Hacker News with Generative AI: Number Theory

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 9 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 16 days ago | 3 comments

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

Mathematics, Number Theory

579 points by pkaeding 25 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 32 days ago | 0 comments

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

Mathematics, Number Theory, History, Data

93 points by quickfox 33 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 36 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 37 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 68 days ago | 0 comments

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

Mathematics, Prime Numbers, Number Theory, Videos

4 points by selectnull 87 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 88 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 88 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 94 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 95 days ago | 40 comments

Terence Tao on O1 (mathstodon.xyz)

Mathematics, Terence Tao, Number Theory

664 points by dselsam 126 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 136 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 170 days ago | 147 comments

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