequence) - Numberphile by (26 November 2024) ► It is a pity that this video just scratches the surface of interesting subjects.
- ∞ + 1
- Infinity plus one by (14 January 2017) ► ω, Zeno’s paradox and Hilbert’s Hotel.
- The size of infinity by (21 January 2017) ► Integers, rational numbers and algebraic numbers are countable.
- A bigger infinity by (28 January 2017) ► The usual proof that reals are uncountable using Cantor’s diagonal.
- An even biggerer infinity by (4 February 2017) ► Power sets, Cantor’s theorem, and the continuum hypothesis.
- Exacting and ultraexacting cardinals
- Is Mathematics Mostly Chaos or Mostly Order? — Two new notions of infinity challenge a long-standing plan to define the mathematical universe. by (20 June 2025) ► , , and believe that they found cardinals refuting ’s conjecture.
- Mathematicians Discover a Strange New Infinity↓ by (3 December 2025) ► This description of exacting cardinals, ultra-exacting cardinals, and the ultrafinitists is so basic that it is little interest.