Hacker News with Generative AI: Number Theory

Reptends and Reciprocals (gregegan.net)
Is there an integer d whose reciprocal, 1/d, has a decimal representation with a recurring block of digits exactly 10 digits long, containing all ten decimal digits?

Mathematics, Number Theory, Puzzles

13 points by pavel_lishin 3 days ago | 2 comments

Is 1 Prime, and Does It Matter? (wordpress.com)
If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance they’ll say “That’s an excellent question” or “It’s kind of an interesting story…”

Mathematics, Number Theory, Prime Numbers

92 points by jamespropp 4 days ago | 151 comments

A cute proof that makes e natural (poshenloh.com)
This webpage pulls out the part of the article which uses Pre-Calculus language to explain what is so natural about e, while intuitively connecting the following two important properties:

Mathematics, Proof, Number Theory

101 points by georgecmu 9 days ago | 43 comments

Loader's Number (fandom.com)

Mathematics, Number Theory, Trivia

63 points by lisper 21 days ago | 10 comments

Lehmer's Continued Fraction Factorization Algorithm (leetarxiv.substack.com)
In 1931, at Stanford University, D.H Lehmer and R.E. Powers1 published a general integer factorization algorithm based on the theory of continued fractions.2

Mathematics, Algorithms, Number Theory

18 points by muragekibicho 27 days ago | 5 comments

Peano's Axioms (principlesofcryptography.com)
Thinking of numbers intuitively brings to mind the simplest and most fundamental set of numbers, namely the set of natural numbers. These numbers are used to count objects like cars, books, pens, etc. If we associate natural numbers such as 1, 2, 3, etc. with counting, then with what corresponding concepts do we relate numbers like -4, \sqrt{3} \text{ and } \frac{22}{7}?

Mathematics, Number Theory, Set Theory

91 points by ulugh 32 days ago | 33 comments

Powers of 2 with all even digits (oeis.org)
Powers of 2 with all even digits.

Mathematics, Number Theory

265 points by Hbruz0 37 days ago | 116 comments

Ten Digit Problems (2011) [pdf] (ox.ac.uk)

Mathematics, Research Papers, Number Theory

54 points by cpp_frog 50 days ago | 2 comments

Quaternions and spherical trigonometry (wordpress.com)
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers:

Mathematics, Algebra, Number Theory, Geometry

124 points by t55 85 days ago | 48 comments

Where do those undergraduate divisibility problems come from? (grossack.site)
Oftentimes in your “intro to proofs” class or your first “discrete math” class or something similar, you’ll be shown problems of the form “prove that for $n^6 + n^3 + 2n^2 + 2n$ is a multiple of $6$ for every $n$”… But where do these problems come from? And have you ever stopped to think how magical this is?

Mathematics, Proofs, Education, Number Theory

161 points by mathgenius 96 days ago | 52 comments

Prime numbers so memorable that people hunt for them (scientificamerican.com)
Math enthusiasts challenge one another to find special prime numbers, including those that are palindromes and Smarandache numbers

Mathematics, Prime Numbers, Number Theory

185 points by georgecmu 98 days ago | 103 comments

Rational or not? This basic math question took decades to answer (quantamagazine.org)
It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.

Mathematics, Number Theory, Science

173 points by nsoonhui 107 days ago | 137 comments

Show HN: 2025 = sum(I^3) for I = 0..9 (ycombinator.com)
This year's number is kinda fun:<p>2025 = 0^3 + 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3<p>Which is equivalent to:<p>2025 = (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ^ 2 = 45 ^ 2<p>Next time this will happen is 1000 years from now, in 3025. See y'all then!

Mathematics, Number Theory, Programming, Show HN

12 points by temporalparts 114 days ago | 3 comments

The number pi has an evil twin (mathstodon.xyz)

Mathematics, Number Theory

579 points by pkaeding 123 days ago | 207 comments

The Year in Math (quantamagazine.org)
Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.

Mathematics, Geometry, Number Theory, Artificial Intelligence

15 points by isaacfrond 130 days ago | 0 comments

The First 50M Prime Numbers (1975) [pdf] (mpim-bonn.mpg.de)

Mathematics, Number Theory, History, Data

93 points by quickfox 131 days ago | 39 comments

Mathematicians uncover a new way to count prime numbers (quantamagazine.org)
A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers.

Mathematics, Prime Numbers, Number Theory

199 points by nsoonhui 134 days ago | 88 comments

Mathematicians Uncover a New Way to Count Prime Numbers (quantamagazine.org)
A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers.

Mathematics, Prime Numbers, Number Theory

9 points by pseudolus 135 days ago | 0 comments

The Postage Stamp Problem (johndcook.com)
I recently stumbled upon the Postage Stamp Problem. Given two relatively prime positive numbers a and b, show that any sufficiently large number N, there exists positive integers x and y such that

Mathematics, Number Theory, Algorithms

6 points by azhenley 166 days ago | 0 comments

A Man Who Found the Biggest Prime [video] (youtube.com)

Mathematics, Prime Numbers, Number Theory, Videos

4 points by selectnull 185 days ago | 0 comments

Vampire Number (wolfram.com)
A number with an even number of digits formed by multiplying a pair of -digit numbers (where the digits are taken from the original number in any order) and together. Pairs of trailing zeros are not allowed. If is a vampire number, then and are called its "fangs."

Mathematics, Number Theory

65 points by dustfinger 186 days ago | 13 comments

New largest prime number found See all 41,024,320 digits [video] (youtube.com)

Mathematics, Prime Numbers, Number Theory, Science, Video

10 points by Alifatisk 186 days ago | 7 comments

Goldbach's Conjecture (wikipedia.org)
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

Mathematics, Number Theory, Unsolved Problems

6 points by mkaic 192 days ago | 0 comments

Big advance on simple-sounding math problem was a century in the making (quantamagazine.org)
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.

Mathematics, Number Theory, Prime Numbers, Conjectures

129 points by isaacfrond 193 days ago | 40 comments

Terence Tao on O1 (mathstodon.xyz)

Mathematics, Terence Tao, Number Theory

664 points by dselsam 223 days ago | 483 comments

666 = sum(range(1,37)) and other sequences (oeis.org)
Displaying 1-10 of 1826 results found.

Mathematics, Number Theory, Sequences

12 points by wslh 234 days ago | 3 comments

Breakthrough a step toward revealing hidden structure of prime numbers (science.org)

Mathematics, Number Theory, Prime Numbers

400 points by igitur 268 days ago | 147 comments

What Is the Riemann Hypothesis and Why Do People Want to Solve It (iflscience.com)