Hacker News with Generative AI: Number Theory

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

17 points by muragekibicho 3 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 9 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 13 days ago | 116 comments

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

Mathematics, Research Papers, Number Theory

54 points by cpp_frog 26 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 62 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 72 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 74 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 83 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 90 days ago | 3 comments

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

Mathematics, Number Theory

579 points by pkaeding 99 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 106 days ago | 0 comments

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

Mathematics, Number Theory, History, Data

93 points by quickfox 107 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 110 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 111 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 143 days ago | 0 comments

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

Mathematics, Prime Numbers, Number Theory, Videos

4 points by selectnull 162 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 162 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 163 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 169 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 169 days ago | 40 comments

Terence Tao on O1 (mathstodon.xyz)

Mathematics, Terence Tao, Number Theory

664 points by dselsam 200 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 210 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 244 days ago | 147 comments

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